Admissible Rules of Lukasiewicz Logic

We investigate admissible rules of Łukasiewicz multi-valued propositional logic. We show that admissibility of multiple-conclusion rules in Łukasiewicz logic, as well as validity of universal sentences in free MV-algebras, is decidable (in PSPACE).

[1]  Nancy A. Lynch,et al.  Log Space Recognition and Translation of Parenthesis Languages , 1977, JACM.

[2]  Rosalie Iemhoff,et al.  Intermediate Logics and Visser's Rules , 2005, Notre Dame J. Formal Log..

[3]  A. V. Chagrov.  Decidable modal logic with undecidable admissibility problem , 1992 .

[4]  Emil Jerábek,et al.  Bases of Admissible Rules of Lukasiewicz Logic , 2010, J. Log. Comput..

[5]  Vladimir V. Rybakov,et al.  Admissibility of Logical Inference Rules , 2011 .

[6]  Robert McNaughton,et al.  A Theorem About Infinite-Valued Sentential Logic , 1951, J. Symb. Log..

[7]  Rosalie Iemho.  On the Admissible Rules of Intuitionistic Propositional Logic , 2008 .

[8]  P. Lorenzen.  Einführung in die operative Logik und Mathematik , 1955 .

[9]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[10]  Petr Cintula,et al.  Structural Completeness in Fuzzy Logics , 2009, Notre Dame J. Formal Log..

[11]  Rosalie Iemhoff,et al.  On the rules of intermediate logics , 2006, Arch. Math. Log..

[12]  James G. Raftery,et al.  Structural Completeness in Substructural Logics , 2008, Log. J. IGPL.

[13]  Omer Reingold,et al.  Undirected connectivity in log-space , 2008, JACM.

[14]  Daniele Mundici,et al.  Satisfiability in Many-Valued Sentential Logic is NP-Complete , 1987, Theor. Comput. Sci..

[15]  Rosalie Iemhoff,et al.  On the admissible rules of intuitionistic propositional logic , 2001, Journal of Symbolic Logic.

[16]  Silvio Ghilardi,et al.  Unification in intuitionistic logic , 1999, Journal of Symbolic Logic.

[17]  Tadeusz Prucnal,et al.  On two problems of Harvey Friedman , 1979 .

[18]  Harvey M. Friedman,et al.  One hundred and two problems in mathematical logic , 1975, Journal of Symbolic Logic.

[19]  Frank Wolter,et al.  Undecidability of the unification and admissibility problems for modal and description logics , 2006, TOCL.

[20]  Silvio Ghilardi,et al.  Best Solving Modal Equations , 2000, Ann. Pure Appl. Log..

[21]  Wojciech Dzik.  Unification in some substructural logics of BL-algebras and hoops , 2008, Reports Math. Log..

[22]  D. J. Shoesmith,et al.  Multiple-Conclusion Logic , 1978 .

[23]  Marcus Kracht.  Book Review: V. V. Rybakov. Admissibility of Logical Inference Rules , 1999, Notre Dame J. Formal Log..

[24]  Piotr Wojtylak.  On structural completeness of many-valued logics , 1978 .

[25]  Vladimir V. Rybakov,et al.  Logical consecutions in discrete linear temporal logic , 2005, Journal of Symbolic Logic.

[26]  Silvio Ghilardi,et al.  Unification Through Projectivity , 1997, J. Log. Comput..

[27]  Vladimir V. Rybakov.  Logical Consecutions in Intransitive Temporal Linear Logic of Finite Intervals , 2005, J. Log. Comput..

[28]  Emil Jerábek,et al.  Complexity of admissible rules , 2007, Arch. Math. Log..

[29]  Petr Cintula.  Short note: on the redundancy of axiom (A3) in BL and MTL , 2005, Soft Comput..

[30]  Emil Jerábek,et al.  Admissible Rules of Modal Logics , 2005, J. Log. Comput..

[31]  Vladimir V. Rybakov,et al.  Linear Temporal Logic with Until and Before on Integer Numbers, Deciding Algorithms , 2006, CSR.