An interactive semantics of logic programming

TL;DR

This paper introduces a new semantic framework for logic programming using tile logic, revealing hidden interactions and coordination mechanisms, and extending to constraint systems.

Contribution

It provides a finitary presentation of abstract unification and a concurrent, coordinated abstract semantics consistent with traditional logic programming semantics.

Findings

Finitary presentation of abstract unification

Concurrent and coordinated abstract semantics

Extension to handle constraint systems

Abstract

We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational machinery of such a programming paradigm. The semantic framework we have chosen for presenting our results is tile logic, which has the advantage of allowing a uniform treatment of goals and observations and of applying abstract categorical tools for proving the results. As main contributions, we mention the finitary presentation of abstract unification, and a concurrent and coordinated abstract semantics consistent with the most common semantics of logic programming. Moreover, the compositionality of the tile semantics is guaranteed by standard results, as it reduces to check that the tile systems associated to logic programs enjoy the tile decomposition property. An extension of the approach for handling constraint systems is also discussed.