Johan van Benthem



Research


Modal logic, mathematics and computation

            

My 1977 Ph.D. thesis was on general model theory of modal logic ('Correspondence Theory', Handbook of Philosophical Logic, Kluwer-Springer, 1984, 2001; Modal Logic and Classical Logic, Bibliopolis, Napoli, 1985). Modal logic is my usual working style, for its balance between expressive power and computational complexity, but also a tandem approach to modal and classical languages (see the survey with Patrick Blackburn, Handbook of Modal Logic, Elsevier, Amsterdam, 2006). In the 1990s, I turned to modal logics of information and computation. Two samples: 'Program Operations that are Safe for Bisimulation', Studia Logica 60:2 (1998), 311-330, and 'Information Flow Across Chu Spaces', Bulletin of the IGPL 8:6 (2000), 719-731. A related theme were decidable fragments of logical systems and remodelling strategies for lowering complexity: as in the Guarded Fragment with Andreka & Nemeti (Journal of Philosophical Logic, 27:3 (1998), 217-274; cf. Guards, Bounds, and Generalized Semantics, Journal of Logic, Language and Information, 14 (2005), 263- 279). Current interest: modal process theories, fixed-point logics for induction and recursion, and links to abstract model theory:


Logic and natural language

               

In the 1980s, I moved to logic in natural language. Essays in Logical Semantics (Kluwer, Dordrecht, 1986) is on generalized quantifier theory. Language in Action (Elsevier, Amsterdam & MIT Press, Cambridge MA, 1991) extended this to categorial grammar, proof theory, and lambda calculus. I retain an interest in substructural logics that keep track of resources (Inference in Action, Publications de l'Institut. Mathématique, Nouvelle Série 82 (96), 2008, Beograd, 3-16), in realistic calculi for natural logic (M. Chakraborty et al., eds., 2008, Logic, Navya-Nyaya & Applications, College Publications, London), and in new views of natural language in the light of logical dynamics ('Natural Language and Logic of Agency', Journal of Logic, Language and Information 23:3, 2014, 367–382). 


Logical dynamics of information and agency

           

Modal and linguistic themes meet in Exploring Logical Dynamics (CSLI Publications, Stanford, 1996), making speech acts and other informational events first-class citizens in logic. Logical dynamics has evolved toward agents processing information, pursuing goals, and socially interacting with other agents, becoming a study of intelligent interaction. My main technical tool here is dynamic-epistemic logic:

These strands come together in the book Logical Dynamics of Information and Interaction, Cambridge University Press, 2011 (supporting website).

Here is an electronic portal to research in dynamic-epistemic logic in Amsterdam and worldwide.


Logic and games

            

While information dynamics describes purposeful agents involved in social processes of communication, their longer-term strategic interactions become especially vivid in the setting of games. I have lectured on the interface of logic, computer science and game theory since 1999. For a personal view, see the interview in Game Theory: Five Questions (Automated Press, 2007, ed. by V. Hendricks & P. Guldborg Hansen, Copenhagen, 9-19. Here are some samples of my approach:

The book Logic in Games (MIT Press, 2014) investigates two directions in tandem whose entanglement forms the DNA of the field: game logics describing the structure of games, and logic games casting basic logical tasks themselves as games. The resulting mix of logic and game theory forms a Theory of Play where players are put into focus using techniques from logical dynamics.


Logic and philosophy

Logic and philosophy have a complex historical relationship, and I have worked on many of their interfaces. Here are some recent samples:

Further material.
A complete collection of my papers on logic and philosophy is available on a restricted-access website: write to johan.vanbenthem@uva.nl to get a key.


Space and time

         

In 1983, I published The Logic of Time (Kluwer, Dordrecht) on temporal structure using logic as a tool of analysis, but also as a way of constructing new temporal ontologies. For a broader view of temporal logic, see my chapter in the Handbook of Logic and AI (Oxford University Press, 1995, 241-350). While dynamic logics mainly involve flow of time, their natural counterpart are logics of spatial structures:


Logic and cognition

Like many colleagues, I am becoming sensitive to the importance of empirical facts about reasoning, and I believe that contacts between logic and cognitive science may well be to the benefit of both fields, complementing many of the above themes. See the special issue of the journal Topoi 26:1 (2007) on 'Logic and Psychology', co-edited with Helen and Wilfrid Hodges. Here are two position papers:


History of logic

I have written little on the history of logic and related fields, though enough to realize that our past may be as interesting as our future. Here are a few case studies:


Coda

For a personal view of logic tying all this together, see the Scientific Autobiography in this Collection, as well as my Valedictory Lecture Fanning the Flames of Reason, which has also appeared in the Dutch Nieuw Archief voor Wiskunde, and the journal Studies in Logic in China.


Universiteit van Amsterdam Logic in Action Stanford University ILLC

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