Abduction with Penalization in Logic Programming

Title: Abduction with Penalization in Logic Programming

Abstract: Abduction is a form of reasoning that seeks to explain observations by invoking the most likely underlying causes. In the context of logic programming, abduction has been proposed as a method for dealing with incomplete information. This paper explores abduction with penalization, a form of abductive reasoning that assigns a penalty to each hypothesis, with the goal of favoring solutions with lower penalties. This approach is shown to be applicable to various problems, including the Traveling Salesman Problem, which can be encoded elegantly using abduction with penalization.

Research Question: How can abduction with penalization be applied to logic programming to solve complex problems?

Methodology: The paper proposes a formal model for abduction with penalization in logic programming. It extends the abductive framework proposed by Kakas and Mancarella and assigns a penalty to each hypothesis. The weight of a solution is determined by the sum of the penalties of the hypotheses in the solution. Minimum-weight solutions are preferred due to their likelihood of occurrence.

Results: The paper demonstrates the high expressiveness of the proposed formalism by encoding various problems, including the Traveling Salesman Problem. The resulting encodings are simple and elegant, providing a novel approach to solving these problems. The complexity of the decisional problems arising in this framework is also analyzed.

Implications: Abduction with penalization in logic programming offers a powerful tool for solving complex problems. It provides a natural way to represent and solve optimization problems and other problems that involve incomplete information. The approach's simplicity and elegance make it an attractive choice for various applications.

Link to Article: https://arxiv.org/abs/0111010v1 Authors: arXiv ID: 0111010v1