Towards automated first-order abduction: the cut-based approach

Traditional abduction imposes as a precondition the restriction that the background information may not derive the goal data. In first-order logic such precondition is, in general, undecidable. To avoid such problem, we present a first-order cutbased abduction method, which has KE-tableaux as its underlying inference system. This inference system allows for the automation of non-analytic proofs in a tableau setting, which permits a generalization of traditional abduction that avoids the undecidable precondition problem. After demonstrating the correctness of the method, we show how this method can be dynamically iterated in a process that leads to the construction of non-analytic first-order proofs and, in some terminating cases, to refutations as well.

[1]  Akihiro Yamamoto,et al.  Which Hypotheses Can Be Found with Inverse Entailment? , 1997, ILP.

[2]  Walter Alexandre Carnielli.  Surviving Abduction , 2006, Log. J. IGPL.

[3]  Francesco M. Donini,et al.  A Uniform Tableaux-Based Approach to Concept Abduction and Contraction in ALN , 2004, Description Logics.

[4]  Marcello D'Agostino,et al.  The Taming of the Cut. Classical Refutations with Analytic Cut , 1994, J. Log. Comput..

[5]  Marcello D'Agostino,et al.  Are tableaux an improvement on truth-tables? , 1992, J. Log. Lang. Inf..

[6]  David Poole,et al.  A Logical Framework for Default Reasoning , 1988, Artif. Intell..

[7]  Paolo Mancarella,et al.  Abductive Logic Programming , 1992, LPNMR.

[8]  Samuel R. Buss,et al.  Some remarks on lengths of propositional proofs , 1995, Arch. Math. Log..

[9]  Johan de Kleer,et al.  An Assumption-Based TMS , 1987, Artif. Intell..

[10]  Atocha Aliseda-Llera,et al.  Seeking explanations: abduction in logic, philosophy of science and artificial intelligence , 1998 .

[11]  Reinhold Letz,et al.  The Disconnection Tableau Calculus , 2007, Journal of Automated Reasoning.

[12]  Dov M. Gabbay,et al.  Cut-Based Abduction , 2008, Log. J. IGPL.

[13]  Raymond Reiter,et al.  Foundations of Assumption-based Truth Maintenance Systems: Preliminary Report , 1987, AAAI.

[14]  George Boolos,et al.  Don't eliminate cut , 1984, J. Philos. Log..

[15]  Ángel Nepomuceno-Fernández,et al.  Towards Abductive Reasoning in First-order Logic , 2006, Log. J. IGPL.

[16]  Katsumi Inoue,et al.  SOLAR: An automated deduction system for consequence finding , 2010, AI Commun..

[17]  Marcello D'Agostino,et al.  Tableau Methods for Classical Propositional Logic , 1999 .

[18]  Harald Ganzinger,et al.  Resolution Theorem Proving , 2001, Handbook of Automated Reasoning.

[19]  Murray Shanahan,et al.  Prediction is Deduction but Explanation is Abduction , 1989, IJCAI.

[20]  Robert A. Kowalski,et al.  Abduction Compared with Negation by Failure , 1989, ICLP.

[21]  R. Goodstein.  FIRST-ORDER LOGIC , 1969 .

[22]  Jean-Paul Billon,et al.  The Disconnection Method - A Confluent Integration of Unification in the Analytic Framework , 1996, TABLEAUX.

[23]  David Poole,et al.  Representing Knowledge for Logic-Based Diagnosis , 1988, FGCS.

[24]  Fiora Pirri,et al.  First order abduction via tableau and sequent calculi , 1993, Log. J. IGPL.

[25]  Dov M. Gabbay,et al.  Advice on Abductive Logic , 2006, Log. J. IGPL.

[26]  S. Semmes,et al.  A Graphic Apology for Symmetry and Implicitness , 2000 .