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  1.  31
    Tractability and the Computational Mind.Rineke Verbrugge & Jakub Szymanik - 2018 - In Mark Sprevak & Matteo Colombo (eds.), The Routledge Handbook of the Computational Mind. Oxford, UK: pp. 339-353.
    We overview logical and computational explanations of the notion of tractability as applied in cognitive science. We start by introducing the basics of mathematical theories of complexity: computability theory, computational complexity theory, and descriptive complexity theory. Computational philosophy of mind often identifies mental algorithms with computable functions. However, with the development of programming practice it has become apparent that for some computable problems finding effective algorithms is hardly possible. Some problems need too much computational resource, e.g., time or memory, to (...)
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  2.  57
    Children’s Application of Theory of Mind in Reasoning and Language.Liesbeth Flobbe, Rineke Verbrugge, Petra Hendriks & Irene Krämer - 2008 - Journal of Logic, Language and Information 17 (4):417-442.
    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 the application of (...)
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  3.  40
    Hidden Protocols: Modifying Our Expectations in an Evolving World.Hans Van Ditmarsch, Sujata Ghosh, Rineke Verbrugge & Yanjing Wang - 2014 - Artificial Intelligence 208 (1):18--40.
    When agents know a protocol, this leads them to have expectations about future observations. Agents can update their knowledge by matching their actual observations with the expected ones. They eliminate states where they do not match. In this paper, we study how agents perceive protocols that are not commonly known, and propose a semantics-driven logical framework to reason about knowledge in such scenarios. In particular, we introduce the notion of epistemic expectation models and a propositional dynamic logic-style epistemic logic for (...)
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  4.  93
    Logic and Social Cognition.Rineke Verbrugge - 2009 - Journal of Philosophical Logic 38 (6):649-680.
    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 intelligent interaction, it is important that the (...)
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  5.  20
    Logic and Social Cognition the Facts Matter, and so Do Computational Models.Rineke Verbrugge - 2009 - Journal of Philosophical Logic 38 (6):649-680.
    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 intelligent interaction, it is important that the (...)
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  6.  19
    Modeling Inference of Mental States: As Simple as Possible, as Complex as Necessary.Ben Meijering, Niels A. Taatgen, Hedderik van Rijn & Rineke Verbrugge - 2014 - Interaction Studies 15 (3):455-477.
    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 games, people apply simple strategies at first. They (...)
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  7. Strategic Reasoning: Building Cognitive Models From Logical Formulas.Sujata Ghosh, Ben Meijering & Rineke Verbrugge - 2014 - Journal of Logic, Language and Information 23 (1):1-29.
    This paper presents an attempt to bridge the gap between logical and cognitive treatments of strategic reasoning in games. There have been extensive formal debates about the merits of the principle of backward induction among game theorists and logicians. Experimental economists and psychologists have shown that human subjects, perhaps due to their bounded resources, do not always follow the backward induction strategy, leading to unexpected outcomes. Recently, based on an eye-tracking study, it has turned out that even human subjects who (...)
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  8.  4
    Studying Strategies and Types of Players: Experiments, Logics and Cognitive Models.Sujata Ghosh & Rineke Verbrugge - 2018 - Synthese 195 (10):4265-4307.
    How do people reason about their opponent in turn-taking games? Often, people do not make the decisions that game theory would prescribe. We present a logic that can play a key role in understanding how people make their decisions, by delineating all plausible reasoning strategies in a systematic manner. This in turn makes it possible to construct a corresponding set of computational models in a cognitive architecture. These models can be run and fitted to the participants’ data in terms of (...)
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  9.  32
    Learning to Apply Theory of Mind.Rineke Verbrugge & Lisette Mol - 2008 - Journal of Logic, Language and Information 17 (4):489-511.
    In everyday life it is often important to have a mental model of the knowledge, beliefs, desires, and intentions of other people. Sometimes it is even useful to to have a correct model of their model of our own mental states: a second-order Theory of Mind. In order to investigate to what extent adults use and acquire complex skills and strategies in the domains of Theory of Mind and the related skill of natural language use, we conducted an experiment. It (...)
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  10.  26
    Intermediate Logics and the de Jongh Property.Dick de Jongh, Rineke Verbrugge & Albert Visser - 2011 - Archive for Mathematical Logic 50 (1-2):197-213.
