Two formalizations of context: A comparison

Abstract

We investigate the relationship between two well known formalizations of context: Propositional Logic of Context (PLC) [4], and Local Models Semantics (LMS) [11]. We start with a summary of the desiderata for a logic of context, mainly inspired by McCarthy’s paper on generality in AI [15] and his notes on formalizing context [16]. We briefly present LMS, and its axiomatization using MultiContext Systems (MCS) [14]. Then we present a revised (and simplified) version of PLC, and we show that local vocabularies – as they defined in [4] – are inessential in the semantics of PLC. The central part of the paper is the definition of a class of LMS (and its axiomatization in MCS, called MMCC), which is provably equivalent to the axiomatization of PLC as described in [4]. Finally, we go back to the general desiderata and discuss in detail how the two formalisms fulfill (or do not fulfill) each of them.