Justifications for Programs with Disjunctive and Causal-choice Rules

TL;DR

This paper extends stable model semantics for disjunctive logic programs by incorporating algebraic justifications for atoms, introduces causal-choice rules, and explores their semantic implications and examples.

Contribution

It introduces a new semantic framework for disjunctive logic programs with causal justifications and causal-choice rules, expanding the understanding of explanations in logic programming.

Findings

Defines causal stable models for disjunctive programs.

Introduces causal-choice rules capturing causal relationships.

Provides illustrative examples of the new semantics.

Abstract

In this paper, we study an extension of the stable model semantics for disjunctive logic programs where each true atom in a model is associated with an algebraic expression (in terms of rule labels) that represents its justifications. As in our previous work for non-disjunctive programs, these justifications are obtained in a purely semantic way, by algebraic operations (product, addition and application) on a lattice of causal values. Our new definition extends the concept of causal stable model to disjunctive logic programs and satisfies that each (standard) stable model corresponds to a disjoint class of causal stable models sharing the same truth assignments, but possibly varying the obtained explanations. We provide a pair of illustrative examples showing the behaviour of the new semantics and discuss the need of introducing a new type of rule, which we call causal-choice. This type of rule intuitively captures the idea of "$A$ may cause $B$" and, when causal information is disregarded, amounts to a usual choice rule under the standard stable model semantics. (Under consideration for publication in Theory and Practice of Logic Programming)