Learning Łukasiewicz logic

The integration between connectionist learning and logic-based reasoning is a longstanding foundational question in artificial intelligence, cognitive systems, and computer science in general. Research into neural-symbolic integration aims to tackle this challenge, developing approaches bridging the gap between sub-symbolic and symbolic representation and computation. In this line of work the core method has been suggested as a way of translating logic programs into a multilayer perceptron computing least models of the programs. In particular, a variant of the core method for three valued Łukasiewicz logic has proven to be applicable to cognitive modelling among others in the context of Byrne’s suppression task. Building on the underlying formal results and the corresponding computational framework, the present article provides a modified core method suitable for the supervised learning of Łukasiewicz logic (and of a closely-related variant thereof), implements and executes the corresponding supervised learning with the backpropagation algorithm and, finally, constructs a rule extraction method in order to close the neural-symbolic cycle. The resulting system is then evaluated in several empirical test cases, and recommendations for future developments are derived.     

How our brains reason logically

The aim of this article is to strengthen links between cognitive brain research and formal logic. The work covers three fundamental sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional “if...then”, reasoning in the predicate calculus, i.e. inferences based on quantifiers such as “all”, “some”, “none”, and reasoning with n-place relations. Studies with brain-damaged patients and neuroimaging experiments indicate that such logical inferences are implemented in overlapping but different bilateral cortical networks, including parts of the fronto-temporal cortex, the posterior parietal cortex, and the visual cortices. I argue that these findings show that we do not use a single deterministic strategy for solving logical reasoning problems. This account resolves many disputes about how humans reason logically and why we sometimes deviate from the norms of formal logic.

Transitive and pseudo-transitive inferences

Given that A is longer than B, and that B is longer than C, even 5-year-old children can infer that A is longer than C. Theories of reasoning based on formal rules of inference invoke simple axioms ("meaning postulates") to capture such transitive inferences. An alternative theory proposes instead that reasoners construct mental models of the situation described by the premises in order to draw such inferences. An unexpected consequence of the model theory is that if adult reasoners construct simple models of typical situations, then they should infer transitive relations where, in certain cases, none exists. We report four studies corroborating the occurrence of these "pseudo-transitive" fallacies. Experiment 1 established that individuals' diagrams of certain non-transitive relations yield transitive conclusions. Experiment 2 showed that these premises also give rise to fallacious transitive inferences. Experiment 3 established that when the context suggested alternatives to the simple models, the participants made fewer errors. Experiment 4 showed that tense is an important aspect of meaning which affects whether individuals draw transitive conclusions. We discuss the implications of these results for various theories of reasoning.     

Situated robotics: from learning to teaching by imitation

This paper presents an approach to imitation learning in robotics focusing on low level behaviours, so that they do not need to be encoded into sets and rules, but learnt in an intuitive way. Its main novelty is that, rather than trying to analyse natural human actions and adapting them to robot kinematics, humans adapt themselves to the robot via a proper interface to make it perform the desired action. As an example, we present a successful experiment to learn a purely reactive navigation behaviour using robotic platforms. Using Case Based Reasoning, the platform learns from a human driver how to behave in the presence of obstacles, so that no kinematics studies or explicit rules are required.     

Threat, Authoritarianism, and Selective Exposure to Information

We examined the hypothesis that threat alters the cognitive strategies used by high authoritarians in seeking out new political information from the environment. In a laboratory experiment, threat was manipulated through a "mortality salience" manipulation used in research on terror management theory ( Pyszczynski, Solomon & Greenberg, 2003 ). Subjects (N = 92) were then invited to read one of three editorial articles on the topic of capital punishment. We found that in the absence of threat, both low and high authoritarians were responsive to salient norms of evenhandedness in information selection, preferring exposure to a two-sided article that presents the merits of both sides of an issue to an article that selectively touts the benefits of the pro or con side of the issue. However, in the presence of threat, high but not low authoritarians became significantly more interested in exposure to an article containing uniformly pro-attitudinal arguments, and significantly less interested in a balanced, two-sided article. Finally, a path analysis indicated that selective exposure to attitude-congruent information led to more internally consistent policy attitudes and inhibited attitude change. Discussion focuses on the role of threat in conditioning the cognitive and attitudinal effects of authoritarianism.     

Emerging Infectious Diseases: Coping with Uncertainty

The world’s scientific community must be in a state of constant readiness to address the threat posed by newly emerging infectious diseases. Whether the disease in question is SARS in humans or BSE in animals, scientists must be able to put into action various disease containment measures when everything from the causative pathogen to route(s) of transmission is essentially uncertain. A robust epistemic framework, which will inform decision-making, is required under such conditions of uncertainty. I will argue that this framework should have reasoning at its center and, specifically, that forms of reasoning beyond deduction and induction should be countenanced by scientists who are confronted with emerging infectious diseases. In previous articles, I have presented a case for treating certain so-called traditional informal fallacies as rationally acceptable forms of argument that can facilitate scientific inquiry when little is known about an emerging disease. In this article, I want to extend that analysis by highlighting the unique features of these arguments that makes them specially adapted to cope with conditions of uncertainty. Of course, such a view of the informal fallacies must at least be consistent with the reasoning practices of scientists, and particularly those scientists (viz. epidemiologists) whose task it is to track and respond to newly emerging infectious diseases. To this end, I draw upon examples of scientific reasoning from the UK’s BSE crisis, a crisis that posed a significant threat to both human and animal health.

The initial representation in reasoning towards an interpretation of conditional sentences

All accounts of human reasoning (whether presented at the symbolic or subsymbolic level) have to reckon with the temporal organization of the human processing systems and the ephemeral nature of the representations it uses. We present three new empirical tests for the hypothesis that people commence the interpretational process by constructing a minimal initial representation. In the case of if A then C the initial representation captures the occurrence of the consequent, C, within the context of the antecedent, A. Conditional inference problems are created by a categorical premise that affirms or denies A or C. The initial representation allows an inference when the explicitly represented information matches (e.g., the categorical premise A affirms the antecedent “A”) but not when it mismatches (e.g., “not-A” denies A). Experiments 1 and 2 confirmed that people tend to accept the conclusion that “nothing follows” for the denial problems, as indeed they do not have a determinate initial-model conclusion. Experiment 3 demonstrated the other way round that the effect of problem type (affirmation versus denial) is reduced when we impede the possibility of inferring a determinate conclusion on the basis of the initial representation of both the affirmation and the denial problems.     

Attention switching and working memory spans

Barrouillet and Camos () concluded from their developmental study on working memory that when performing complex span tasks, individuals maintain memory items by switching rapidly their attention from processing to storage while performing the concurrent task. Thus, a processing component that would require a continuous attentional focusing should have a highly detrimental effect on span. The present study verifies two predictions issuing from this hypothesis by comparing the classical self‐paced reading and operation span tasks with new computer‐paced tasks in adults. First, any increase in the pace at which the processing component of a working memory span task has to be performed impedes switching and then leads to lower spans. Second, when presented at a fast pace, even simple activities such as reading letters or adding and subtracting 1 to small numbers have an effect on spans as detrimental as complex activities like reading and understanding sentences or solving complex equations.