Transition Semantics - The Dynamics of Dependence Logic

TL;DR

This paper introduces Transition Logic, a variant of Dynamic Game Logic, to provide a new perspective on Dependence Logic by interpreting formulas as reachability assertions in games of imperfect information.

Contribution

It develops Transition Logic and shows its relationship with Dependence Logic, offering a novel interpretative framework based on game reachability concepts.

Findings

Transition Logic is developed as a variant of Dynamic Game Logic.

Dependence Logic is interpreted through reachability in games of imperfect information.

The paper establishes an expressive equivalence between Dependence Logic variants and game-based semantics.

Abstract

We examine the relationship between Dependence Logic and game logics. A variant of Dynamic Game Logic, called Transition Logic, is developed, and we show that its relationship with Dependence Logic is comparable to the one between First-Order Logic and Dynamic Game Logic discussed by van Benthem. This suggests a new perspective on the interpretation of Dependence Logic formulas, in terms of assertions about reachability in games of im- perfect information against Nature. We then capitalize on this intuition by developing expressively equivalent variants of Dependence Logic in which this interpretation is taken to the foreground.