Claudia Schon1,, Ulrich Furbach1, Marco Ragni2 1 Institute for Computer
Science, University of Koblenz, 56070 Koblenz, Germany, {uli,schon}@uni-
koblenz.de, 2 Predictive Analytics, Technical University Chemnitz, 09126
Chemnitz, Germany<EMAIL_ADDRESS>
# Modeling Associative Reasoning Processes

###### Abstract

The human capability to reason about one domain by using knowledge of other
domains has been researched for more than 50 years, but models that are
formally sound and predict cognitive process are sparse. We propose a formally
sound method that models associative reasoning by adapting logical reasoning
mechanisms. In particular it is shown that the combination with large
commensense knowledge within a single reasoning system demands for an
efficient and powerful association technique. This approach is also used for
modelling mind-wandering and the Remote Associates Test (RAT) for testing
creativity. In a general discussion we show implications of the model for a
broad variety of cognitive phenomena including consciousness.

###### keywords:

Cognitive science commonsense reasoning automated reasoning
creativityphilosophy of mind consciousness.

##  1 Introduction

Associative thinking and reasoning, i.e., the capability to relate one concept
with another by uncontrolled, sometimes subconscious thinking, is ubiquitous
in our everyday life. It is a driving force for scientific progress, it is
relevant for psychoanalysis, and cultural activities such as art are
impossible to think without it [48]. Associative thinking is a core topic in
cognitive psychology and has been systematically researched by the seminal
work of Mednick for about half a century [[, e.g.,]]Mednick1962, but only few
and often domain restricted cognitive modeling approaches have been proposed
so far [21, 8, 42].

Consider a simple associative task taken from fRAT [10].

######  Problem 1.

Your task for the functional Remote Association Task (fRAT) is to find for
three given words such as the following:

_Tulip_ _Daisy_ _Vase_

exactly one word that can be associated with them all in a meaningful way. For
this example above an answer is _Flower_ (there can be other solutions too),
because all three given words can relate to flower.

In contrast to deductive or algebraic reasoning processes with a well-defined
domain and operations, problems such as the one above cannot be solved by
applying just a set of known rules. Such problems require a form of insight,
which is a “sudden realization that appears to be correct” [56] and creative
thinking [42]. Creative processes can differ from individual to individual and
there is no straightforward algorithm known that needs just be applied to
solve such problems, and hence developing computational and cognitive models
is difficult. General concepts need to be identified and compared and in
principle there can be infinitely many of such concepts. As we can see from
the problem above, semantic processes are relevant. Other instances of such
types of problems can be found in commonsense reasoning. The follwing example
is from a benchmark collection for commonsense problems:

######  Problem 2.

An example taken from the Choice of Plausible Alternatives (COPA) Challenge
[46]:

Assume that the pond froze over for the winter.

What happened as a result?

  1. 1.

People skated on the pond.

  2. 2.

People brought boats to the pond.

Another benchmark for commonsense reasoning with examples of this kind is the
Winograd Schema Challenge [31]. All these benchmarks have in common that it is
not difficult for humans to come up with the correct response together with an
explanation. To tackle general problems such as the ones above, an extensive
amout of background knowledge is necessary, from a cognitive modeling
perspective. For Problem 2 this includes the knowledge that a frozen pond has
a solid surface consisting of ice, that it is possible to skate on ice and
that boats are usually not used on frozen ponds. Since commonsense reasoning
problems cannot be assigned to a specific domain, it is not possible to
represent all this knowledge manually which is one of the reasons why these
problems currently pose real challenges for artificial intelligence (AI) (for
more information, see [32]). Understanding the human ability to draw
meaningful conclusions in everyday situations is therefore not only relevant
for cognitive science, but for AI too. Understanding how we solve such
everyday problems may tell us more about human cognition than well-defined
abstract problems. The general task is to reverse-engineer _how_ associative
reasoning can work on the cognitive level. We will focus here on Marr’s
computational level [33]. The reverse-engineering needs to be understandable –
in the sense of explainable AI. For this reason, we do not aim for a
connectionistic or neural network based approach. We expect from a model for
creative thinking to – at least some extend – whitebox the blackbox processes
of associative thinking. This requires to use symbolic and knowledge rich
modeling approaches.

Since AI considers problems related to commonsense reasoning as challenging
and largely unsolved, it is obvious, that there are no simple algorithmic
realizations for such associative processes. Following the basic paradigm of
‘cognition is computation’ and as long as we do not have computational models
for general associative thinking, the gap between theories for associative
thinking and cognitive models persists. To bridge this gap, in the following
we will systematically introduce problems and domains such as commonsense
reasoning and creativity thinking, among others and the current state of art
in modeling. We demonstrate the importance of the need of a unified
computational model for associative thinking that is (i) formally, as it is
grounded in formal logics, (ii) able to approach concrete and core problems
relevant for associative thinking, and (iii) providing new insights and
hypothesis for the field.

Beyond answering the core research question – _Is it possible to model
associative thinking by combining formally represented background knowledge,
statistical methods, and automatic reasoning systems?_ there are several more
aspects this work will contribute too: It will provide a framework to analyze
the impact of knowledge and inference processes and how different aspects are
selected by cognitive processes. This framework is based on first-order
predicate logic for the reasoning mechanism and on various up-to date
formalisms for very large knowledge bases. It will provide a testable,
prototype implementation of the approach in Section  _Associative Reasoning_.
It will apply the approach to mind-wandering in Section  _Mind-wandering_ and
in Section  _Creativity_ human chains of associations as well as creative
thinking are adressed. Furthermore the field of conscious and unconscious
thinking will be touched in Section  _General Discussion_.

##  2 Associative Thinking and Common Sense Reasoning

Associative reasoning such as Problem 1 above is a part of creative thinking
[36, 43], as it requires “to associate multiple remote items” [43]. It “brings
mutually remote ideas into contiguity facilitates creative solving” and
believed that “the organization of an individual’s associations will influence
the probability and speed of attainment of a creative solution [36]” cited
after [43]. Connected to finding an associative word is _abductive reasoning_
, where the task is to find for observation(s) a best fitting explanation.
Consider the following problem:

######  Problem 3.

The following is from the abductive reasoning domain. Example from the aNLI
(Abductive natural language inference) benchmarks [9]. Assume that two
temporally successive observations are given:

  * $O_{1}$:

It was a very hot summer day.

  * $O_{2}$:

He felt much better.

What is the more plausible hypothesis?

  * $H^{-}$:

He decided to run in the heat.

  * $H^{+}$:

He drank a glass of ice cold water.

For you as a human it is not difficult to imagine what could be the reason for
$O_{2}$, but from a modeling perspective the underlying processes depend on
knowledge and mental models. Formally, for an observation $O_{1}$ at time
$t_{1}$ and an observation $O_{2}$ at time $t_{2}$ with $t_{2}>t_{1}$, the
task is to determine the more plausible explanation $H^{+}$ from the two given
hypotheses $H^{+}$ and $H^{-}$. Abductive reasoning, the search for the best
explanation and to have “commonsense” understanding about how the world may
work are obviously connected. Reasoning about plausibility is obviously
connected to commonsense reasoning and requires some form of a model about the
world. What fits this model of the world is _plausible_. Another approach uses
a core inference system, where the inference rules are obtained from
transcriptions of various reasoning tasks that people have solved [12]. Their
proposed system has two shortcommings: it has not been evaluated against a
benchmark and the proposed system has been developed before knowledge became
available in large quantities in a formalized manner and therefore does not
address our core research problem – how it is possible to find associated
knowledge in large knowledge bases? Consider the following problem:

######  Problem 4.

Example from the SWAG dataset [57].

On stage, a woman takes a seat at the piano. She

  1. a)

sits on a bench as her sister plays with the doll.

