Non-deterministic matrices and modular semantics of rules

Abstract

We show by way of example how one can provide in a lot of cases simple modular semantics for rules of inference, so that the semantics of a system is obtained by joining the semantics of its rules in the most straight-forward way. Our main tool for this task is the use of finite matrices, which are multi-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set of options. The method is applied in the area of logics with a formal consistency operator (known as LFIs), allowing us to provide in a modular way effective, finite semantics for thousands of different LFIs.© 2007 Birkhäuser Verlag Basel/Switzerland.