FQHT: The Logic of Stable Models for Logic Programs with Intensional Functions

We study a logical system FQHT that is appropriate for reasoning about nonmonotonic theories with intensional functions as treated in the approach of [Bartholomew and Lee, 2012]. We provide a logical semantics, a Gentzen style proof theory and establish completeness results. The adequacy of the approach is demonstrated by showing that it captures the Bartholemew/Lee semantics and satisfies a strong equivalence property.

[1]  Enrico Giunchiglia,et al.  Nonmonotonic causal theories , 2004, Artif. Intell..

[2]  S. Shelah,et al.  Annals of Pure and Applied Logic , 1991 .

[3]  Pedro Cabalar,et al.  Partial Functions and Equality in Answer Set Programming , 2008, ICLP.

[4]  Pedro Cabalar.  Functional answer set programming , 2011, Theory Pract. Log. Program..

[5]  Joohyung Lee,et al.  A New Perspective on Stable Models , 2007, IJCAI.

[6]  Fangzhen Lin,et al.  Answer Set Programming with Functions , 2008, KR.

[7]  Luis Fariñas del Cerro,et al.  Bi-state Logic , 2012, Correct Reasoning.

[8]  David Pearce,et al.  A First Order Nonmonotonic Extension of Constructive Logic , 2005, Stud Logica.

[9]  Marcello Balduccini,et al.  A "Conservative" Approach to Extending Answer Set Programming with Non-Herbrand Functions , 2012, Correct Reasoning.

[10]  Joohyung Lee,et al.  Stable Models of Formulas with Intensional Functions , 2012, KR.

[11]  Enrico Pontelli,et al.  Proceedings of the 24th International Conference on Logic Programming , 2008 .

[12]  Grigori Mints.  Cut-free formulations for a quantified logic of here and there , 2010, Ann. Pure Appl. Log..

[13]  James W. Garson,et al.  Quantification in Modal Logic , 1984 .

[14]  David Pearce,et al.  A Characterization of Strong Equivalence for Logic Programs with Variables , 2007, LPNMR.

[15]  Vladimir Lifschitz,et al.  Logic Programs with Intensional Functions , 2012, KR.

[16]  V. S. Costa,et al.  Theory and Practice of Logic Programming , 2010 .