Explicit Evidence Systems with Common Knowledge

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic

Propositional games with explicit strategies

This paper presents a game semantics for LP, Artemov’s Logic of Proofs. The language of LP extends that of propositional logic by adding formula-labeling terms, permitting us to take a term t and an LP formula A and form the new formula t:A. We define a game semantics for this logic that interprets terms as winning strategies on the formulas they label, so t:A may be read as “t is a winning strategy on A. ” LP may thus be seen as a logic containing in-language descriptions of winning strategies on its own formulas. We apply our semantics to show how winnable instances of certain extensive games with perfect information may be embedded into LP. This allows us to use LP to derive a winning strategy on the embedding, from which we can extract a winning strategy on the original, non-embedded game. As a concrete illustration of this method, we compute a winning strategy for a winnable instance of the well-known game Nim.