•  198
    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
  •  24
    Provability logic
    Stanford 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
  •  262
    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
  •  163
    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.
  •  108
    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.
  •  28
    Hybrid logics with infinitary proof systems
    with Gerard Renardel de Lavalette and Barteld Kooi
    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.
  •  120
    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
  •  132
    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
  •  163
    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