# 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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