Constraint Logics (abstract)

This research exploits the view of constraint programming as computation in a logical system, namely constraint logic. The basic ingredients of constraint logic are: constraint models for the semantics (they form a comma-category over the model of built-ins), generalised polynomials in the role of basic syntactic ingredient, and a constraint satisfaction relation between semantics and syntax. We show that constraint logic is an institution, and we internalise the study of constraint logic to the abstract framework of category-based equational logic, thus openning the door for considering constraint logic programming over non-standard structures (such as CPO's, topologies, graphs, categories, etc.). By embedding constraint logic into category-based equational logic, we integrate the constraint logic programming paradigm into (category-based) equational logic programming. Results include completeness of constraint logic deduction, a novel Herbrand theorem for constraint logic programming characterising Herbrand models as initial models in cosntraint logic, and logical foundations for modular combination of constraint solvers based on amalgamated sums of Herbrand models in the constraint logic institution.

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