Special Session LIRa Seminar on Games, Multi-valued Logics and Model Transformations

In the context of multi-agent systems, agents sometimes play several interactive roles at the same time. In many contexts in daily life, interactions can be modeled as games, for example, negotiations, auctions, social dilemma games, and market games. In those contexts, parallel games assume a great deal of importance. Indeed, a prominent feature of an agent playing several interactive roles in parallel is the ability to learn from experience. One important way to do so is to transfer strategic moves from one game to the other. In this talk we will describe some logical frameworks that we have developed over the past few years, which consider different aspects of parallelism in games.

References: 1. J. van Benthem, S. Ghosh and F. Liu: Modelling Simultaneous games with Dynamic logic, Knowledge, Rationality and Action, a special section of Synthese, 165(2): 247 – 268, 2008.

2. S. Ghosh, R. Ramanujam and S. Simon: Playing extensive form games in parallel, In J. Dix et al, eds, Proceedings of the 11th Workshop on Computational Logics in Multi-agent Systems, CLIMA XI, LNAI 6245, Springer, 153-170, 2010.

Every three-valued logic can be conservatively translated into the modal logic S5 and every four-valued logic can be conservatively translated into minimal modal logic. These are the general theorems we set out to prove. After we have established this general claim, we give an elegant translation of Priest’s Logic of Paradox LP and Kleene’s strong three-valued logic K3. This translation is then used to characterize properties of possible implications that could be added to these two three-valued logics.

We will investigate some operations transforming the collection of finite first-order structures, Q, into the class of finite models Q*. We will be mainly concerned with various type-lifting transformations, e.g., Ramseyification or shifting to second-order (collective) structures, motivated by the semantic study of natural language (but other interesting examples may be found in different domains). We will be mostly interested in comparing Q and Q* with respect to computational complexity and definability.

References: 1) Juha Kontinen and Jakub Szymanik. A Remark on Collective Quantification, Journal of Logic, Language and Information, Vol. 17, No. 2, 2008, pp. 131-140.

2) Jakub Szymanik. Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language, Linguistics and Philosophy, Vol. 33, Iss. 3, 2010, pp. 215-250.

3) Juha Kontinen and Jakub Szymanik. Characterizing Definability of Second-Order Generalized Quantifiers, Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642, L. Beklemishev and R. De Queiroz (Eds.), 2011, pp. 187-200.