  2. b)

smiles with someone as the music plays.

  3. c)

is in the crowd, watching the dancers.

  4. d)

nervously sets her fingers on the keys.

This form of reasoning is clearly non-deductive, but these problems are very
everyday-like. At the same time these presented problems are part of cognitive
tests and tasks spanning a variety of analogical and common sense reasoning
both from psychology and AI [10, 57, 9, 46].

Another example are the problems in the Winograd Schema Challenge [31]. These
problems consist of one sentence mentioning two parties and a reference to one
of the parties with the help of a pronoun or possessive adjective. The task is
to determine the party this pronoun or possesive adjective refers to. The
difficulty results from the construction of these examples: The sentence
always contains a special word where the replacement with an alternate causes
the answer to switch. This is an example of a pair of problems in the Winograd
Schema Challenge:

######  Problem 5.

Examples from the Winograd Schema Challenge [31]:

The town councillors refused to give the angry demonstrators a permit because
they feared violence. Who feared violence?

  1. Answer 0:

the town councillors

  2. Answer 1:

the angry demonstrators

Using the alternate _fear_ for the special word _advocated_ leads to the
following example:

The town councillors refused to give the angry demonstrators a permit because
they advocated violence. Who advocated violence?

  1. Answer 0:

the town councillors

  2. Answer 1:

the angry demonstrators

Still other benchmarks aim to test a system’s ability to continue telling a
story. The Story Cloze Test is one of these benchmarks and is based on the
ROCStories Corpora [39]. One ROCStory consists of a five-sentence story. An
associated associated Story Cloze Test uses the first four sentences as a
description of a situation and the task is to determine the next sentence from
two alternatives, where the right choice is the original fifth sentence from
the corresponding ROCStory. This is an example problem from the Story Cloze
Test dataset:

######  Problem 6.

Example from the Story Cloze Test dataset [39]. Given the four sentences
below. Is A1 or A2 most likely to be the next sentence.

Karen was assigned a roommate her first year of college. Her roommate asked
her to go to a nearby city for a concert. Karen agreed happily. The show was
absolutely exhilarating.

  1. A1:

Karen became good friends with her roommate.

  2. A2:

Karen hated her roommate.

Some of the presented problems above might be easier than others for a human
reasoner in contrast to a formal system to deal with. What is common to all
problems, however, is that without any background knowledge, it is almost
impossible to solve such problems. Problems that require knowledge are called
_knowledge rich problems_. But how do humans solve such problems on a
cognitive level?

This is still an open question. Despite a large number and variety of
cognitive models for reasoning about knowledge lean problems such as for
deductive reasoning, there are only few approaches for knowledge rich problems
that associative models require.

A way to integrate knowledge by using and adapting a Corpus of Contemporary
American English (COCA) has been done in developing a cognitive model for the
fRAT, the comRAT-C [43]. Basically, for each expression in the problem, it
searches the corpus to identify concepts. For this list of putative concepts,
that can be connected to each other a selection is made. A variant of comRAT-c
uses the frequency as an additional selector for the preferred response of
participants. comRAT-c is able to solve 64 from the 144 problems. To the best
of our knowledge this system has not been applied to the other types of
problems presented above. Symbolical approaches steming from abductive and
deontic reasoning, in other words approaches grounded in logic have been
applied for solving a variant of COPA problems [18]. In [24], for example, the
Winograd Schema Challenge problems are manually represented in the situation
calculus, a variant of first-order logic. For each problem, matching knowledge
is manually formalized and added. Then, again manually, it is decided whether
abductive or deductive reasoning is more promising and then reasoning is
performed. In contrast, we aim at modeling the human ability to deal with
large amounts of background knowledge. Therefore, we use pre-existing sources
such as ontologies and knowledge graphs as background knowledge, from which we
automatically extract knowledge suitable for a problem using associative
selection. In [35], the commonsense reasoning benchmarks _Triangle Choice of
Plausible Challenge (Triangle COPA)_ are presented together with a solution
approach based on weighted abduction. In these benchmark problems, situations,
similar to the well-known experiments of [25], are described and the task is
to answer questions about these situations. The abduction-based approach to
solve these problems also relies on manually formalizing suitable background
knowledge for each problem and does not consider the human ability to deal
with large amounts of background knowledge.

While recently adverserial approaches [52] have been proposed, a core point is
that models that can explain human plausible reasoning need some form of
symbolic form to understand how these systems reason and use knowledge.

Table 1: An overview of different tasks and tests for associative thinking and common sense reasoning. Task | Short Name | Example | Citation
---|---|---|---
Remote association test | fRAT | 1 | [10]
Causal commonsense reasoning | COPA | 2 | [46]
Abductive natural language inference | aNLI | 3 | [9]
Grounded commonsense inference | SWAG | 4 | [57]
Winograd Schema Challenge |  | 5 | [31]
Story Cloze Tests |  | 6 | [39]

Classical models for human reasoning dealing with large amounts of background
knowledge do not represent this associative character and select background
knowledge only based on syntactic equality of symbols. This completely ignores
the meaning of symbols such as _pond_ in Problem 2 above and the context in
which these symbols are used. However, when modeling human reasoning and
associative thinking, it is precisely the meaning of symbols and the context
in which they were used that is of great importance. This is why, a
combination of symbolic and statistical methods by integrating word
similarities into the selection process is necessary. Word similarities allow
us to model the associative nature of human thinking and gain context-specific
background knowledge.

We can summarize that to solve the variety of problems of associative,
commonsense, and abductive reasoning we need models that can (i) handle large
amounts of background knowledge, (ii) select background knowledge in an
associative way, (iii) comprises concepts and meaning, and (iv) is able to
reason. In the following, we will present such a system. Table 1 provides an
overview of the benchmarks presented. For the development of our approach, we
have focused on fRAT and COPA. This choice allows us to cover creativity with
the fRAT problems and also to consider the area of causal commonsense
reasoning, which is the topic of the problems in COPA. However, the approaches
we have developed can be applied to other benchmarks and we have also
conducted preliminary experiments on the Story Cloze tests.

##  3 Associative Reasoning

Until now, we talked about various kinds of reasoning, like human, abductive
or commonsense reasoning. Automated reasoning is one of the most traditional
disciplines in Artificial Intelligence research. At the very beginning it was
mainly aiming to prove mathematical theorems, but nowadays it is used as a
major method in many other disciplines, like software and hardware
verification, knowledge representation and even in modeling within cognitive
science systems. The latter is a topic tackling commonsense reasoning
benchmarks like the COPA Challenge [46] with the help of automated reasoning
([49]). See Problem 2 for an example problem from COPA. There are numerous
other approaches to solve these problems with the help of statistical methods
from machine learning, which offer good results [15, 45, 47]. As already
mentioned in the introduction, the problem with these statistical methods is
the lack of explanatory power. It is very difficult in these systems to get an
explanation together with the given answer and therefore it is unclear what
was actually learned [41].

As far as explainability is concerned, logic- or knowledge-based approaches
are much better suited. The core within the system developed by [49] is a
classical first-order logic theorem prover based on a tableau calculus. It
will be discussed in this section for two reasons: Firstly, the prover is
manipulating a single proof object, the tableau, which carries information
about the state of the proof attempt at any time. In this way, it provides
detailed information about the inferences performed at a given time. Secondly,
the system is extended by a mechanism which allows to incorporate associative
steps within very large knowledge bases which are connected to the system. The
tableau and the control mechanism for these associations are explained in this
section. It is important to note, that this first-order logical method can
serve as a core system for many variants of reasoning, like abductive or
deontic reasoning. In the following subsection we depict this classical
logical proof procedure and in another subsection we show how to take the
meaning of symbols into account for associative steps.

