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166Logic and Social Cognition: The Facts Matter, and So Do Computational ModelsJournal of Philosophical Logic 38 (6): 649-680. 2009.This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intel…Read more
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172A communication algorithm for teamwork in multi-agent environmentsJournal of Applied Non-Classical Logics 19 (4): 431-461. 2009.Using a knowledge-based approach, we derive a protocol, MACOM1, for the sequence transmission problem from one agent to a group of agents. The protocol is correct for communication media where deletion and reordering errors may occur. Furthermore, it is shown that after k rounds the agents in the group attain depth k general knowledge about the members of the group and the values of the messages. Then, we adjust this algorithm for multi-agent communication for the process of teamwork. MACOM1 sol…Read more
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107Review: J.-J. Ch. Meyer, W. van Der Hoek, Epistemic Logic for AI and Computer Science (review)Journal of Symbolic Logic 64 (4): 1837-1840. 1999.
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179A small reflection principle for bounded arithmeticJournal of Symbolic Logic 59 (3): 785-812. 1994.We investigate the theory IΔ 0 + Ω 1 and strengthen [Bu86. Theorem 8.6] to the following: if NP ≠ co-NP. then Σ-completeness for witness comparison formulas is not provable in bounded arithmetic. i.e. $I\delta_0 + \Omega_1 + \nvdash \forall b \forall c (\exists a(\operatorname{Prf}(a.c) \wedge \forall = \leq a \neg \operatorname{Prf} (z.b))\\ \rightarrow \operatorname{Prov} (\ulcorner \exists a(\operatorname{Prf}(a. \bar{c}) \wedge \forall z \leq a \neg \operatorname{Prf}(z.\bar{b})) \urcorner))…Read more
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209Children’s Application of Theory of Mind in Reasoning and LanguageJournal of Logic, Language and Information 17 (4): 417-442. 2008.Many social situations require a mental model of the knowledge, beliefs, goals, and intentions of others: a Theory of Mind (ToM). If a person can reason about other people’s beliefs about his own beliefs or intentions, he is demonstrating second-order ToM reasoning. A standard task to test second-order ToM reasoning is the second-order false belief task. A different approach to investigating ToM reasoning is through its application in a strategic game. Another task that is believed to involve th…Read more
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24Provability logicStanford Encyclopedia of Philosophy. 2008.Provability logic is a modal logic that is used to investigate what arithmetical theories can express in a restricted language about their provability predicates. The logic has been inspired by developments in meta-mathematics such as Gödel’s incompleteness theorems of 1931 and Löb’s theorem of 1953. As a modal logic, provability logic has been studied since the early seventies, and has had important applications in the foundations of mathematics. From a philosophical point of view, provability …Read more
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267Modeling inference of mental states: As simple as possible, as complex as necessaryInteraction Studies 15 (3): 455-477. 2014.Behavior oftentimes allows for many possible interpretations in terms of mental states, such as goals, beliefs, desires, and intentions. Reasoning about the relation between behavior and mental states is therefore considered to be an effortful process. We argue that people use simple strategies to deal with high cognitive demands of mental state inference. To test this hypothesis, we developed a computational cognitive model, which was able to simulate previous empirical findings: In two-player …Read more
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182Intermediate Logics and the de Jongh propertyArchive for Mathematical Logic 50 (1-2): 197-213. 2011.We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.
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117Intermediate Logics and the de Jongh propertyArchive for Mathematical Logic 50 (1-2): 197-213. 2011.We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.
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University of GroningenFaculty of Philosophy
Department of Artificial Intelligence, Bernoulli Institute, Faculty of Science and EngineeringProfessor
Groningen, Groningen, Netherlands
Areas of Interest
Logic and Philosophy of Logic |
Epistemology |
Science, Logic, and Mathematics |