On combinations of propositional dynamic logic and doxastic modal logics

Reasoning About Games

“…Mono-modal versions of the axiomatics and semantics described in this section come from [14,15]. Additional axioms special to particular games will be added later.…”

“…These game axioms will not be axiom schemes, and so the resulting logics will not be closed under substitution-they will not be normal. This makes for difficulties when completeness and decidability are concerned, a primary consideration of [14,15], but not a relevant issue here. Logics will not be investigated as such, but rather their applicability to particular problems.…”

“…In [14,15] three are considered. The first is a No Learning condition, given by the following axiom scheme, where i is any agent.…”

“…In order to make this paper relatively self-contained, we sketch what is needed from the combination of epistemic and dynamic logics. In particular, completeness results from [14,15] will not be needed, only soundness results, and these are straightforward. The game theory side is a different thing, however, and it is recommended that [4,5] be consulted for the motivation.…”

“…We call the logics used here PDL + E. It is a family, rather than a single logic, because assumptions of varying strengths can be made concerning player knowledge, and also various 'cross' axioms can be assumed as to how the epistemic and the dynamic operators relate to each other. The interaction axioms were thoroughly investigated in [14,15]. This paper derives from a technical report, [9].…”