Later, in Section  _General Discussion_ we will discuss to which extend this
entire system can be understood as a cognitive model for an information based
understanding of consciousness.

###  3.1 Reasoning: Logical Proof Procedure

The classical first-order logic system upon which the proposed commonsense
reasoning system is build is Hyper, an automated theorem prover for first-
order logic [7].

For this paper it is not necessary to understand the technical details of a
reasoning system like Hyper, it should be enough to explain its functioning by
means of an example.

We use the following example to illustrate the system.

######  Problem 7.

Example problem 65 from the COPA challenge:

The family took their dog to the veterinarian.

What was the cause of this?

  1. 1.

The dog chewed on a bone.

  2. 2.

The dog injured his paw.

This natural language formulation of the problem is automatically translated
into a logical formulation.

The right part of Figure 1 shows 13 formulae. Most of these formulae
correspond to knowledge represented in ConceptNet [51], some result from
Problem 7, after the translation into first-order logic. The first 5 formulae
are facts and the others are implications, all of them are given in a normal
form.

The left part of Figure 1 is a so called tableau, which is essentially a tree
that was developed by Hyper with the help of inference rules. This tableau is
a data structure which is extended by Hyper during its reasoning process.

The technical aspects of the calculus on how to extend the tree in detail are
not important here. We want to point out, however, that at any stage of the
construction of a tree, a branch represents a (partial) interpretation of the
given formulae, which means that it contains those facts which are assumed to
be true. E.g., the right-most branch in our example corresponds to the
(partial) interpretation

$\\{dog(a),bone(b),chew(c),on(c,b),\mathit{agent(c,a}),manducate(c),eat(c),$
$animal(a),carnivore(a),dog\\_treat(b),\mathit{dog\\_food}(b)\\}$.

The left branch of the tableau is closed, since its nodes $bone(b)$ and
$plant(b)$ are contradictory according to formula (11), which states that
nothing can be a _bone_ and a _plant_. A proof of the entire set of formulae
is found if there is a tableau that contains only closed branches. If no proof
can be found, like in the example in Figure 1, the open branches list literals
that can be derived from the set of clauses. The right branch contains both
$\mathit{bone(b)}$ and $\mathit{dog\\_food(b)}$ meaning that individual $b$ is
a bone and also $\mathit{dog\\_food}$.

Hyper has been used in many different application areas, reaching from
commercial knowledge based systems to intelligent book development [6].
Furthermore, Hyper was used as the main reasoning machinery in natural
language query answering [17] and for cognitive reasoning, in particular
answering commonsense questions [20].

In all of these applications Hyper very rarely managed to find a proof within
the given constraints — in most cases there was a timeout and Hyper’s result
was a branch representing a partial interpretation of the formulae at hand.
However, this is not a disadvantage, because in these cases Hyper can be used
to draw inferences from a statement. Next, we will illustrate how to do this.
For the following we use a running example from the aforementioned COPA
benchmarks. As the example in Problem 7 shows, these problems are formulated
in natural language and require everyday knowledge to be understood and
solved.

In order to draw inferences from a natural language statement with the help of
an automated reasoning system, the problem has to be translated from natural
language to a formal language — in our case this is first-order logic. This
translation is done in a fully automated system called KnEWS [5], which is
based on the Boxer-System [13]. As a running example, we consider the
following sentence, which is a part of Problem 7:

> _The dog chewed on a bone._

The first-order logic translation we get using KnEWS is:

$\displaystyle\exists A($ $\displaystyle dog(A)\land\exists B,C(on(C,B)\land
bone(B)\land agent(C,A)\land chew(C))).$ (1)

While reading the above statement and the corresponding formula you certainly
started thinking about a realistic scenario, e.g. about food intake of dogs or
about the composition of meat and bones. We will discuss later how these
scenarios may be invoked by association. Here, it is important to note, that
we need knowledge in order to solve a task related to the statement. Since our
commonsense reasoning approach is intended to be able to handle problems from
arbitrary domains, it is not possible to add background knowledge manually, as
this would then have to be manually adjusted for each individual example.
Therefore, our approach aims to model the human ability to deal with large
amounts of background knowledge through associative reasoning. Therefore, we
use existing knowledge bases, where many possible facts and relations about
the world are available. If this knowledge is not restricted to a single
domain, if it is general enough to be used for different areas, it gets very
large and hence difficult to handle. In [49] among other sources ConceptNet
[51] is used as background knowledge. ConceptNet is a semantic net structure
and is actually multilingual. The English part contains more than 1.5 million
nodes.

Knowledge in ConceptNet is stored in the form of triples such as _(dog, hasA,
fur)_. Figure 3 shows a small part of the information in ConceptNet connected
to the words _dog_ and _car_. To allow the first-order logic reasoner Hyper to
use ConceptNet as background knowledge, we have translated most of the English
part of ConceptNet to first-order logic. The above triple has been translated
into the following formula:

$\forall X(dog(X)\rightarrow\exists Y(hasA(X,Y)\land\mathit{fur}(Y)))$ (2)

The resulting knowledge base consists of 2,9 million axioms and is therefore
far too large to be completely processed by reasoners. Hence, it is necessary
to select parts of this huge knowledge base which might be relevant for the
task at hand. Note, that this situation is very different from a classical
automated reasoning problem, where all the necessary formulae to find a proof
are given and can be used all together by the reasoning system, without the
necessity to guess parts of it to be loaded into the system.

The left part of Figure 2 illustrates the situation in automated reasoning
with large knowledge bases. The logical representation (Formula (1)) of the
natural language sentence is depicted on the very left together with the
knowledge base, ConceptNet, in the middle of the figure. The task is to select
those parts from the knowledge base which might be helpful for reasoning about
the logical representation.

To this end there are two selection methods sketched: The first one uses
syntactic criteria exclusively for the selection [26]. Depending on the
symbols occurring within the logical representation those parts of the
knowledge base are selected, which contain one of these symbols (additionally
this selection takes the number of occurrences of a symbol into account in
order to prevent that very frequent symbols like _isA_ lead to the selection
of the whole knowledge base). Furthermore, depending on some parameters
knowledge for other symbols occurring in the selected parts of the knowledge
base can be selected. The second selection method uses additional semantic
criteria for associative selection; it is discussed in the following
subsection.

###  3.2 Associative Selection: Meaning of Symbols

In logical reasoning the symbols and names within a formula have no a priori
meaning. In our example from Figure 1 the predicate name _dog_ could be
changed to something completely different, say _cat_ or _p_ , the logical
meaning of the entire set of formulae would be exactly the same, provided the
change would be done consistently within all formulae. And indeed this is a
very important property of logical reasoning: the logical structure of a
formula is of interest — all reasoning is done independent of the used
signature (i.e. symbol names). The situation is completely different if a
human reads the formula (provided she is not a logician). It is very likely
that the symbols _dog_ , _chew_ and _bone_ trigger a certain scenario in the
reader — she reads the formula with the triggered interpretation111whereas in
logical reasoning properties of a formulae are proven with respect to all
possible interpretations. There are numerous results from cognitive science,
which indicate that such an assignment of meaning to symbols is important for
human reasoning. The Wason selection task [55], as an example, is an
experiment where test persons have to solve a simple problem which basically
is a logical implication. Most persons fail if the question is formulated in
an abstract logical way, whereas if they receive the same task, but formulated
with much more everyday context, they perform much better. Another example is
the semantic priming effect: the processing of a stimulus can be influenced by
a preceding stimulus. The word _dog_ for example can be more efficiently
processed, if the preceding word was _animal_ in contrast to something
semantically unrelated, like _planet_.