    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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  11.  26
    Modeling Inference of Mental States: As Simple as Possible, as Complex as Necessary.Ben Meijering, Niels A. Taatgen, Hedderik van Rijn & Rineke Verbrugge - 2014 - Interaction Studiesinteraction Studies Social Behaviour and Communication in Biological and Artificial Systems 15 (3):455-477.
    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 games, people apply simple strategies at first. They (...)
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  12.  38
    Strong Completeness and Limited Canonicity for PDL.Gerard Renardel de Lavalette, Barteld Kooi & Rineke Verbrugge - 2008 - Journal of Logic, Language and Information 17 (1):69-87.
    Propositional dynamic logic is complete but not compact. As a consequence, strong completeness requires an infinitary proof system. In this paper, we present a short proof for strong completeness of $$\mathsf{PDL}$$ relative to an infinitary proof system containing the rule from [α; β n ]φ for all $$n \in {\mathbb{N}}$$, conclude $$[\alpha;\beta^*] \varphi$$. The proof uses a universal canonical model, and it is generalized to other modal logics with infinitary proof rules, such as epistemic knowledge with common knowledge. Also, we (...)
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  13.  37
    Strong Completeness and Limited Canonicity for PDL.Gerard Renardel de Lavalette, Barteld Kooi & Rineke Verbrugge - 2009 - Journal of Logic, Language and Information 18 (2):291-292.
  14.  10
    On the Provability Logic of Bounded Arithmetic.Rineke Verbrugge & Alessandro Berarducci - 1991 - Annals of Pure and Applied Logic 61 (1-2):75-93.
    Let PLω be the provability logic of IΔ0 + ω1. We prove some containments of the form L ⊆ PLω < Th(C) where L is the provability logic of PA and Th(C) is a suitable class of Kripke frames.
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  15.  50
    A Small Reflection Principle for Bounded Arithmetic.Rineke Verbrugge & Albert Visser - 1994 - Journal of Symbolic Logic 59 (3):785-812.
    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. $I\delta_0 + \Omega_1 + \nvdash \forall b \forall c (\exists a(\operatorname{Prf}(a.c) \wedge \forall = \leq a \neg \operatorname{Prf} (z.b))\\ \rightarrow \operatorname{Prov} (\ulcorner \exists a(\operatorname{Prf}(a. \bar{c}) \wedge \forall z \leq a \neg \operatorname{Prf}(z.\bar{b})) \urcorner)).$ Next we study a "small reflection principle" in bounded arithmetic. We prove that for (...)
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  16.  5
    Intermediate Logics and the de Jongh Property.Dick Jongh, Rineke Verbrugge & Albert Visser - 2011 - Archive for Mathematical Logic 50 (1-2):197-213.
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  17.  20
    Hybrid Logics with Infinitary Proof Systems.Rineke Verbrugge, Gerard Renardel de Lavalette & Barteld Kooi - unknown
    We 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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  18.  17
    A Communication Algorithm for Teamwork in Multi-Agent Environments.Egon van Baars & Rineke Verbrugge - 2009 - Journal of Applied Non-Classical Logics 19 (4):431-461.
    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 solves (...)
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  19.  16
    Review: J.-J. Ch. Meyer, W. Van Der Hoek, Epistemic Logic for AI and Computer Science. [REVIEW]Rineke Verbrugge - 1999 - Journal of Symbolic Logic 64 (4):1837-1840.
  20.  14
    Logic and Cognition: Special Issue of Best Papers of the ESSLLI 2012 Workshop.Jakub Szymanik & Rineke Verbrugge - 2013 - Journal of Logic, Language and Information 22 (4):357-362.
    The explanatory power of logic is vast and therefore it has proved a valuable tool for many disciplines, including the building-blocks of cognitive science, such as philosophy, computer science, mathematics, artificial intelligence, and linguistics. Logic has a great track record in providing interesting insights by means of formalization, and as such it is very useful in disambiguating psychological theories. Logically formalized cognitive theories are not only the source of unequivocal experimental hypotheses, but they also lend themselves naturally to computational modeling. (...)
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  21.  7
    Provability Logic.Rineke Verbrugge - 2008 - Stanford Encyclopedia of Philosophy.
    -/- 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 logic is interesting because (...)
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