Game values and equilibria for undetermined sentences of Dependence Logic
Pietro Galliani
Abstract:
Logics of imperfect information, such as IF-Logic or Dependence Logic,
admit a game-theoretic semantics: every formula \phi corresponds to a
game H(\phi) between a Verifier and a Falsifier, and the formula is
true [false] if and only if the Verifier [Falsifier] has a winning
strategy.
Since the rule of the excluded middle does not hold in these logics,
it is possible for a game H(\phi) to be undetermined; this thesis
attempts to examine the values of such games, that is, the maximum
expected payoffs that the Verifier is able to guarantee.
For finite models, the resulting "Probabilistic Dependence Logic" can
be shown, by means of the Minimax Theorem, to admit a compositional
semantics similar to Hodgesâ€™ one for Slash Logic.