Computing interpolants in implicational logics

Abstract I present a new syntactical method for proving the Interpolation Theorem for the implicational fragment of intuitionistic logic and its substructural subsystems. This method, like Prawitz’s, works on natural deductions rather than sequent derivations, and, unlike existing methods, always finds a ‘strongest’ interpolant under a certain restricted but reasonable notion of what counts as an ‘interpolant’.

[1]  Makoto Kanazawa,et al.  Learning Word-to-Meaning Mappings in Logical Semantics , 2001 .

[2]  Daniel J. Dougherty,et al.  A Decidable Variant of Higher Order Matching , 2002, RTA.

[3]  Andrew M. Pitts,et al.  On an interpretation of second order quantification in first order intuitionistic propositional logic , 1992, Journal of Symbolic Logic.

[4]  G. Gentzen.  Untersuchungen über das logische Schließen. I , 1935 .

[5]  Sabine Broda,et al.  On Principal Types of BCK- lambda -Terms , 2007, WoLLIC.

[6]  A..  Interpolants , cut elimination and flow graphs for the propositional calculus , 1997 .

[7]  Mariangiola Dezani-Ciancaglini,et al.  Theories of Types and Proofs , 1998 .

[8]  D. Prawitz.  Natural Deduction: A Proof-Theoretical Study , 1965 .

[9]  G. Mints.  A Short Introduction to Intuitionistic Logic , 2000 .

[10]  Djordje Cubric.  Interpolation property for bicartesian closed categories , 1994, Arch. Math. Log..

[11]  Helmut Schwichtenberg,et al.  Basic proof theory , 1996, Cambridge tracts in theoretical computer science.

[12]  Mirjana Borisavljevic.  A Cut-Elimination Proof in Intuitionistic Predicate Logic , 1999, Ann. Pure Appl. Log..

[13]  Paul Dekker,et al.  Proceedings of the Fourteenth Amsterdam Colloquium , 2003 .

[14]  Hiroakira Ono,et al.  Proof-Theoretic Methods in Nonclassical Logic --an Introduction , 1998 .

[15]  Mati Pentus.  Product-Free Lambek Calculus and Context-Free Grammars , 1997, J. Symb. Log..

[16]  Helmut Schwichtenberg,et al.  Basic proof theory, Second Edition , 2000 .

[17]  Martin Stokhof,et al.  Proceedings of the Thirteenth Amsterdam Colloquium , 2001 .