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76Generalized quantification as substructural logicJournal of Symbolic Logic 61 (3): 1006-1044. 1996.We show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables. In the case of generalized quantifiers, explicit attention to relations of dependence becomes indispensible for setting up proof systems. It is shown that this can be done by turning variables into structu…Read more
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32Generalized Quantification as Substructural LogicJournal of Symbolic Logic 61 (3). 1996.We show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables. In the case of generalized quantifiers, explicit attention to relations of dependence becomes indispensible for setting up proof systems. It is shown that this can be done by turning variables into structu…Read more
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25Correspondence and Completeness for Generalized QuantifiersLogic Journal of the IGPL 3 (2-3): 167-190. 1995.
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27An Introduction to the Special Issue on Question ProcessingLogic and Logical Philosophy 26 (3): 285-288. 2017.An Introduction to the Special Issue on Question Processing.
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170Abstracte begrippen en concrete werkelijkheid - Twee vragen voor Hans RadderAlgemeen Nederlands Tijdschrift voor Wijsbegeerte 106 (1): 69-74. 2014.Amsterdam University Press is a leading publisher of academic books, journals and textbooks in the Humanities and Social Sciences. Our aim is to make current research available to scholars, students, innovators, and the general public. AUP stands for scholarly excellence, global presence, and engagement with the international academic community.
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74Von Mises' definition of random sequences reconsideredJournal of Symbolic Logic 52 (3): 725-755. 1987.We review briefly the attempts to define random sequences. These attempts suggest two theorems: one concerning the number of subsequence selection procedures that transform a random sequence into a random sequence; the other concerning the relationship between definitions of randomness based on subsequence selection and those based on statistical tests.
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265Naturalising Mathematics? A Wittgensteinian PerspectivePhilosophies 7 (4): 85. 2022.There is a noticeable gap between results of cognitive neuroscientific research into basic mathematical abilities and philosophical and empirical investigations of mathematics as a distinct intellectual activity. The paper explores the relevance of a Wittgensteinian framework for dealing with this discrepancy.
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48Abstracties en idealisaties: de constructie van de moderne taalkundeTijdschrift Voor Filosofie 72 (4): 749-776. 2010.The paper addresses the way in which modern linguistics, − in particular, but not exclusively, the generative tradition − , has constructed its core concepts. It argues that a particular form of construction, reminiscent of, but crucially different from, abstrac- tion, which is dubbed ‘idealisation’, plays a central role here. The resemblances and differences between abstractions and idealisations are investigated, and consequences of the reliance on idealisations are reviewed.
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42Logic as Marr's Computational Level: Four Case StudiesTopics in Cognitive Science 7 (2): 287-298. 2015.We sketch four applications of Marr's levels‐of‐analysis methodology to the relations between logic and experimental data in the cognitive neuroscience of language and reasoning. The first part of the paper illustrates the explanatory power of computational level theories based on logic. We show that a Bayesian treatment of the suppression task in reasoning with conditionals is ruled out by EEG data, supporting instead an analysis based on defeasible logic. Further, we describe how results from …Read more
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32William A. Dembski. Randomness by design. Noûs, vol. 25 , pp. 75–106Journal of Symbolic Logic 57 (2): 758-759. 1992.
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32An Introduction to the Special Issue on Logic, Cognition and ArgumentationLogic and Logical Philosophy 27 (4): 417. 2018.
