15 research outputs found
Investigating diagrammatic reasoning with deep neural networks
Diagrams in mechanised reasoning systems are typically en- coded into symbolic representations that can be easily processed with rule-based expert systems. This relies on human experts to define the framework of diagram-to-symbol mapping and the set of rules to reason with the symbols. We present a new method of using Deep artificial Neu- ral Networks (DNN) to learn continuous, vector-form representations of diagrams without any human input, and entirely from datasets of dia- grammatic reasoning problems. Based on this DNN, we developed a novel reasoning system, Euler-Net, to solve syllogisms with Euler diagrams. Euler-Net takes two Euler diagrams representing the premises in a syl- logism as input, and outputs either a categorical (subset, intersection or disjoint) or diagrammatic conclusion (generating an Euler diagram rep- resenting the conclusion) to the syllogism. Euler-Net can achieve 99.5% accuracy for generating syllogism conclusion. We analyse the learned representations of the diagrams, and show that meaningful information can be extracted from such neural representations. We propose that our framework can be applied to other types of diagrams, especially the ones we don’t know how to formalise symbolically. Furthermore, we propose to investigate the relation between our artificial DNN and human neural circuitry when performing diagrammatic reasoning
A cognitive theory of graphical and linguistic reasoning: Logic and implementation
We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form; and (b) the implementational differences that affect facility of inference. Our theory proposes that graphical representations limit abstraction and thereby aid processibility. We discuss the ideas of specificity and abstraction, and their cognitive relevance. Empirical support comes from tasks involving (i) the manipulation of external graphics; and (ii) no external graphics. For (i), we take Euler's Circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals, and with Mental Models' representations. We demonstrate equivalence of the graphical Euler system, and the non-graphical Mental Models system. For (ii), we discuss text comprehension, and the mental ..
Neural Diagrammatic Reasoning
Diagrams have been shown to be effective tools for humans to represent and reason about
complex concepts. They have been widely used to represent concepts in science teaching, to
communicate workflow in industries and to measure human fluid intelligence. Mechanised
reasoning systems typically encode diagrams into symbolic representations that can be
easily processed with rule-based expert systems. This relies on human experts to define the
framework of diagram-to-symbol mapping and the set of rules to reason with the symbols.
This means the reasoning systems cannot be easily adapted to other diagrams without
a new set of human-defined representation mapping and reasoning rules. Moreover such
systems are not able to cope with diagram inputs as raw and possibly noisy images. The
need for human input and the lack of robustness to noise significantly limit the applications
of mechanised diagrammatic reasoning systems.
A key research question then arises: can we develop human-like reasoning systems that
learn to reason robustly without predefined reasoning rules? To answer this question, I
propose Neural Diagrammatic Reasoning, a new family of diagrammatic reasoning
systems which does not have the drawbacks of mechanised reasoning systems. The new
systems are based on deep neural networks, a recently popular machine learning method
that achieved human-level performance on a range of perception tasks such as object
detection, speech recognition and natural language processing. The proposed systems are
able to learn both diagram to symbol mapping and implicit reasoning rules only from data,
with no prior human input about symbols and rules in the reasoning tasks. Specifically I
developed EulerNet, a novel neural network model that solves Euler diagram syllogism
tasks with 99.5% accuracy. Experiments show that EulerNet learns useful representations
of the diagrams and tasks, and is robust to noise and deformation in the input data. I
also developed MXGNet, a novel multiplex graph neural architecture that solves Raven
Progressive Matrices (RPM) tasks. MXGNet achieves state-of-the-art accuracies on two
popular RPM datasets. In addition, I developed Discrete-AIR, an unsupervised learning
architecture that learns semi-symbolic representations of diagrams without any labels.
Lastly I designed a novel inductive bias module that can be readily used in today’s deep
neural networks to improve their generalisation capability on relational reasoning tasks.EPSRC Studentship and Cambridge Trust Scholarshi
Human reasoning and cognitive science
In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain
Exploring individual differences in deductive reasoning as a function of 'autistic'-like traits
From a logical viewpoint, people must reason to as well as from interpretations in deductive
reasoning tasks. There are two main interpretative stances (e.g., Stenning & van
Lambalgen, 2004, 2005, 2008): credulous, the act of trying to infer the speaker's intended
model; and sceptical, an adversarial strategy. A range of contextual factors in
uence interpretation,
but there are also differences between individuals across situations. Taking
an individual differences approach, this thesis focuses on reasoning in relation to milder
variants of the autism spectrum condition (ASC) phenotype in a typically developing (TD)
population. Earlier work on discourse processing in ASC using the `suppression' task (van
Lambalgen & Smid, 2004; Pijnacker et al., In press) shows that some aspects of reasoning
to interpretations are different in the ASC population. Given that autistic traits involve
impairment, e.g., in pragmatic language, and peaks of ability, e.g., in perceptual tasks, it
was hypothesised that autistic traits would predict features of the inferences people in the
TD population draw.
Data were collected from university students on a range of reasoning tasks making it
possible to investigate the extent to which interpretation is consistent across task within
individuals. Tasks chosen were: conditional reasoning using the `suppression' task and
Wason's selection task; one and two-premise Aristotelian quantifer reasoning; the Linda
problem; and Raven's Advanced Progressive Matrices. Autistic traits were assessed using
the Autism Spectrum Quotient (Baron-Cohen et al., 2001), used previously to study
autistic traits in TD individuals, and the Broad Autism Phenotype Questionnaire (Hurley
et al., 2007).
Autistic traits predicted patterns of inference in many of the tasks. The earlier suppression
task result in ASC was replicated and extended in our TD population. Different
dimensions of autistic trait related differentially to features of the inferences drawn. Some
of the inferences drawn were recognisably related to the credulous versus sceptical distinction
and correlated cross-task whilst others were seemingly related to more general topdown
versus bottom-up processing preferences. These results provide further evidence of
the existence of qualitative individual differences in deductive reasoning. They also show
the importance of seeking cross-task correlates to move beyond studies of individual tasks
and study reasoning to and from interpretations in the same individual
World and Logic
What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of language, logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us