Semantics for "Enough-Certainty" and Fitting's Embedding of Classical Logic in S4

In this work we look at how Fitting’s embedding of first-order classical logic into first-order S4 can help in reasoning when we are interested in satisfaction “in most cases”, when first-order properties are allowed to fail in cases that are considered insignificant. We extend classical semantics by combining a Kripke-style model construction of “significant” events as possible worlds with the forcing-Fitting-style semantics construction by embedding classical logic into S4. We provide various examples. Our main running example is an application to symbolic security protocol verification with complexity-theoretic guarantees. In particular, we show how Fitting’s embedding emerges entirely naturally when verifying trace properties in computer security. 1998 ACM Subject Classification F.3.1 Logics and Meanings of Programs