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 {\em abduction with penalization} in logic programming. 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 from logic programs, which extends the abductive framework proposed by Kakas and Mancarella. We show the high expressiveness of this formalism, by encoding a couple of relevant problems, including the well-know Traveling Salesman Problem from optimization theory, in this abductive framework. The resulting encodings are very simple and elegant. We analyze the complexity of the main decisional problems arising in this framework. An interesting result in this course is that ``negation comes for free.'' Indeed, the addition of (even unstratified) negation does not cause any further increase to the complexity of the abductive reasoning tasks (which remains the same as for not-free programs).
Connection-minimal Abduction in EL via Translation to FOL -- Technical Report
Max-Planck-Institut für Informatik（马克斯·普朗克信息学研究所）；Graduate School of Computer Science（计算机科学研究生院）；TU Dresden（德累斯顿工业大学）；Université de Lorraine（洛林大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；LORIA（洛林信息学及其应用研究实验室）
Université de Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800（波尔多大学、法国国家科学研究中心、波尔多INP、LaBRI、UMR 5800）；Japanese-French Laboratory for Informatics, CNRS, NII, IRL 2537（日法信息实验室、法国国家科学研究中心、日本信息产业技术研究所、IRL 2537）；National Institute of Informatics, Tokyo, Japan（日本信息处理研究所）
