Semantics for "enough-certainty" and fitting's embedding of classical logic in S4

Abstract

In this work we look at how Fitting's embedding of first-order classical logic into first-order S4 can help reasoning when we are interested satisfaction in most cases, when first-order properties are allowed to fail 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 computer security.