
Authors:
Mamoru KANEKO
Title:Axiomatic considerations of Nash equilibrium
Pages:612
File:bibtex
Abstract ( + )
The Nash equilibrium concept has been playing a central role in game theory. Nevertheless, its meaning or interpretation has not been fully explicated. In this paper, we consider the epistemic foundation of Nash equilibrium from the viewpoint of the oneshot play interpretation. In this interpretation, each player makes his strategy choice before the game is actually played. For his decision making, each player thinks about his strategy choice as well as the other player's choice, and also about the other's thinking about their choices. Here each player is assumed to be very rational. Therefore it would be natural to describe the players' reasoning processes in some epistemic logic. Specifically, we adopt infinitary epistemic logic (S4) with the knowledge operators of two players, and provide an epistemic axiomatization of Nash equilibrium. It states that a final decision for each player is a Nash strategy for him with the common knowledge property. We also evaluate our epistemic axiomatization in a metatheoretical manner.

Authors:
Richard KENNAWAY, JanWillem KLOP, Ronan SLEEP and FerJan de VRIES
Title:From finite to infinite lambda calculi
Pages:1320
File:bibtex
Abstract ( + )
In a previous paper we have established the theory of transfinite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. This results in several new Boehm models of the lambda calculus, and new unifying descriptions of existing models.

Authors:
Larisa MAKSIMOWA
Title:On variable separation in modal logics
Pages:2125
File:bibtex
Abstract ( + )
It was proved that interpolation properties of propositional normal modal logics (n.m.l.) are closely connected with amalgamation properties of associated varieties of modal algebras. In this paper we find an algebraic equivalent of the Hallden property in modal logics, namely, we prove that the Halldencompleteness in any n.m.l. is equivalent to the socalled SuperEmbedding Property of a suitable class of modal algebras. The Joint Embedding Property of this class of algebras is equivalent to the PseudoRelevance Property. We consider connections of the abovementioned properties with interpolation and amalgamation. Also an algebraic equivalent of the Principle of Variable Separation in superintuitionistic logics will befound.

Authors:
Andrei MANTSIVODA
Title:The semantics of flang
Pages:2630
File:bibtex
Abstract ( + )
In this paper we present denotational and operational semantics of Flang. Flang is a functionallogic language with constraints. The semantics of Flang are based on the ideas of Σprogramming and concurrent constraint programming. The denotational semantics of Flang programs is defined using the notion of the least fixed point. A Σ^{+}machine introduced below describes the procedural semantics of Flang.

Authors:
Aart MIDDELDORP and Hans ZANTEMA
Title:Simple termination of rewrite systems
Pages:3136
File:bibtex
Abstract ( + )
In this paper we investigate the concept of simple termination. A term rewriting system (TRS for short) is called simply terminating if its termination can be proved by means of a simplification order. We propose a new definition of simplification order and we investigate the properties of the resulting class ofsimply terminating systems.

Authors:
Vladimir V.RYBAKOV
Title:Even tabular modal logics sometimes do not have independent base for admissible rules
Pages:3740
File:bibtex
Abstract ( + )
Preserving the set of theorems of every given logical system (as the essence of logical systems), we can vary the set of axioms and inference rules in order to make the axiomatic system more powerful and convenient. The class of all derivation rules that can be adjoined to the system without enlarging the set of provable theorems is the class of admissible rules. This class does not depend on the choice of axiomatic system for given logic, therefore "the admissibility" is stable notion, an invariant. All valid rules are admissible, but not conversely. The study of admissible inference rules for particular important systems was conducted since 1975 but a very natural question has not been answered: whether any tabular modal (superintuitionistic) logic (which is generated by a finite modal algebra, or pseudoboolean algebra, correspondingly) has a finite base for admissible rules? The aim of this paper is to solve this problem by counterexamples. We found some finite modal and pseudoboolean algebras such that logics generated by them have no even independent base for admissible rules (in particular, any finite base is imposible).

Authors:
Tatsuya SHIMURA
Title:On completeness of intermediate predicate logics with respect to Kripke semantics
Pages:4145
File:bibtex
Abstract ( + )
In spite of the existence of many examples of incomplete logics, it is an important problem to find intermediate predicate logics complete with respect to Kripke frame (or Kripke sheaf) semantics because they are closed under substitution. But, most of known completeness proofs of finitely axiomatizable logics are difficult to apply to other logics since they are highly dependent on the specific properties of given logics. So, it is preferable to find a general methods of completeness proof. We give some results on this problem using canonical formulas of propositional logics.

Authors:
Frank WOLTER
Title:Decidability of tense logics
Pages:4650
File:bibtex
Abstract ( + )
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