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33The logic and topology of kant’s temporal continuumReview of Symbolic Logic 11 (1): 160-206. 2018.In this paper we provide a mathematical model of Kant’s temporal continuum that yields formal correlates for Kant’s informal treatment of this concept in theCritique of Pure Reasonand in other works of his critical period. We show that the formal model satisfies Kant’s synthetic a priori principles for time and that it even illuminates what “faculties and functions” must be in place, as “conditions for the possibility of experience”, for time to satisfy such principles. We then present a mathema…Read more
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23Semantic Interpretation as Computation in Nonmonotonic Logic: The Real Meaning of the Suppression TaskCognitive Science 29 (6): 919-960. 2005.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 pa…Read more
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14Discourse Processing in Attention-Deficit Hyperactivity Disorder (ADHD)Journal of Logic, Language and Information 17 (4): 467-487. 2008.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 …Read more
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46The Processing Consequences of the Imperfective Paradox: ArticlesJournal of Semantics 24 (4): 307-330. 2007.In this paper we present a semantic analysis of the imperfective paradox based on the Event Calculus, a planning formalism characterizing a class of models which can be computed by connectionist networks. We report the results of a questionnaire that support the semantic theory and suggest that different aspectual classes of VPs in the progressive give rise to different entailment patterns. Further, a processing model is outlined, combining the semantic analysis with the psycholinguistic princip…Read more
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17Logic in the study of psychiatric disorders: executive function and rule-followingTopoi 26 (1): 97-114. 2007.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 …Read more
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20The processing consequences of the imperfective paradoxJournal of Semantics 24 (4): 307-330. 2007.In this paper we present a semantic analysis of the imperfective paradox based on the Event Calculus, a planning formalism characterizing a class of models which can be computed by connectionist networks. We report the results of a questionnaire that support the semantic theory and suggest that different aspectual classes of VPs in the progressive give rise to different entailment patterns. Further, a processing model is outlined, combining the semantic analysis with the psycholinguistic princip…Read more
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40A Logic of VisionLinguistics and Philosophy 23 (1). 2000.This essay attempts to develop a psychologically informed semantics of perception reports, whose predictions match with the linguistic data. As suggested by the quotation from Miller and Johnson-Laird, we take a hallmark of perception to be its fallible nature; the resulting semantics thus necessarily differs from situation semantics. On the psychological side, our main inspiration is Marr's (1982) theory of vision, which can easily accomodate fallible perception. In Marr's theory, vision is a m…Read more
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77“Nonmonotonic” does not mean “probabilistic”Behavioral and Brain Sciences 32 (1): 102-103. 2009.Oaksford & Chater (O&C) advocate Bayesian probability as a way to deal formally with the pervasive nonmonotonicity of common sense reasoning. We show that some forms of nonmonotonicity cannot be treated by Bayesian methods
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30On a Spector Ultrapower for the Solovay ModelMathematical Logic Quarterly 43 (3): 389-395. 1997.We prove that a Spector‐like ultrapower extension ???? of a countable Solovay model ???? (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension ????[a], where a is a random real over ????. The proof involves the Solovay almost everywhere uniformization technique.
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45The processing consequences of compositionalityIn Markus Werning, Wolfram Hinzen & Edouard Machery (eds.), The Oxford Handbook of Compositionality, Oxford University Press. 2012.Compositionality remains effective as an explanation of cases in which processing complexity increases due to syntactic factors only. It falls short of accounting for situations in which complexity arises from interactions with the sentence or discourse context, perceptual cues, and stored knowledge. The idea of compositionality as a methodological principle is appealing, but imputing the complexity to one component of the grammar or another, instead of enriching the notion of composition, is no…Read more
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53The axiomatization of randomnessJournal of Symbolic Logic 55 (3): 1143-1167. 1990.We present a faithful axiomatization of von Mises' notion of a random sequence, using an abstract independence relation. A byproduct is a quantifier elimination theorem for Friedman's "almost all" quantifier in terms of this independence relation
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104Algorithmic information theoryJournal of Symbolic Logic 54 (4): 1389-1400. 1989.We present a critical discussion of the claim (most forcefully propounded by Chaitin) that algorithmic information theory sheds new light on Godel's first incompleteness theorem
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10Language Evolution: Enlarging the PictureIn David McFarland, Keith Stenning & Maggie McGonigle (eds.), The Complex Mind: An Interdisciplinary Approach, Palgrave-macmillan. pp. 264-282. 2012.
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27The representation of Takeuti's $$\begin{array}{*{20}c} \parallel \\ \_ \\ \end{array} $$ -operatorStudia Logica 42 (4): 407-415. 1983.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 …Read more
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3172A formalization of kant’s transcendental logicReview of Symbolic Logic 4 (2): 254-289. 2011.Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kantgeneralformaltranscendental logics 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 Kants logic is after all a distinguished subsystem o…Read more
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