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89Review: 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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156A 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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183Children’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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246Modeling 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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150Intermediate 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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97Intermediate 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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28We provide a strongly complete infinitary proof system for hybrid logic. This proof system can be extended with countably many sequents. Thus, although these logics may be non-compact, strong completeness proofs are provided for infinitary hybrid versions of non-compact logics like ancestral logic and Segerberg’s modal logic with the bounded chain condition. This extends the completeness result for hybrid logics by Gargov, Passy, and Tinchev.
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111Modeling 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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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 |