Checking Proof Transformations with ASP

Proof transformation is an important proof theoretic technique that has b een used for showing a number of foundational results about proof systems. For instance, it is used for showing the admissibility of the cutrule and the completeness of proof search strategies, such as uniform provability and the focusing discipline. However, in order to check the validity of a proof transformation, such a s when one inference rule permutes over another, one needs to consider the combination of how inference r ules may be applied. Therefore, checking the correctness of proof transformations is prone to human e rror. This paper o ffers the means to automatize the check of such transformations by using Answer Set Prog ramming (ASP).

[1]  Frank Pfenning,et al.  A linear logical framework , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[2]  Anna Zamansky,et al.  Cut-free sequent calculi for C-systems with generalized finite-valued semantics , 2013, J. Log. Comput..

[3]  Sara Negri,et al.  Proof Analysis in Modal Logic , 2005, J. Philos. Log..

[4]  Dale Miller,et al.  From Proofs to Focused Proofs: A Modular Proof of Focalization in Linear Logic , 2007, CSL.

[5]  Guy Perrier,et al.  On Proof Normalization in Linear Logic , 1992, Theor. Comput. Sci..

[6]  JEAN-MARC ANDREOLI,et al.  Logic Programming with Focusing Proofs in Linear Logic , 1992, J. Log. Comput..

[7]  Gerhard Gentzen,et al.  Investigations into Logical Deduction , 1970 .

[8]  Tristan Crolard,et al.  Subtractive logic , 2001, Theor. Comput. Sci..

[9]  Michael Gelfond,et al.  Logic Programs with Classical Negation , 1990, ICLP.

[10]  Cecylia Rauszer,et al.  A formalization of the propositional calculus of H-B logic , 1974 .

[11]  F. Pfenning,et al.  Automating the meta theory of deductive systems , 2000 .

[12]  Robert J. Simmons,et al.  Substructural Operational Semantics as Ordered Logic Programming , 2009, 2009 24th Annual IEEE Symposium on Logic In Computer Science.

[13]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[14]  James Harland,et al.  A contribution to automated-oriented reasoning about permutability of sequent calculi rules , 2013, Comput. Sci. Inf. Syst..

[15]  Wolfgang Faber,et al.  The DLV system for knowledge representation and reasoning , 2002, TOCL.

[16]  Gopalan Nadathur,et al.  Uniform Proofs as a Foundation for Logic Programming , 1991, Ann. Pure Appl. Log..

[17]  Dale Miller,et al.  A formal framework for specifying sequent calculus proof systems , 2013, Theor. Comput. Sci..

[18]  Elaine Pimentel,et al.  Specifying Proof Systems in Linear Logic with Subexponentials , 2010, LSFA.

[19]  Ilkka Niemelä,et al.  Smodels - An Implementation of the Stable Model and Well-Founded Semantics for Normal LP , 1997, LPNMR.

[20]  Frank Pfenning,et al.  A Linear Logical Framework , 2002, Inf. Comput..

[21]  Dale Miller,et al.  A Framework for Proof Systems , 2010, Journal of Automated Reasoning.