Multicontext logic for semigroups of contexts

A multicontext logic with algebraic structure is proosed, 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. 2A local models semantics for algenraic context composition are 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