Michiel Van Lambalgen

Executive function has become an important concept in explanations of psychiatric disorders, but we currently lack comprehensive models of normal executive function and of its malfunctions. Here we illustrate how defeasible logical analysis can aid progress in this area. We illustrate using autism and attention deficit hyperactivity disorder (ADHD) as example disorders, and show how logical analysis reveals commonalities between linguistic and non-linguistic behaviours within each disorder, and how contrasting sub-components of executive function are involved across disorders. This analysis reveals how logical analysis is as applicable to fast, automatic and unconscious reasoning as it is to slow deliberate cogitation.

Gaisi Takeuti has recently proposed a new operation on orthomodular latticesL, $\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $ :P(L)»L. The properties of $\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $ suggest that the value of $\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $ (A) (A) $ \subseteq $ L) corresponds to the degree in which the elements ofA behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular latticesL and the existence of two-valued homomorphisms onL.

Interpretation is the process whereby a hearer reasons to an interpretation of a speaker's discourse. The hearer normally adopts a credulous attitude to the discourse, at least for the purposes of interpreting it. That is to say the hearer tries to accommodate the truth of all the speaker's utterances in deriving an intended model. We present a nonmonotonic logical model of this process which defines unique minimal preferred models and efficiently simulates a kind of closed-world reasoning of particular interest for human cognition. Byrne's “suppression” data (Byrne, 1989) are used to illustrate how variants on this logic can capture and motivate subtly different interpretative stances which different subjects adopt, thus indicating where more fine-grained empirical data are required to understand what subjects are doing in this task. We then show that this logical competence model can be implemented in spreading activation network models. A one pass process interprets the textual input by constructing a network which then computes minimal preferred models for (3-valued) valuations of the set of propositions of the text. The neural implementation distinguishes easy forward reasoning from more complex backward reasoning in a way that may be useful in explaining directionality in human reasoning.

Modern logic provides accounts of both interpretation and derivation which work together to provide abstract frameworks for modelling the sensitivity of human reasoning to task, context and content. Cognitive theories have underplayed the importance of interpretative processes. We illustrate, using Wason's [Q. J. Exp. Psychol. 20 (1968) 273] selection task, how better empirical cognitive investigations and theories can be built directly on logical accounts when this imbalance is redressed. Subjects quite reasonably experience great difficulty in assigning logical form to descriptively interpreted rules in this task and materials, though not to deontically interpreted ones. The main empirical contrasts in reasoning performance are precisely between these interpretations, so better semantic theory can explain the main empirical effects. However, a more adequate notion of logical form than that typically employed in the psychology of reasoning is required, and we offer a richer alternative. Prima facie evidence that subjects do in fact experience the predicted difficulties in interpreting descriptive materials is provided by analyses of socratic tutoring dialogues. Experimental verification that these difficulties do in fact affect subjects' performance in the standard task is provided by six novel experimental conditions each designed to test different aspects of the semantic predictions. The results bear out the predictions. The semantic distinction between descriptive and deontic rules interacts with the task specifics to provide powerful generalisations about reasoning which surface in detailed explanations of many disparate observations. We conclude that semantic analyses have more direct benefits for psychological investigation than is usually credited, and conversely, that the extraordinary pragmatic circumstances of psychological experiments yield much thought provoking data for semantic analysis. © 2004 Cognitive Science Society, Inc. All rights reserved.Subjects quite reasonably experience great difficulty in assigning logical form to descriptively interpreted rules in this task and materials, though not to deontically interpreted ones. The main empirical contracts in reasoning performance are precisely between these interpretatins, so better semantic theory can explain the main empirical effects. Howevers, a more adequate nation of logical from than that typically employed in the psychology of reasoning in required, and we offer a richer alternative.Prima facie evidence that subjects do in fact experience the predicted difficulties in interpreting descriptive materials is provided by analyses of socratic tutoring dialogues. Experimental verification that these difficulties do in fact affect subjects' performance in the standard task is provided by six novel experimental conditions each designed to test different aspects of the semantic predications.The resluts bear out the predictions. The semantic distinction between descriptive and deontic rules interacts with the task specifics to provide powerful generalisations about reasoning which surface in detailed explanations of many disparate observations. We conclude that semantic analyses have more direct benefits for psychological investigation than is usually credited, and conversely, that the extraordinary pragmatic circumstances of psychological experiments yield much thought provoking data for semantic analysis.

Although Kant envisaged a prominent role for logic in the argumentative structure of his Critique of pure reason [12], logicians and philosophers have generally judged Kant’s logic negatively. What Kant called ‘general’ or ‘formal’ logic has been dismissed as a fairly arbitrary subsystem of first order logic, and what he called ‘transcendental logic’ is considered to be not a logic at all: no syntax, no semantics, no definition of validity. Against this, we argue that Kant’s ‘transcendental logic’ is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first order logic. The main technical application of the formalism developed here is a formal proof that Kant’s Table of Judgements in §9 of the Critique of pure reason, is indeed, as Kant claimed, complete for the kind of semantics he had in mind. This result implies that Kant’s ’general’ logic is after all a distinguished subsystem of first order logic, namely what is known as geometric logic.

ADHD is a psychiatric disorder characterised by persistent and developmentally inappropriate levels of inattention, impulsivity and hyperactivity. It is known that children with ADHD tend to produce incoherent discourses, e.g. by narrating events out of sequence. Here the aetiology of ADHD becomes of interest. One prominent theory is that ADHD is an executive function disorder, showing deficiencies of planning. Given the close link between planning, verb tense and discourse coherence postulated in van Lambalgen and Hamm (The proper treatment of events, 2004), we predicted specific deviations in the verb tenses produced by children with ADHD. Here we report on an experiment corroborating these predictions.

This reply to Oaksford and Chater’s ’s critical discussion of our use of logic programming to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings.

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of rest and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises.