Abstract

This work proposes a new semantics named "context semantics", which interprets predicate modal logic in which the modality symbols means logical validity. Although the possible world semantics is the most well-known method for semantics of modal logic, it is not so useful or so essential in studying the predicate modal logic. Especially, the transworld identification always makes serious problem. In order to avoid the problem, we propose the new semantics. Our semantics interprets a formula with finite information. This point is the most essential difference between our semantics and possible world semantics.