We use such a semantic similarity as a base for our associative steps aiming
at a selection of formulae from the knowledge base, that may be helpful for
the reasoning process. The semantics of “a word is characterized by the
company it keeps” [16] — which is the basic idea of distributed semantics of
language, as it was popularized by Firth already in the beginning of the 20th
century. Recently it became obvious that this kind of semantics is very useful
for statistic based machine learning. Word embeddings offer an implementation
for such semantics. Based on very large corpora of natural language text the
words are related to other words which occur in a certain neighborhood. This
results in a multidimensional vector space which relates words that are used
together very frequently close together — this leads to a kind of similarity
measure for words. In our model, different word embeddings come to use: The
ConceptNet Numberbatch [51] word embedding, pre-trained GloVe word
vectors222GloVe word vectors Common Crawl (840B tokens, 2.2M vocab, cased,
300d vectors, 2.03 GB download at https://nlp.stanford.edu/projects/glove/)
and a word embedding learnt on personal stories from blog entries [46].
ConceptNet Numberbatch is a word embedding combining and enhancing several
pretrained embeddings with knowledge from ConceptNet.

The semantics of symbols within our formulae is given by a word embedding,
which we can use to find semantically similar symbols for the selection
process. As a result not only formulae containing the symbols _dog_ , _chew_
and _bone_ are selected, but also those containing similar symbols like for
example _manducate_ and _remasticate_. This method is described and evaluated
in detail in [19].

Figure 1: Formulae on the right, hyper tableau for the formulae on the left.
The left branch of the tableau is closed, the right branch is open. The
literals in the open branch constitute a partial interpretation of the formula
set.  Figure 2: On the left: Syntactic selection uses symbols from the formula
to select parts of the background knowlege, depicted with black arrows and
regions. Associative selection takes the meaning of symbol names into account
by additionally selecting formulae containing symbols which are similar
according to a word embedding (depicted by blue arrows and regions). On the
right: A snapshot during a Hyper run. The (green) path of the tree, Hyper is
working on, can be interpreted as the working memory; whereas the long-time
memory is representated by the knowledge base.
(Information on source of some parts of the graphics: Picture of network:
[22], CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Visualization
of Word Embedding: _Euskara: Hitz batzuen errepresentazioa_ by Aelu013, CC BY-
SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/deed.en) (word
removed).)

Figure 1 depicts an extract of the selected background knowledge for Formula
(1) on the right hand side: Formulae (6) - (13) correspond to selected
background knowledge for the symbols in Formula (1) and exemplary for the
symbol _manducate_ which is similar to _chew_. Formulae (1) - (5) correspond
to the normal form of Formula (1).

Even if much background knowledge is added, this background knowledge will
never be able to represent the complete human background knowledge and will
always remain incomplete. Therefore, automatic theorem provers can only rarely
prove statements or entailements in natural language. For example, it would
hardly be possible with an automatic theorem prover to prove that the
statement _The dog chewed on a bone_ implies the statement _The dog is
content_. This is because the second statement is not a logical consequence of
the first one. It is rather the case, that _The dog is content_ is more likely
to be a consequence than the statement _The dog is injured_. This kind of
reasoning is also called cognitive reasoning.

Therefore, we do not aim at the construction of proofs but rather to analyse
the inferences performed by Hyper after a certain amount of reasoning (see the
green path in the right part of Figure 2) together with those parts of the
knowledge which is selected by associations.

As we have seen, one of the main problems in the above depicted commonsense
reasoning task is the selection of appropriate parts of knowledge. Within the
knowledge base we have two different kinds of networks or connection layers.
One layer is given by the structure of the knowledge base. E.g. two concepts
_dog_ and _mammal_ may be connected by a relation _IsA_ , or _car_ and
_engine_ by the relation _HasA_ , as it is depicted in Figure 3.

bone$\vdots$$\vdots$fur$\vdots$$\vdots$dogHasADesiresmammalisA$\vdots$$\vdots$poodleRelatedTo$\vdots$$\vdots$carengineHasA$\vdots$$\vdots$garageAtLocation$\vdots$$\vdots$convertibleIsA$\vdots$$\vdots$$\vdots$$\vdots$
Figure 3: Small part of the information in ConceptNet for the words _dog_ and
_car_. In reality, node _dog_ e.g. has more than $660$ ingoing and $610$
outgoing edges.

In Figure 2 this layer is the dense and colorful network. The second layer is
defined by the word embedding, which relates concepts according to their
occurrences within a text corpus, e.g. _dog_ may be related to _betting_ if
the text corpus on which the word embedding was learnt is about dog races.
This second layer corresponds to associative connections between words, it is
depicted by the purple bubbles which show the associations. Paying attention
to these associative links allows us to model the associative nature of human
processing of large amounts of background knowledge in our selection. All in
all, we have a highly complex network consisting of these different
connections with the logical reasoning system Hyper using the different
connection layers.  In the following sections, this entire system is applied
to various associative tasks.

##  4 Mind-wandering

Mind-wandering in humans takes place when a person is awake, turned away from
the outside world, thinking of nothing concrete, indulging in daydreams.
Associative thinking plays an important role in mind-wandering were thoughts
typically move from one concept to another in an uncontrolled manner.
Neuroscientists have shown that in these states free from external stimuli,
the so-called idle or default mode network is active [44]. These mental time-
outs provide an opportunity to spontaneously run through thoughts, produce new
perspectives, simulate scenarios that can be helpful for processing the past
or planning actions. When the person’s attention is taken up again by a task,
the energy of the default mode network is lowered so that he or she can
concentrate on the task at hand. A study [27] argues that up to 40% of the
time a human mind is wandering around.

Mind-wandering also has interesting positive effects such as finding creative
solutions to a problem, which has been shown in [38]. In this section we show
that a variant of the approach introduced in this paper can be used to model
the process of mind-wandering. We denote this variant as _mind-wandering
system_.

###  4.1 Overview of the Mind-wandering System

The mind-wandering process is started from an initial formula, such as Formula
(1) from Section  _Associative Reasoning_. In the first step, the system
performs a associative selection as described in the previous section to
select suitable background knowledge for this formula. The formula together
with the selected background knowledge is transferred to Hyper, which performs
inferences and returns a (possibly partial) interpretation. This
interpretation corresponds to the green path of the tree in the right part of
Figure 2 and contains everything Hyper was able to derive within a given time
limit. Since the selected background knowledge is very broad, the
interpretation also contains very broad information. To find a focus, the
symbols occurring in the interpretation are clustered according to their word
meaning and a cluster is selected as focus. For the symbols in the focus, new
background knowledge is selected and passed to Hyper again together with the
focus. Hyper again performs inferences. This process can be repeated as many
times as desired. A detailed description of the individual steps of the system
follows.

###  4.2 Background Knowledge and Associative Selection

The associative selection from the knowledge base starts with a set of symbols
called the current _context_ , which consists of the symbols from a starting
formula like for example Formula (1) and similar symbols. Adding the similar
symbols from the associative selection steps ensures that the current
_context_ also represents the associative links in the knowledge base. We use
this context as a running example in this section.

Selecting all formulae from the knowledge base in which one of the context
symbols occurs results in a large set of formulae. Using all these formulae
would be too unfocused w.r.t. the considered context, so a filtering step
removes all formulae in which other symbols occurring in the formula are not
within a certain range of similarity to the symbols in the context. To measure
similarity, cosine similarity in a word embedding is used. The interval in
which the similarity must fall for a formula to be selected is passed to the
system by two parameters. With the help of these parameters it is possible to
control how far the background knowledge is allowed to move away from the
context symbols. With a suitable interval it is possible to select a formula
like (2) which represents knowledge about dogs and fur while preventing to
select a formula like

$\forall x(poodle(x)\rightarrow\exists y(\mathit{relatedTo(x,y)}\land
dog(y)))$ (3)

Currently, the system can use either the ConceptNet Numberbatch [51] word
embedding or a word embedding learnt on personal stories from blog entries
provided by [46].

