TY - CONF
T1 - Semantic games for first-order entailment with algorithmic players
AU - Genot, Emmanuel
AU - Jacot, Justine
PY - 2014
Y1 - 2014
N2 - If semantic consequence is analyzed with extensive games, logical reasoning can be accounted for by looking at how players solve entailment games. However, earlier approaches to game semantics cannot achieve this reduction, by want of explicitly dened preferences for players. Moreover, although entailment games
can naturally translate the idea of argumentation about a common ground, a cognitive interpretation is undermined by the complexity of strategic reasoning. We thus describe a class of semantic extensive entailment game with algorithmic players, who have preferences for parsimonious spending of computational resources and thus compute partial strategies under qualitative uncertainty about future histories. We prove the existence of local preferences for moves and of strategic fixpoints that allow to map game-trees to tableaux proofs, and exhibit a strategy prole that solves the fixpoint selection problem, and can be mapped to systematic constructions of semantic trees, yielding a completeness result by translation. We then discuss the correspondence between proof heuristics and strategies in our games, the relations of our games to gts, and possible extensions to other entailment relations. We conclude that the main interest of our result lies in the possibility to bridge argumentative and cognitive models of logical reasoning, rather than in new meta-theoretic results. All proofs are given in appendix.
AB - If semantic consequence is analyzed with extensive games, logical reasoning can be accounted for by looking at how players solve entailment games. However, earlier approaches to game semantics cannot achieve this reduction, by want of explicitly dened preferences for players. Moreover, although entailment games
can naturally translate the idea of argumentation about a common ground, a cognitive interpretation is undermined by the complexity of strategic reasoning. We thus describe a class of semantic extensive entailment game with algorithmic players, who have preferences for parsimonious spending of computational resources and thus compute partial strategies under qualitative uncertainty about future histories. We prove the existence of local preferences for moves and of strategic fixpoints that allow to map game-trees to tableaux proofs, and exhibit a strategy prole that solves the fixpoint selection problem, and can be mapped to systematic constructions of semantic trees, yielding a completeness result by translation. We then discuss the correspondence between proof heuristics and strategies in our games, the relations of our games to gts, and possible extensions to other entailment relations. We conclude that the main interest of our result lies in the possibility to bridge argumentative and cognitive models of logical reasoning, rather than in new meta-theoretic results. All proofs are given in appendix.
M3 - Paper, not in proceeding
T2 - The Eleventh Conference on Logic and the Foundations of Game and Decision Theory
Y2 - 27 July 2014 through 30 July 2014
ER -