S4LPand Local Realizability

The logic S4LP combines the modal logic S4 with the justification logic LP, both axiomatically and semantically. We introduce a simple restriction on the behavior of constants in S4LP, having no effect on the LP sublogic. Under this restriction some powerful derived rules are established. Then these are used to show completeness relative to a semantics having what we call the local realizability property: at each world and for each formula true at that world there is a realization also true at that world, where a realization is the result of replacing all modal operators with explicit justification terms. This is a part of a project to understand the deeper aspects of Artemov’s Realization Theorem.