Proof-Terms for Classical and Intuitionistic Resolution (Extended Abstract)

We exploit a system of realizers for classical logic, and a translation from resolution into the sequent calculus, to assess the intuitionistic force of classical resolution for a fragment of intuitionistic logic. This approach is in contrast to formulating locally intuitionistically sound resolution rules. The techniques use the λμe-calculus, a development of Parigot's λμ-calculus.

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

[2]  Melvin Fitting,et al.  Resolution for Intuitionistic Logic , 1987, ISMIS.

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

[4]  Hans Jürgen Ohlbach,et al.  A Resolution Calculus for Modal Logics , 1988, CADE.

[5]  Lincoln A. Wallen Generating connection calculi from tableau and sequent based proof systems , 1975 .

[6]  David J. Pym,et al.  Logic Programming via Proof-valued Computations , 1992, ALPUK.

[7]  Raymond M. Smullyan First-Order Logic. Preliminaries , 1968 .

[8]  David J. Pym,et al.  On the Intuitionistic Force of Classical Search (Extended Abstract) , 1996, TABLEAUX.

[9]  W. Bibel Computationally Improved Versions of Herbrand's Theorem , 1982 .

[10]  Grigori Mints,et al.  Gentzen-type systems and resolution rules. Part I. Propositional logic , 1990, Conference on Computer Logic.

[11]  David J. Pym,et al.  Proof-search in the lII-calculus , 1991 .

[12]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[13]  Michael Gelfond,et al.  Theory of deductive systems and its applications , 1987 .

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

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

[16]  Lincoln A. Wallen Matrix Proof Methods for Modal Logics , 1987, IJCAI.