•  664
    In recent years, the human ability to reasoning about mental states of others in order to explain and predict their behavior has come to be a highly active area of research. Researchers from a wide range of fields { from biology and psychology through linguistics to game theory and logic{ contribute new ideas and results. This interdisciplinary workshop, collocated with the Thirteenth International Conference on Theoretical Aspects of Rationality and Knowledge (TARK XIII), aims to shed light on …Read more
  •  408
    Tractability and the computational mind
    In Mark Sprevak & Matteo Colombo (eds.), The Routledge Handbook of the Computational Mind, Routledge. pp. 339-353. 2018.
    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 effecti…Read more
  •  402
    Strategic Reasoning: Building Cognitive Models from Logical Formulas
    with Sujata Ghosh and Ben Meijering
    Journal of Logic, Language and Information 23 (1): 1-29. 2014.
    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…Read more
  •  339
    Hidden protocols: Modifying our expectations in an evolving world
    with Hans van Ditmarsch, Sujata Ghosh, and Yanjing Wang
    Artificial Intelligence 208 (1): 18--40. 2014.
    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 propositio…Read more
  •  309
    Over the last decade, multi-agent systems have come to form one of the key tech- nologies for software development. The Formal Approaches to Multi-Agent Systems (FAMAS) workshop series brings together researchers from the fields of logic, theoreti- cal computer science and multi-agent systems in order to discuss formal techniques for specifying and verifying multi-agent systems. FAMAS addresses the issues of logics for multi-agent systems, formal methods for verification, for example model check…Read more
  •  256
    This special issue of the Logic Journal of the IGPL includes revised and updated versions of the best work presented at the fourth edition of the workshop Formal Ap- proaches to Multi-Agent Systems, FAMAS'09, which took place in Turin, Italy, from 7 to 11 September, 2009, under the umbrella of the Multi-Agent Logics, Languages, and Organisations Federated Workshops (MALLOW). Just like its predecessor, research reported in this FAMAS 2009 special issue is very much inspired by practical concerns…Read more
  •  200
    Modeling inference of mental states: As simple as possible, as complex as necessary
    with Ben Meijering, Niels A. Taatgen, and Hedderik van Rijn
    Interaction 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
  •  154
    Logic and Social Cognition: The Facts Matter, and So Do Computational Models
    Journal 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
  •  151
    Children’s Application of Theory of Mind in Reasoning and Language
    with Liesbeth Flobbe, Petra Hendriks, and Irene Krämer
    Journal 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
  •  136
    A small reflection principle for bounded arithmetic
    Journal 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
  •  132
    Strong Completeness and Limited Canonicity for PDL
    with Gerard Renardel de Lavalette and Barteld Kooi
    Journal of Logic, Language and Information 17 (1): 69-87. 2008.
    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 kno…Read more
  •  129
    Efficient Metamathematics
    Dissertation, Universiteit van Amsterdam. 1993.
  •  119
    Strong Completeness and Limited Canonicity for PDL
    with Gerard Renardel de Lavalette and Barteld Kooi
    Journal of Logic, Language and Information 18 (2): 291-292. 2009.
  •  115
    Intermediate Logics and the de Jongh property
    Archive 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.
  •  110
    A communication algorithm for teamwork in multi-agent environments
    with Egon van Baars
    Journal 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
  •  109
    Editors’ Review and Introduction: Lying in Logic, Language, and Cognition
    with Hans Ditmarsch and Petra Hendriks
    Topics in Cognitive Science 12 (2): 466-484. 2020.
    Editors van Ditmarsch, Hendriks and Verbrugge of this special issue of topiCS on lying describe some recent trends in research on lying from a multidisciplinary perspective, including logic, philosophy, linguistics, psychology, cognitive science, behavioral economics, and artificial intelligence. Furthermore, they outline the seven contributions to this special issue.
  •  99
    Learning to apply theory of mind
    with Lisette Mol
    Journal of Logic, Language and Information 17 (4): 489-511. 2008.
    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 was based on a strategic game of imperfe…Read more
  •  92
    On the provability logic of bounded arithmetic
    with Alessandro Berarducci
    Annals of Pure and Applied Logic 61 (1-2): 75-93. 1991.
    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
  •  91
    Studying strategies and types of players: experiments, logics and cognitive models
    with Sujata Ghosh
    Synthese 195 (10): 4265-4307. 2018.
    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 deci…Read more
  •  85
    How Knowledge Triggers Obligation
    with Davide Grossi, Barteld Kooi, and Xingchi Su
    Obligations can be affected by knowledge. Several approaches exist to formalize knowledge-based obligations, but no formalism has been developed yet to capture the dynamic interaction between knowledge and obligations. We introduce the dynamic extension of an existing logic for knowledge-based obligations here. We motivate the logic by analyzing several scenarios and by showing how it can capture in an original manner several fundamental deontic notions such as absolute, prima facie and all-thin…Read more
  •  84
    The Wisdom of the Small Crowd: Myside Bias and Group Discussion
    with Edoardo Baccini, Stephan Hartmann, and Zoé Christoff
    Journal of Artificial Societies and Social Simulation. forthcoming.
    The my-side bias is a well-documented cognitive bias in the evaluation of arguments, in which reasoners in a discussion tend to overvalue arguments that confirm their prior beliefs, while undervaluing arguments that attack their prior beliefs. The first part of this paper develops and justifies a Bayesian model of myside bias at the level of individual reasoning. In the second part, this Bayesian model is implemented in an agent-based model of group discussion among myside-biased agents. The age…Read more
  •  84
    Creating collective intention through dialogue
    Logic Journal of the IGPL 9 (2): 289-304. 2001.
    The process of cooperative problem solving can be divided into four stages. First, finding potential team members, then forming a team followed by constructing a plan for that team. Finally, the plan is executed by the team. Traditionally, very simple protocols like the Contract Net protocol are used for performing the first two stages of the process. In an open environment however, there can be discussion among the agents in order to form a team that can achieve the collective intention of solv…Read more
  •  81
    Modeling inference of mental states: As simple as possible, as complex as necessary
    with Ben Meijering, Niels A. Taatgen, and Hedderik van Rijn
    Interaction 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
  •  81
    Solutions to the Knower Paradox in the Light of Haack’s Criteria
    with Mirjam de Vos and Barteld Kooi
    Journal of Philosophical Logic 52 (4): 1101-1132. 2023.
    The knower paradox states that the statement ‘We know that this statement is false’ leads to inconsistency. This article presents a fresh look at this paradox and some well-known solutions from the literature. Paul Égré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, originally described by Skyrms, Anderson, and Solovay. In this article, some background is explained to cla…Read more
  •  71
    Editors’ Review and Introduction: Lying in Logic, Language, and Cognition
    with Hans van Ditmarsch and Petra Hendriks
    Topics in Cognitive Science 12 (2): 466-484. 2020.
    Editors van Ditmarsch, Hendriks and Verbrugge of this special issue of topiCS on lying describe some recent trends in research on lying from a multidisciplinary perspective, including logic, philosophy, linguistics, psychology, cognitive science, behavioral economics, and artificial intelligence. Furthermore, they outline the seven contributions to this special issue.
  •  65
    Intermediate Logics and the de Jongh property
    Archive 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.