Unifiability and Admissibility in Finite Algebras

Unifiability of finite sets of equations and admissibility of quasiequations in finite algebras are decidable problems, but a naive approach is computationally unfeasible even for small algebras. Algorithms are given here for obtaining more efficient proof systems deciding these problems, and some applications of the algorithms are described.

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

[2]  Christian G. Fermüller,et al.  Automated Deduction for Many-Valued Logics , 2001, Handbook of Automated Reasoning.

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

[4]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[5]  Bernhard Beckert,et al.  The Tableau-based Theorem Prover 3TAP Version 4.0 , 1996, CADE.

[6]  Emil Jerábek Admissible Rules of Lukasiewicz Logic , 2010, J. Log. Comput..

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

[8]  Viorica Sofronie-Stokkermans,et al.  On unification for bounded distributive lattices , 2007, TOCL.

[9]  Silvio Ghilardi,et al.  A Resolution/Tableaux Algorithm for Projective Approximations in IPC , 2002, Log. J. IGPL.

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

[11]  Franz Baader,et al.  Unification theory , 1986, Decis. Support Syst..

[12]  Stanley Burris,et al.  A course in universal algebra , 1981, Graduate texts in mathematics.

[13]  Paliath Narendran,et al.  Unification Theory , 2001, Handbook of Automated Reasoning.

[14]  Richard Zach,et al.  Proof Theory of Finite-valued Logics , 1993 .

[15]  Reiner Hähnle,et al.  Automated deduction in multiple-valued logics , 1993, International series of monographs on computer science.

[16]  George Metcalfe,et al.  Admissibility in De Morgan algebras , 2012, Soft Comput..

[17]  Franz Baader,et al.  Unification in the Description Logic EL , 2009, Description Logics.

[18]  J. Raftery,et al.  Positive Sugihara monoids , 2007 .

[19]  Renate A. Schmidt,et al.  A Tableau Method for Checking Rule Admissibility in S4 , 2010, M4M.

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

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

[22]  M. A. McRobbie,et al.  Automated Deduction — Cade-13 , 1996, Lecture Notes in Computer Science.

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

[24]  Petr Cintula,et al.  Admissible rules in the implication-negation fragment of intuitionistic logic , 2010, Ann. Pure Appl. Log..

[25]  V. Gorbunov,et al.  Algebraic theory of quasivarieties , 1998 .

[26]  Rosalie Iemhoff,et al.  Proof theory for admissible rules , 2009, Ann. Pure Appl. Log..