Games in Logic, Language and ComputationThursday June 20, 2002
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The sixth edition of the workshop on Games in Logic, Language and Computation (GLLC6) will be held on Thursday June 20, 2002. The workshop is hosted by the University of Utrecht, and is organized by Boudewijn de Bruin, Balder ten Cate, Paul Harrenstein, Wiebe van der Hoek and John-Jules Meyer. The informal workshop series "Games in Logic, Language and Computation" focuses on the application of game theory in linguistics, logic and computer science, as well as on the (logical) foundations of game theory. Earlier meetings have taken place in Amsterdam, Nunspeet and Groningen. The provisional program is as follows (abstracts below).
This schedule makes it possible for those interested to attend a talk by Prof. Jim Lambek entitled 'What is the world of mathematics?' (abstract below), which will take place at the same location from 14.00 until 15.00. |
Alastair Butler (Universiteit van Amsterdam)
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The herd instinct is the tendency to associate or conform with
one's own kind for support, etc. This talk argues that such
interaction is a general property of grammar. This suggests that
dependencies which are ill-formed in isolation can be ``saved''
by the presence of well-formed dependencies. This turns out to
be the case. For example, Baker (1970) observed that ``what''
in (1a) cannot have matrix scope, while it can in (1b). Under
a herding story, ``what'' can have matrix scope in (1b) because
of the well-formed presence of ``who'' in the matrix clause.
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Francien Dechesne (KUB Tilburg / TU Eindhoven)
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| Hintikka describes the semantical games for Independence Friendly logic (IF-logic) in terms of the game rules. We show how this representation can be translated in the standard mathematical model for extensive form games. We intend the game model to be a framework in which we can reason with mathematical rigor about strategies, hence about truth and falsity in Game Theoretical Semantics (GTS). We discuss negation normal forms, and compare the notion of Skolem function with the game theoretical notion of strategy. |
Hans van Ditmarsch (University of Otago)
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| Given some deal of cards, it is possible to communicate your hand to another player without yet another player learning any of your cards. Every solution to this problem consists of a sequence of safe communications, an interesting new form of update. Certain unsafe communications turn out to be unsuccessful updates. Each communication can be about a set of alternative card deals only, and even about a set of alternatives to your own hand only. We solve a specific cards problem and summarily discuss some combinatorial issues that are not of logical interest. Generalizations appear to be relevant to cryptology. |
Helle Hansen (Universiteit Amsterdam)
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| Rights of agents (constitutions) can be formalised using Coalition Logic. Adding an inference rule for Nash-consistency will guarantee that any multi-agent system implementing these rights will be stable, i.e., for any preferences the agents might have, there will be rights they can exercise such that no individual deviation will be profitable. A formal analysis of Gibbard's paradox is obtained by applying this logic, and meta-theoretic results are provided, in particular a complete axiomatisation. |
Paul Harrenstein (Universiteit Utrecht)
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| We propose a notion of consequence for propositional languages based on a equilibrium concept that is a generalization of that of Nash. This notion is relative to a partititioning of the propositional variables and is to hold between a family of theories with the partitioning a indexset and a formula. With any such partition and family of theories a strategic game can be associated, in which the strategy profiles coincide with valuations for the propositional language. Given a partition, a formula then follows from a family of theories if and only if that formula holds in all equilibria of the game associated with that partition and family of theories. Some metatheoretical results concerning this this notion of consequence we obtain by comparing it to the classical one. |
Wiebe van der Hoek (Universiteit Utrecht / University of Liverpool)
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| We give a general approach to characterizing minimal information in a modal context. Our modal treatment can be used for many applications, but is especially relevant under epistemic interpretations of the operator $\Box$. Relative to an arbitrary modal system, we give three characterizations of minimal information and provide conditions under which these characterizations are equivalent. We then study information orders based on bisimulations and Ehrenfeucht-Fraïssé games. Moving to the area of epistemic logics, we show that for one of these orders almost all systems trivialize the notion of minimal information. An other order which we present is much more promising as it permits to minimize with respect to positive knowledge. The resulting notion of minimality coincides with well-established accounts of minimal knowledge in S5. For S4 we compare the two orders. |
Rosja Mastop (Universiteit van Amsterdam)
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| The founding father of deontic logic, G. H. von Wright, argued against viewing obligation and permission as dual in the sense of normal modal logic. The reason being that having or giving a permission expresses a guarantee not to be hindered when one wants to act upon it, rather than merely the absence of prohibitions. Nevertheless, it is not very clear what the logic of obligation and permission should be, under this `strong' reading of permission. First I will explain von Wright's solution and argue that it is not satisfactory. I then propose an alternative based on Pauly's logic for coalitional effectivity in games. |
Joachim Lambek (McGill University)
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| It may be argued that the language of mathematics is about the category of sets, although the definite article requires some justification. As possible worlds of mathematics we may admit all models of type theory, by which we mean all local toposes. For an intuitionist, there is a distinguished local topos, namely the so-called free topos, which may be constructed as the Tarski-Lindenbaum category of intuitionistic type theory. However, for a classical mathematician, to pick a distinguished model may be as difficult as to define the notion of truth in classical type theory, which Tarski has shown to be impossible. |