Enablers and Inhibitors in Causal Justifications of Logic Programs

TL;DR

This paper extends logic programming by associating justifications with causal explanations and conditions like enablers and inhibitors, comparing these with existing approaches under the well-founded semantics.

Contribution

It introduces a novel extension of LP with algebraic justifications including enablers and inhibitors, and formally relates it to existing justification frameworks.

Findings

Extends LP with algebraic justifications including enablers and inhibitors.

Shows the new approach extends WnP and CG justifications.

Establishes a formal relation between WnP and CG approaches.

Abstract

To appear in Theory and Practice of Logic Programming (TPLP). In this paper we propose an extension of logic programming (LP) where each default literal derived from the well-founded model is associated to a justification represented as an algebraic expression. This expression contains both causal explanations (in the form of proof graphs built with rule labels) and terms under the scope of negation that stand for conditions that enable or disable the application of causal rules. Using some examples, we discuss how these new conditions, we respectively call "enablers" and "inhibitors", are intimately related to default negation and have an essentially different nature from regular cause-effect relations. The most important result is a formal comparison to the recent algebraic approaches for justifications in LP: "Why-not Provenance" (WnP) and "Causal Graphs" (CG). We show that the current approach extends both WnP and CG justifications under the Well-Founded Semantics and, as a byproduct, we also establish a formal relation between these two approaches.