Abductive Logic Programs with Penalization: Semantics, Complexity and Implementation

TL;DR

This paper introduces a novel abductive reasoning framework with penalization in logic programming, extending existing models to naturally encode optimization, diagnosis, and planning problems, and analyzes its complexity and implementation.

Contribution

It defines a formal model for abduction with penalization in logic programming, extending prior frameworks, and provides a practical implementation with complexity analysis.

Findings

The framework can encode diverse optimization and diagnostic problems.

The computational complexity of key problems is thoroughly analyzed.

A system supporting the framework is implemented on the DLV engine.

Abstract

Abduction, first proposed in the setting of classical logics, has been studied with growing interest in the logic programming area during the last years. In this paper we study abduction with penalization in the logic programming framework. This form of abductive reasoning, which has not been previously analyzed in logic programming, turns out to represent several relevant problems, including optimization problems, very naturally. We define a formal model for abduction with penalization over logic programs, which extends the abductive framework proposed by Kakas and Mancarella. We address knowledge representation issues, encoding a number of problems in our abductive framework. In particular, we consider some relevant problems, taken from different domains, ranging from optimization theory to diagnosis and planning; their encodings turn out to be simple and elegant in our formalism. We thoroughly analyze the computational complexity of the main problems arising in the context of abduction with penalization from logic programs. Finally, we implement a system supporting the proposed abductive framework on top of the DLV engine. To this end, we design a translation from abduction problems with penalties into logic programs with weak constraints. We prove that this approach is sound and complete.