Introduction to Guarded Logics

Abstract

Guarded logics are a family of logical formalisms that generalize certain desirable properties of modal logics from transition systems to the setting of arbitrary relational structures. Modal logics are widely used in a number of areas in computer science, particularly for the specification and verification of hardware and software systems, for knowledge representation, in databases, and in artificial intelligence. The most basic modal logic is propositional modal logic ML, which is just the fixed-point free part of the μ-calculus (see Chapter 10). But modal logics, broadly conceived, form a family of many different formalisms, including temporal logics, description logics, process logics, etc, many of which are also closely related to automata. An important reason for the successful applications of modal logics is their good balance between expressive power and computational complexity. This means that on the one hand, the relevant statements for many applications are expressible in these logics, and on the other hand, the usual reasoning tasks are decidable and admit reasonably efficient algorithms.