Abduction, ASP and Open Logic Programs

TL;DR

This paper explores the relationships between open logic programs, abduction, and answer set programming (ASP), demonstrating that open programs generalize the other frameworks and proposing extensions and reductions to enhance understanding and applications.

Contribution

It provides a thorough investigation showing open logic programs generalize abduction and ASP, and introduces extensions and reductions for improved reasoning and application possibilities.

Findings

Open logic programs generalize abduction and ASP.

Reductions from open inference to abduction and ASP are possible.

Extensions of abduction under the generalized stable model semantics are proposed.

Abstract

Open logic programs and open entailment have been recently proposed as an abstract framework for the verification of incomplete specifications based upon normal logic programs and the stable model semantics. There are obvious analogies between open predicates and abducible predicates. However, despite superficial similarities, there are features of open programs that have no immediate counterpart in the framework of abduction and viceversa. Similarly, open programs cannot be immediately simulated with answer set programming (ASP). In this paper we start a thorough investigation of the relationships between open inference, abduction and ASP. We shall prove that open programs generalize the other two frameworks. The generalized framework suggests interesting extensions of abduction under the generalized stable model semantics. In some cases, we will be able to reduce open inference to abduction and ASP, thereby estimating its computational complexity. At the same time, the aforementioned reduction opens the way to new applications of abduction and ASP.