Modal Propositional Semantics for Reason Maintenance Systems

Abstract

Non-monotonic logics are examined and found to be inadequate as descriptions of reason maintenance systems (sometimes called truth maintenance systems). A logic is proposed that directly addresses the problem of characterizing the mental states of a reasoning agent attempting to reason with respect to some object theory. The proposed logic, propositional dynamic logic of derivation (PDLD), is given a semantics, and a sound and complete axiomatization. The descriptive power of PDLD is demonstrated by expressing various inferential control policies as PDLD formulae. In this note I will elaborate the propositional fragment of an axiomatic semantics of reason maintenance systems (RMS's) [Do2]. The development of such a semantics stems from the desire to provide a declarative specification language for RMS's with particular emphasis on the description of the control of their reasoning processes, and to serve as a formal setting within which to compare and contrast the properties of different RMS's.