###  4.3 Reasoning

The selected set of formulae together with Formula (1) is passed to the Hyper
reasoner. Hyper is started with a timeout of 30 seconds and calculates during
this time a possibly partial interpretation for the input formulae. This
interpretation represents knowledge that can be inferred from Hyper’s input.
In the next step, the system analyses Hyper’s output. Since the input formulae
are still very broad despite the filter methods mentioned above, the (partial)
interpretation also contains very broad knowledge inferred from Hyper’s input.
First the mind-wandering system extracts all predicate symbols from Hyper’s
output and removes from this set all symbols from the current context to
prevent the mind-wandering process from getting stuck. Hyper’s model produced
for the running example contains 122 symbols which are thematically widely
spread: from _ears, skin, flesh, wolf, calcium, animal, collar_ and
_vertebrate_ to _woof_ and _barking_ , many terms are represented.

###  4.4 Finding a Focus

To determine a focus in the multitude of these symbols, the mind-wandering
system performs a clustering on these symbols using KMeans and the cosine
similarity of a word embedding as similarity measure. Currently, the number of
clusters created corresponds to the number of symbols in the (partial)
interpretation divided by 4. In future work, different values for the number
of clusters will be considered. Next, the system orders the resulting clusters
by their cosine similarity to the symbols in the current context and chooses
one of the clusters as the focus.

Figure 4: Symbols occurring in a Hyper model in a step of a mind-wandering
chain. The different polygons correspond to the clusters produced by k-means
clustering. The word _carpet_ is a cluster with only one element. The figure
was generated by automatically reducing the 300-dimensional ConceptNet
Numberbatch word vectors to 2d vectors.

The choice of the cluster to work with next is related to associative
thinking. The thematic distance between the chosen cluster and the current
context of the mind-wandering chain corresponds to the difference between
concepts that are related to each other during associative thinking. For the
experiments, the cluster in the middle of the sorted sequence is chosen as the
focus in order to allow the mind-wandering process to move away from the
current context. Other choices are possible and can be used to simulate
different variants of associative thinking (with very strong or rather weaker
connections between the concepts related to another). In the running example,
in the first iteration of the mind-wandering process this led to selecting the
cluster consisting of the symbols _animal_ and _animals_ as the new focus.
Figure 4 shows the symbols occurring in one of Hyper’s models corresponding to
a later step in the mind-wandering process. The different colored polygons
represent the clusters formed for these symbols. In the example, four clusters
were created (one for each colored polygon and one for the one-worded cluster
_carpet_). The cluster consisting of the symbols _outside_ , _front_ and
_outdoor_ was selected in this case. Other choices for the focus cluster are
possible and can be selected with the help of a parameter. After selecting a
cluster, the system creates a simple formula from the symbols in the focus
cluster and performs associative selection of background knowledge suitable
for this formula as described above. In this selection, the symbols from the
focus cluster together with similar symbols are used as new context symbols.
The described process is repeated a desired number of times or until the
process does not deliver any new symbols.

###  4.5 Experimental Results

Starting from the symbols in the initial formula, the symbols in the selected
focus clusters represent the result of the mind-wandering process. Starting
from Formula (1) containing the symbols _dog_ , _chew_ and _bone_ the
described system provides for example the following sequence of sets of focus
symbols:

$\displaystyle 1:\\{$ $\displaystyle\mathit{dog,chew,bone}\\}$ $\displaystyle
2:\\{$ $\displaystyle\mathit{animal,animals}\\}$ $\displaystyle 3:\\{$
$\displaystyle\mathit{gardening}\\}$ $\displaystyle 4:\\{$
$\displaystyle\mathit{garden,horticulture,farming}\\}$ $\displaystyle 5:\\{$
$\displaystyle\mathit{mowing,lawn,yard}\\}$ $\displaystyle 6:\\{$
$\displaystyle\mathit{outside,front,outdoor}\\}$ $\displaystyle 7:\\{$
$\displaystyle\mathit{weather}\\}$ $\displaystyle 8:\\{$
$\displaystyle\mathit{thunder,lightning}\\}$ $\displaystyle 9:\\{$
$\displaystyle\mathit{cloud,sky,clouds}\\}$ $\displaystyle 10:\\{$
$\displaystyle\mathit{water}\\}\hphantom{covering,pattern,textile,fastened,worn,wool,coat,material}$

This corresponds to a mind-wandering chain which focuses on animals leads to
gardening and finally addresses weather aspects which leads to water.

It should be noted that the system has many parameters to control this mind-
wandering process. For the experiments, different parameter combinations were
automatically tried out and the sequences of focus symbols generated in this
way were manually inspected. Different parameter values led to a different
chain which finally ends at fashion:

Figure 5: Illustration of a mind-wandering chain. Each color represents the
symbols of one step of the mind-wandering chain. The nodes representing _fur_
, _coats_ and _wool_ have multiple colours because they belong to more than
one step of the mind-wandering chain. For example _wool_ belongs to steps 3, 5
and 7. The figure was generated by automatically reducing the 300-dimensional
ConceptNet Numberbatch word vectors to 2d vectors.

$\displaystyle 1:\\{$ $\displaystyle\mathit{dog,chew,bone}\\}$ $\displaystyle
2:\\{$ $\displaystyle\mathit{furry,tail,fur}\\}$ $\displaystyle 3:\\{$
$\displaystyle\mathit{coats,wool,coat}\\}$ $\displaystyle 4:\\{$
$\displaystyle\mathit{fur}\\}$ $\displaystyle 5:\\{$
$\displaystyle\mathit{animal,pet,hair,coat,pelt,wool}\\}$ $\displaystyle
6:\\{$
$\displaystyle\mathit{sleeves,robe,braided,leather,fur,garment,buttoned,styled,pockets,}$
$\displaystyle\mathit{strand,woven,cloth,wearable}\\}$ $\displaystyle 7:\\{$
$\displaystyle\mathit{coats,covering,pattern,textile,fastened,worn,wool,coat,material,pelt}\\}$
$\displaystyle 8:\\{$ $\displaystyle\mathit{wearing,robe,suit,shirt}\\}$

Figure 5 illustrates this mind-wandering chain. Each color represents one step
of the mind-wandering chain with all its elements.

The presented experiments are only a first feasibility study. In addition to
that, we did first experiments of the application of mind-wandering in the
commonsense reasoning area where we consider commonsense reasoning benchmarks
like the Choice of Plausible Alternatives Challenge [46]. To solve these
benchmarks we start a mind-wandering process for both answer candidates and to
choose the answer where the result of the mind-wandering process is closer to
the sentence _The family took their dog to the veterinarian_. The distance
between a mind-wandering chain and a sentence could be measured for example
using cosine similarity of the correspondig vectors of a word embedding. One
example for a mind-wandering chain produced by the mind-wandering process is:

$\displaystyle 1:\\{$ $\displaystyle\mathit{dog,injured,paw}\\}$
$\displaystyle 2:\\{$ $\displaystyle\mathit{hurt}\\}$ $\displaystyle 3:\\{$
$\displaystyle\mathit{injured,ouch,bruise,harm,painful,injure,ache}\\}$
$\displaystyle 4:\\{$
$\displaystyle\mathit{twinges,discomfort,dangerous,contusion,hurt,wound}\\}$
$\displaystyle 5:\\{$
$\displaystyle\mathit{incision,stitches,gauze,scar,healing,scab,bandaged,cuts}\\}$
$\displaystyle 6:\\{$
$\displaystyle\mathit{regenerate,tissue,scalpel,crusted,skin,bleed,scratch,fungus,wound}\\}$
$\displaystyle 7:\\{$ $\displaystyle\mathit{disease}\\}$ $\displaystyle 8:\\{$
$\displaystyle\mathit{infection}\\}$

