Equilibrium semantics of languages of imperfect information

https://doi.org/10.1016/j.apal.2009.07.019Get rights and content
Under an Elsevier user license
open archive

Abstract

In this paper, we introduce a new approach to independent quantifiers, as originally introduced in Informational independence as a semantic phenomenon by Hintikka and Sandu (1989) [9] under the header of independence-friendly (IF) languages. Unlike other approaches, which rely heavily on compositional methods, we shall analyze independent quantifiers via equilibriums in strategic games. In this approach, coined equilibrium semantics, the value of an IF sentence on a particular structure is determined by the expected utility of the existential player in any of the game’s equilibriums. This approach was suggested in Henkin quantifiers and complete problems by Blass and Gurevich (1986) [2] but has not been taken up before. We prove that each rational number can be realized by an IF sentence. We also give a lower and upper bound on the expressive power of IF logic under equilibrium semantics.

MSC

91A80
03C13
03C80
68Q19

Keywords

Independence-friendly logic
Game-theoretic semantics
Nash equilibrium
Combinatorial game theory
Descriptive complexity

Cited by (0)