TR-2007020: S4LP and Local Realizability

The logic S4LP combines the modal logic S4 with the justification logic LP. This is the case both axiomatically and semantically, though of course the real story is in the details. We introduce a simple restriction on the behavior of constants in S4LP, a restriction that has no effect on the LP sublogic. With this assumed, some very powerful derived rules are established. Then these are used to show we have completeness relative to a semantics having what we call the local realizability property. This means that at each world of such a model, 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 part of a attempt to understand the deeper aspects of Artemov’s Realization Theorem, though it is not yet clear just how the results obtained here relate to that theorem.