Compared to the two mind-wandering chains starting from _The dog chewed on a
bone._ presented above, this mind-wandering chain is clearly closer to the
sentence _The family took their dog to the veterinarian_. However, this is
only one of the mind-wandering chains produced by the mind-wandering process.
There are other mind-wandering chains that do not point in the direction of a
visit to the veterinarian like the following one:

$\displaystyle 1:\\{$ $\displaystyle\mathit{dog,injured,paw}\\}$
$\displaystyle 2:\\{$ $\displaystyle\mathit{hurt}\\}$ $\displaystyle 3:\\{$
$\displaystyle\mathit{limb,injure,dislocated,wounded}\\}$ $\displaystyle
4:\\{$
$\displaystyle\mathit{disfigure,damage,harm,damaged,maimed,hurt,wound}\\}$
$\displaystyle 5:\\{$ $\displaystyle\mathit{battle,fight}\\}$ $\displaystyle
6:\\{$
$\displaystyle\mathit{boxing,contest,struggle,conflict,crusade,oppose,action}\\}$
$\displaystyle 7:\\{$
$\displaystyle\mathit{military}\\}\hphantom{,action,action,action,actionaction,action,action,action}$

Therefore, in future work we plan to always generate several mind-wandering
chains for each answer alternative and then select the answer whose mind-
wandering chains are on average closer to the desired sentence.

##  5 Creativity

This section applies our technique of associative selection in large knowledge
bases to modelling creativity tasks. A very common test to measure human
creativity is the Alternate Uses Task [23]: Subjects are asked to find as many
alternative uses as possible for certain objects such as a brick in a given
time window. It is obvious that for the solution of such a task knowledge
about the object plays a crucial role: the fact that a brick is heavy, hard,
stable and cuboid-shaped represents important background information.
Moreover, associative thinking is used to link this information with the
properties of other objects in order to find an alternative use for the brick.

Another possibility to measure creativity constitute the Remote Associates
Test (RAT) [37, 34] and functionally Remote Associates Test (fRAT) [10]. In
RAT, three words like _cottage_ , _swiss_ and _cake_ are given and the task is
to find a fourth word that connects these three words. For this example, the
solution is _cheese_ , since there is _cottage cheese_ , _swiss cheese_ and
_cheese cake_. fRAT is similar to RAT such that it also presents three words
and the task is to find a fourth connecting word. In contrast to RAT, however,
a functional relationship between the three words and the target word has to
be found. For example, for the words _tulip_ , _daisy_ , _vase_ the connecting
word _flower_ has to be found. To solve the problems in RAT and fRAT, a broad
knowledge is needed. The solution of the above fRAT task requires the
knowledge that _tulips_ and _daisies_ are flowers. In addition, the subject
must have the knowledge that a _vase_ is a container in which flowers are
kept. The difficulty in these tasks is to find a connection in the knowledge
belonging to the three given words. Humans rely on associative thinking to
find this connection.

Therefore, in order to model human creativity in AI systems, these systems
must be able to combine knowledge from different domains and have to be able
to model associative thinking. In everyday life, the human ability to connect
knowledge even goes so far that people easily come up with an explanation for
seemingly unrelated observations:

> Imagine you see some snow and a carrot next to a sleigh.

The obvious explanation, that the snow and the carrot are the remains of a
melted snowman, requires the combination of knowledge from different fields.
For an AI system to come up with such an explanation, a purely syntactic
selection of background knowledge is not sufficient in many cases, because the
knowledge selected in this way is not broad enough. Syntactic selection would
probably end up selecting the information that carrots are vegetables, snow is
a type of precipitation and a sleigh is a vehicle. However the connection
between these three words would probably not be selected. This example
illustrates that a component modelling associative thinking is mandatory to
enable AI systems to come up with comparable explanations.

Even if we furthermore select knowledge for words similar to snow, carrot and
sleigh, we might end up missing the connection to a snowman. Table 2 lists for
each of the words snow, carrot and sleigh the most similar words found in the
pre-trained GloVe word vectors666GloVe word vectors Common Crawl (840B tokens,
2.2M vocab, cased, 300d vectors, 2.03 GB download at
https://nlp.stanford.edu/projects/glove/).

worddd | 10 most similar words
---|---
snow | winter, snowfall, snowy, snows, rain, snowing, Snow, snowstorm,
| weather, sleet
carrot | carrots, celery, potato, onion, zucchini, cabbage, broccoli, cauliflower,
| turnip, cucumber
sleigh | Sleigh, sleighs, sled, reindeer, horse-drawn, reindeers, trundle, seldge,
| sleds, headboard
Table 2: 10 most similar words for _snow_ , _carrot_ and _sleigh_ according to
pre-trained GloVe word vectors. Words are sorted in descending order according
to their similarity to the respective word in the left column.

Even if we select knowledge for all the similar words listed in Table 2 the
knowledge about snowmen will probably not be selected.

Therefore, it is important that the available information (the three words
_snow_ , _carrot_ and _sleigh_) is first linked to a context and knowledge is
selected for this context. However, determining this context is not trivial.
One commonly used way would be to calculate the mean value for the word
vectors of the words of interest (_snow_ , _carrot_ and _sleigh_) and then
determine the most similar words for this mean value (like done in [1]). This
results in the following 20 words (sorted in descending order according to
their distance to the mean value):

$\displaystyle\mathit{pumpkin,snowman,carrots,reindeer,winter,snowy,}$
$\displaystyle\mathit{sledding,sled,potato,ice,snowflakes,potatoes,turnip,}$
$\displaystyle\mathit{cabbage,apples,autumn,wintry,frosty,bunny,pumpkins}$ (4)

Figure 6: Illustration777Figure 7 was generated by automatically reducing the
300-dimensional GloVe word vectors to 2d vectors. of the words most similar to
the mean of the context words _carrot_ , _sleigh_ and _snow_. The three
context words are depicted in red, the mean in yellow. The words depicted in
blue correspond to the 20 words most similar to the mean and are listed in
Equation 4.

As we can see, the snowman already appears in second place in this set. Even
though this is an approach to determining context that is often chosen, it is
immediately noticeable that the result contains many unwanted words that are
obviously not part of the context. Among the 20 words listed, 8 are vegetables
or fruits. If we determine the distances of the vegetables and fruits to the
three context words (_snow_ , _carrot_ , _sleigh_) we notice that they are
only close to _carrot_ and the distance to _snow_ and _sleigh_ is quite high.
Figure 7 illustrates nicely, that the vegetables and fruits have a high
closeness to the mean determined from the context words, but they have a high
variance as far as the closeness to the individual context words is concerned.
Since it is actually desirable that the words determined are close to the mean
and have low variance with respect to proximity to each context word, we
include variance in experiments to determine which words belong to a context.

In experiments we determined the 100 words which are most similar to our
context words and sorted them by the difference of the distance to the mean of
the context words and the variance to the individual context words. For the
running example with the context words _snow_ , _carrot_ and _sleigh_ , this
results in the following words (sorted in descending order according to the
difference):

> snowman, pumpkin, reindeer, sledding, winter, ice, snowy, snowflakes, sled,
> bunny, pumpkins, pine, snowflake, autumn, frosty, marshmallow, christmas,
> snowmen, snowball, carrots

These words only contain three vegetables. The _snowman_ appears at the first
place of the word list. Furthermore, new words interesting for the context
like _snowball_ , _snowflake_ and _christmas_ appear in the word list.
Compared to the context words presented above, this second list of words
provides a better context for the words _snow_ , _carrot_ and _sleigh_.

