Multicontext Logic for Semigroups of Contexts

Abstract

A multicontext logic with algebraic structure is proposed, where contexts are either primitive or composed from other contexts. Composition of two contexts can support various intuitions: sequence concatenation, set union, multiset union, etc. A local models semantics for algebraic context composition is defined, with a corresponding deductive calculus containing multilanguage bridge rules. Soundness and completeness results are proved for the case of semigroups of contexts, i.e. where context composition is an associative operation. Other properties of context composition, besides associativity, are defined by additional algebraic equations.