Games for Inclusion Logic and Fixed-Point Logic
One of the most intriguing results on logics of dependence and independence is the tight connection between inclusion logic and the least fixed-point logic LFP. Here we re-examine this connection from a game-theoretic point of view. We study the model-checking games for inclusion logic and for posGFP, the fragment of LFP that uses only (non-negated) greatest fixed points. We show that the evaluation problems for both logics can be represented by a special kind of trap condition in safety games. We then study interpretation arguments for games. In combination with our study of traps for inclusion logic and posGFP, game interpretations will give us a model-theoretic construction of translations between the two logics.
KeywordsWinning Strategy Dependence Logic Game Graph Winning Condition Negation Normal Form
- 9.Grädel, E., et al.: Finite Model Theory and Its Applications. Springer, Berlin (2007)Google Scholar
- 11.Hodges, W.: Logics of imperfect information: why sets of assignments? In: van Benthem, J., Löwe, B., Gabbay, D. (eds.) Interactive Logic. Texts in Logic and Games, vol. 1, pp. 117–134. Amsterdam University Press, Amsterdam (2007)Google Scholar