In first experiments, we tested the usefulness of word embeddings for solving
the f-RAT benchmarks. As mentioned above, each f-RAT problem consists of three
query words (like _discuss_ , _gossip_ , _telephone_) together with the answer
(in our example _talk_). For each of the 48 f-RAT problems considered in [42],
we considered the query words and determined the 200 words most similar to the
mean of the query words in the GloVe word vectors. We sorted these 200 words
in descending order of similarity to the mean of the three query words. For 28
of the 48 fRAT problems, we were able to find the answer word we were looking
for among the first 10 similar words. Impressively, the answer word could even
be found among the first 3 similar words in 23 of 48 cases. In addition, we
observed that sorting the similar words according to the difference suggested
above between distance to the mean of the query words and the variance of the
similarity to the individual query words resulted in the answer word appearing
higher up in the sorting in 21 of the 48 problems. Only in 7 of the 48
problems did this sorting result in the answer word appearing further down in
the sorting.

Table 3 shows the experimental results for the first five f-RAT problems given
in [42]. We list the 5 words most similar to the mean of the query word as
well as the 5 words which are most similar to the difference of the mean und
the variance. The answers given in [42] are given in bold face. It is
noticeable that not only the correct answer but also other similar words
listed in the table make sense as an answer for the query. For example for the
query words _sensitive, sob_ and _weep_ , the correct solution is _cry_. The
word _tear_ , which is second among the candidates for answers we have
determined, also represents a possible solution.

But even in cases where the answer word was not found among the first 10
similar words, we found words which could be a solution as well. For instance,
for the query words arrest, badge and deputy the answer cop was not found
among the top 10 words, but the first two hits officer and police could be a
solution as well.

query wordsdd | most similar words: (a) most similar to mean,
---|---
| (b) most similar to difference of mean and variance
question, reply, solution | (a) answer, questions, suggestion, answers,problem
| (b) answer, suggestion, answers, problem, questions
sensitive, sob, weep | (a) cry, tears, sigh, moan, groan
| (b) cry, tears, sigh, crying, moan
antlers, doe, fawn | (a) antlers, deer, elk, moose, fawn
| (b) deer, elk, antlers, moose, whitetail
bud, dandelion, petals | (a) petal, blossom, leaf, blossoms, flower
| (b) blossom, petals, leaf, blossoms, flower
colt, mare, unicorn | (a) stallion, filly, foal, gelding, horse
| (b) stallion, foal, filly, horse, gelding
Table 3: Experimental results for the first 5 f-RAT problems: Query words
together with the 5 words most similar to the mean of the query words.
Furthermore, the 5 words highest difference of similarity to mean of the query
words minus the variance of the distances to the mean. Similarities determined
using pre-trained GloVe word vectors. The gold standard answer is displayed in
bold.

Altogether these first experiments are encouraging and show that the inclusion
of values other than the distance to the mean vector could be useful. In
future work, we plan to investigate this in more detail.

##  6 General Discussion

In the previous sections we have discussed mind-wandering and creativity from
the perspective of associative thinking and we discussed our associative
reasoning system as a cognitive model for these phenomena. But mind-wandering
and creativity also seem to be closely related to consciousness. [4] argues
that mind-wandering is closely related to conscious life-relevant problem
solving and learning. The link between creativity and consciousness seems very
obvious. In the literature, there is even a technique called “stream of
consciousness” that attempts to mimic the character’s thought process (James
Joyce used this technique prominently in Ulysses). In this section we broaden
the discussion by adressing aspects of consciousness in relation to the
associative reasoning system used until now.

Consciousness is a topic in several scientific disciplines, such as
philosophy, psychology, biology or neuroscience. In this paper, we cannot
cover all aspects of consciousness research, but rather focus on one branch of
research that has an obvious connection to our system: Consciousness from an
information-theoretical point of view. For this discussion we use Chalmers’
seminal paper [11] as a starting point. This paper classifies problems around
the notion of consciousness into easy and hard problems. Easy problems include
explanations of certain phenomena, e.g. descriptions of mental states or the
focus of attention or the ability of a system to access its own internal
state. According to Chalmer the really hard problem is that of experience or
qualia. This notion can be circumscribed by something it is like to be, as it
is formulated prominently by [40]. Chalmers is proposing several research
methods aiming at tackling this hard problem of consciousness. In articular he
is proposing an information theory approach which was later taken up by
Tononi:

###  6.1 Information Integration

Integrated Information Theory of [53] avoids the necessity of a
neurobiological correlate of consciousness. It is applicable to arbitrary
networks of information processing units, they need not be neural or
biological. Tononi is proposing a thought experiment: Assume you are facing a
blank screen, which is alternatively on and off and you are instructed to say
“light” or “dark” according to the screen’s status. Of course a simple
photodiode can do exactly the same job, beep when the light is on and silence
when it is off. The difference between you and the photodiode is the so called
“qualia” — you consciously experience “seeing” light or dark. This is a
partially subjective process, a first-person feeling, which we are not able to
measure or compare with that of other persons (a prominent treatment of this
topic is in [40]). One difference between you and the photo diode is that the
diode can switch between two different states, on and off, exclusively whereas
your brain enters one of an extremely large number of states when it
recorgnizes the light. But it is not just the difference in the number of
states, it is also important to take the degree of information integration
into account. If we use a megapixel camera instead of a single photodiode for
differentiating light from dark, this technical device would also enter one of
a very large number of possible states (representing all possible images it
can store). According to Tononi the difference between you and the camera, is
that the millions of pixels within the camera are not connected to each other.
Your brain, however, handles a huge number of information and it integrates
information from various parts of the brain. (For example it is hard to
imagine colours without shapes.) [53] offers a formal definition of
information integration by defining a function $\Phi$, which measures the
capacity of a system to integrate information. To get an idea of this
approach, assume a network of elements which are connected, e.g. a neural
network and take a subset $S$ from this system. Tononi “wants to measure the
information generated when $S$ enters a particular state out of its
repertoire, but only to the extent that such information can be integrated,
i.e. it can result from causal interactions within the system. To do so, we
partition $S$ into $A$ and its complement $B$ …We then give maximum entropy to
the outputs of $A$, i.e. substitute its elements with independent noise
sources of constrained maximum variance. Finally, we determine the entropy of
the resulting responses of $B$ …” [53]. Based on this computation he defines
the _effective information between $A$ and $B$_, which is a measure of the
information shared between the source $A$ and the target $B$. The above
mentioned function $\Phi$ is defined with the help of the notion of effective
information. The entire system is then divided into several bipartitions in
order to find the ones with the highest $\Phi$-value. These so-called
complexes are responsible for integration of information within the system.
Tononi is considering them as the “subject” of experience, being the locus
where information can be integrated. It should be clear, that the computation
of complexes for realistic networks is highly complex and not really feasible.
For some basic graph structures the $\Phi$-values are given in Figure 7.

Figure 7: Information integration for basic digraphs. (A) Directed path. (B)
One-way cycle. (C) Two-way cycle. (D) Fan-out digraph. (E) Fan-in digraph.
Complexes are shaded and values for $\Phi$ are provided in each of the
panels.(Image and caption is taken from [54])

Based on this understanding of consciousness, one can try to test the theory
by considering several neuroanatomical or neurophysiological factors that are
known to influence consciousness of humans. Tononi does this in great detail
in [53], others are developing new Turing tests for AI systems based on this
theory (e.g. [28]). It is not surprising that Integrated Information Theory is
criticized from various directions. With respect to the notion of information
Searle [50] is arguing that information according to Shannon is observer-
dependent, it is ‘only’ a theory about syntax and encoding of contents,
whereas consciousness is ontologically subjective and observer-independent.
Koch and Tononi’s reply [29] is that they use “a non-Shannonian notion of
information—integrated information —- which can be measured as “differences
that make a difference” to a system from its intrinsic perspective, not
relative to an observer. Such a novel notion of information is necessary for
quantifying and characterizing consciousness as it is generated by brains and
perhaps, one day, by machines.” It is important to note, that Integrated
Information Theory offers a way to quantify the degree of consciousness of a
system. This is exactly why we think that it is very well suited to
investigate and to experiment with aspects of consciousness in artificial
systems. We will comment later on applying Integrated Information Theory to
the automated reasoning system Hyper in cases where it uses large knowledge
bases. We will argue that those knowledge bases offer mechanisms for its
integration and that this is necessary in order to do automated reasoning.

