An Algebra of Combined Constraint Solving

21 pages•Published: December 18, 2015

Abstract

The paper describes a project aiming at developing formal foundations
of combined multi-language constraint solving in the form of an algebra of modular systems.
The basis for integration of different formalisms is the classic model theory.
Each atomic module is a class of structures.
It can be given, e.g., by a set of constraints in a constraint formalism
that has an associated solver.
Atomic modules are combined using a small number of algebraic operations.
The algebra simultaneously resembles Codd's relational algebra, (but is defined
on classes of structures instead of relational tables), and process
algebras originated in the work of Milner and Hoare.

The goal of this paper is to establish and justify
the main notions and research directions,
make definitions precise.
We explain several results, but do not give proofs.
The proofs will appear in several forthcoming papers.
We keep this paper as a project description paper to discuss the overall project,
to establish and bridge individual directions.

Keyphrases: answer set programming, computational complexity, knowledge representation and reasoning, mathematical foundations, modular systems, multi language constraint solving

In: Georg Gottlob, Geoff Sutcliffe and Andrei Voronkov (editors). GCAI 2015. Global Conference on Artificial Intelligence, vol 36, pages 275-295.

Links:	https://easychair.org/publications/paper/FQ2t
	https://doi.org/10.29007/976n