A proof-theoretic analysis of the classical propositional matrix method

The matrix method, due to Bibel and Andrews, is a proof procedure designed for automated theorem-proving. We show that underlying this method is a fully structured combinatorial model of conventional classical proof theory. © 2012 The Author, 2012. Published by Oxford University Press.

[1]  Martin Hyland Abstract Interpretation of Proofs: Classical Propositional Calculus , 2004, CSL.

[2]  Wolfgang Bibel,et al.  On Matrices with Connections , 1981, JACM.

[3]  Martin Hyland,et al.  Proof theory in the abstract , 2002, Ann. Pure Appl. Log..

[4]  R. A. G. Seely,et al.  Weakly distributive categories , 1997 .

[5]  François Lamarche,et al.  Constructing free Boolean categories , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[6]  Radha Jagadeesan,et al.  New foundations for the geometry of interaction , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.

[7]  Edmund Robinson Proof Nets for Classical Logic , 2003, J. Log. Comput..

[8]  David J. Pym,et al.  On categorical models of classical logic and the Geometry of Interaction , 2007, Mathematical Structures in Computer Science.

[9]  K. Dosen Cut Elimination in Categories , 1999 .

[10]  David J. Pym,et al.  Order-enriched categorical models of the classical sequent calculus , 2006 .

[11]  David J. Pym,et al.  On the semantics of classical disjunction , 2001 .

[12]  Christian Urban,et al.  Categorical proof theory of classical propositional calculus , 2006, Theor. Comput. Sci..

[13]  Michel Parigot,et al.  Lambda-Mu-Calculus: An Algorithmic Interpretation of Classical Natural Deduction , 1992, LPAR.

[14]  David J. Pym,et al.  On the geometry of interaction for classical logic , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

[15]  Lincoln A. Wallen,et al.  Automated deduction in nonclassical logics , 1990 .

[16]  J. Lambek,et al.  Introduction to higher order categorical logic , 1986 .

[17]  Peter Kulchyski and , 2015 .

[18]  Dominic Hughes Proofs without syntax , 2004 .

[19]  Peter B. Andrews Theorem Proving via General Matings , 1981, JACM.

[20]  J. Girard,et al.  Proofs and types , 1989 .

[21]  François Lamarche,et al.  Naming Proofs in Classical Propositional Logic , 2005, TLCA.