Non-deterministic Matrices and Modular Semantics of Rules
Arnon Avron

Abstract

We show by way of example how one can provide in a lot of cases
simple modular semantics of rules of inference, so that the semantics
of a system is obtained by joining the semantics of its rules
in the most straightforward way. Our main tool for this task is
the use of finite Nmatrices, 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 paraconsistent logics with a formal
consistency operator (knowns as LFIs), allowing us to
provide in a modular way effective, finite semantics for
thousands of different LFIs.