Refering to the small example with the camera pixels from the beginning of
this section, it should be clear, that Integrated Information Theory is not
only about handling large amounts of information, but also about integrating
its parts. In the following subsection we will depict another approach to
consciousness, which can be seen as a special case of the Integrated
Information Theory. It is the Global Workspace Theory developed by [3], which
is mainly focusing on the aspect of handling huge amounts of knowledge.

###  6.2 The Theater of Consciousness

One motivation for Baars Global Workspace Theory [3] is the observation that
the human brain has a very limited working memory. We can actively manipulate
about seven separate things at the same time in our working memory. This is an
astonishing small number in contrast to the more than 100 billion neurons of
the human brain. Another limitation is that human consciousness is limited to
only one single stream of input. We can listen only to one speaker at a time,
we cannot talk to a passenger during driving in heavy traffic and there are
many more examples like this. At the same time there are numerous processes
running in parallel but unconsciously. Global Workspace Theory uses the
metaphor of a theater to model how consciousness enables us to handle the huge
amount of knowledge, memories and sensory input the brain is controlling at
every moment.

Global Workspace Theory assumes a theater consisting of a stage, an
attentional spotlight shining at the stage, actors which represent the
contents, an audience and some people behind the scene. Let’s look at the
parts in more detail:

_The stage._ The working memory consists of verbal and imagined items. Most
parts of the working memory are in the dark, but there are a few active items,
usually the short-term memory.

_The spotlight of attention._ This bright spotlight helps in guiding and
navigating through the working memory. Humans can shift it at will, by
imagining things or events.

_The actors_ are the members of the working memory; they are competing against
each other to gain access to the spotlight of attention.

_Context behind the scene._ Behind the scenes, the director coordinates the
show and stage designers and make-up artists prepare the next scenes.

_The audience._ According to Baars, the audience represents the vast
collection of specialized knowledge. It can be considered as a kind of long-
term memory and consists of specialized properties, which are unconscious.
Navigation through this part of the knowledge is done mostly unconsciously.
This part of the theater is additionally responsible for interpretation of
certain contents e.g., objects, faces or speech – there are some unconscious
automatisms running in the audience.

It is important to note that this model of consciousness, although it uses a
theater metaphor, is very different from a model like the Cartesian theater,
as it it discussed and refused in [14]. A Cartesian theater model would assume
that there is a certain region within the brain, which is the location of
consciousness, this would be a kind of humunculus. In Baars theater, however,
the entire brain is the theater and hence there is no special location, it is
the entire integrated structure which is conscious. This is in very nice
accordance with Tononi’s Integrated Information Theory, described above.

Baars and colleagues also developed an architecture based on the Global
Workspace Theory, which they call LIDA “a comprehensive, conceptual and
computational model covering a large portion of human cognition” [2]. LIDA
consists of a number of software modules, which implement a cognitive cycle
which is derived from the Global Workspace Theory. Baars gives a detailed
justification of LIDA by modelling aspects of human cognition within his
model. There are numerous other cognitive architectures which are used for
different purposes, an extensive overview can be found in [30].

In the following we will follow a very different road — instead of designing a
new architecture based on Global Workspace Theory, we will show that the
reasoning system we have depicted and discussed in this paper can be seen as
an instance of Global Workspace Theory. It is important to note, that the
development of this system was driven by the needs to be used as a reasoner
within a commonsense system together with huge amounts of world knowledge.
This system was not developed as a model for consciousness, but exhibits
nevertheless strong similarity with the Global Workspace Theory and the
Integrated Information Theory as we will demonstrate in the following
subsection.

###  6.3 Looking through the Global Workspace Theory-Glasses

We demonstrate how Hyper in combination with the associative selection within
large knowledge bases can be interpreted as an architecture that implements
the Global Workspace Theory as introduced in the previous section.

_The stage._ The working memory corresponds to the branch of the Hyper tree
which is currently expanded. In the right part of Figure 2 this is the green
path of the tree — it contains the context in which the next reasoning step
will be performed.

_The spotlight of attention._ This bright spotlight selects and highlights
those parts of the (green) branch together with the formulae from the problem
or the selected parts of the knowledge base which are used for the next
reasoning step.

_The actors._ The actors correspond to the application of inference rules on
the set of formulae currently processed by the theorem prover. The result of
the actors’ actions correspond to new formulae derived by an inference step.
The spotlight of attention decides which actor, i.e. inference rule together
with the necessary formulae, from the stage are to be active next.

_Context behind the scene._ Behind the scenes, the reasoner and its control
act as a director.

_Audience._ According to Baars, the audience represents the vast collection of
specialized knowledge. It can be considered as a kind of long-term memory,
namely the knowledge base. We depicted several selection mechanisms for
finding the appropriate parts of the knowledge. The associative selection
mechanism uses word similarities from word embeddings. These word similarities
connect different parts of the background knowledge with each other and thus
allow to transfer existing knowledge to similar areas. The selection
mechanisms can be seen as the unconscious interpretation skills which Baars
located in the audience. In our case we only deal with declarative knowledge,
if we had procedural knowledge as well, this would be part of the audience
too.

Altogether we have a complete Baars’ theater of consciousness consisting of
the reasoner Hyper, together with its control and its background knowledge —
we have a system which can be interpreted as a system with a certain degree of
consciousness according to the ideas presented above. However, it should be
noted that “Metaphors must be used with care. They are always partly wrong,
and we should keep an eye out for occasions when they break down. Yet they
often provide the best starting point we can find.” [3]

##  7 Conclusion and Future Work

Levesque and other AI researchers consider the task to understand _how_ humans
approach commonsense reasoning and _how_ this can be made available for AI-
systems _the real challenge for AI_ [32], but it is even more a problem for
cognitive modeling. Only if we understand the interplay between the cognitive
processes or can – at least show - how these processes can contribute to the
respective competency, we understand better an important aspect of our (human)
cognitive system. In our analysis, we have focussed on some parts of
associative thinking and reasoning as well as on commonsense reasoning and
demonstrated that the presented approach can solve a variety of these tasks.
For this we connected work from research on associative thinking with work on
formal reasoning. We observed that AI systems in the commonsense reasoning
domain face similar problems as humans in everyday reasoning: Both have to
deal with large amounts of knowledge and have to be able to focus on the part
of the knowledge which is relevant for the task at hand. To accomplish this
task, humans rely on associative thinking. We argue that AI systems can use an
instrument similar to associative thinking to deal with this problem as well.

We depicted an implementation of a mind-wandering process with associative
reasoning. Further work has to be done for finding a way to determine what
knowledge is interesting enough to be kept within the focus of the system and
how the knowledge base should be modified according to the results of mind-
wandering. Currently, only one path of the proof tree is considered for the
mind-wandering process. In future work we plan to extend the approach to
consider multiple open branches for mind-wandering.

We have given a brief insight into how associative reasoning with large
amounts of knowledge also play an important role in the field of creativity.
In future work, we will not only consider selection of background knowledge in
the area of creativity, but also investigate how automated reasoning can be
used in this area.

Finally we broadend our view by discussing the associative reasoning system as
a conscious system in the sense of the Integrated Information Theory and the
Global Workspace Theory. Future work on this topic should relate all these
observations to discussions from the area of theory of mind — one of the great
cognitive modeling challenges.

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