Tutorial on Admissible Rules in Gudauri

Most theorems have more than one proof and most theories have more than one axiomatization. Certain proofs or axiomatizations are preferable to others because they are shorter or more transparent or for some other reason. Our aim is to describe or study the possible proofs of a theorem or the possible axiomatizations of a theory. As the former is a special instance of the latter, by considering a theory consisting of one theorem, it suffices to consider theories.

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

[2]  A. Slisenko Studies in constructive mathematics and mathematical logic , 1969 .

[3]  Vladimir V. Rybakov,et al.  Writing out Unifiers in Linear Temporal Logic , 2012, J. Log. Comput..

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

[5]  Katarzyna Slomczynska Algebraic semantics for the (↔, ¬¬)-fragment of IPC , 2012, Math. Log. Q..

[6]  Emil Jerábek,et al.  Blending margins: the modal logic K has nullary unification type , 2015, J. Log. Comput..

[7]  Rosalie Iemhoff,et al.  Unification in fragments of intermediate logics , 2012 .

[8]  Piotr Wojtylak On a Problem of H. Friedman and its Solution by T. Prucnal , 2004, Reports Math. Log..

[9]  Tadeusz Prucnal,et al.  Structural completeness of the first-order predicate calculus , 1975, Math. Log. Q..

[10]  Vladimir V. Rybakov,et al.  Linear Temporal Logic LTL: Basis for Admissible Rules , 2011, J. Log. Comput..

[11]  Albert Visser Substitutions of Sigma10 - sentences: explorations between intuitionistic propositional logic and intuitionistic arithmetic , 2002, Ann. Pure Appl. Log..

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

[13]  Robert K. Meyer,et al.  A Structurally Complete Fragment of Relevant Logic , 1992, Notre Dame J. Formal Log..

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

[15]  Rosalie Iemhoff,et al.  Hypersequent Systems for the Admissible Rules of Modal and Intermediate Logics , 2008, LFCS.

[16]  G. Mints,et al.  Derivability of admissible rules , 1976 .

[17]  Jeroen P. Goudsmit,et al.  On unification and admissible rules in Gabbay-de Jongh logics , 2014, Ann. Pure Appl. Log..

[18]  Tadeusz Prucnal On the structural completeness of some pure implicational propositional calculi , 1972 .

[19]  Vladimir V. Rybakov,et al.  Unification and admissible rules for paraconsistent minimal Johanssons' logic J and positive intuitionistic logic IPC+ , 2013, Ann. Pure Appl. Log..

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

[21]  Mircea Tirnoveanu,et al.  Review: W. A. Pogorzelski, Structural Completeness of the Propositional Calculus , 1975 .

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

[23]  Silvio Ghilardi,et al.  Unification, finite duality and projectivity in varieties of Heyting algebras , 2004, Ann. Pure Appl. Log..

[24]  Emil Jevr'abek Blending margins: The modal logic K has nullary unification type , 2011 .

[25]  Tomasz F. Skura A COMPLETE SYNTACTICAL CHARACTERIZATION OF THE INTUITIONISTIC LOGIC , 2006 .

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

[27]  Wojciech Dzik,et al.  Structural completeness of Gödel's and Dummett's propositional calculi , 1973 .

[28]  Vladimir V. Rybakov,et al.  Rules admissible in transitive temporal logic TS4, sufficient condition , 2010, Theor. Comput. Sci..

[29]  Timothy Williamson,et al.  An Alternative Rule of disjunction in modal logic , 1991, Notre Dame J. Formal Log..

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

[31]  Albert Visser,et al.  Rules and Arithmetics , 1998, Notre Dame J. Formal Log..

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

[33]  Paul Roziere Regles admissibles en calcul propositionnel intuitionniste , 1992 .

[34]  Orna Grumberg,et al.  A game-based framework for CTL counterexamples and 3-valued abstraction-refinement , 2007, TOCL.

[35]  Arnon Avron,et al.  Simple Consequence Relations , 1988, Inf. Comput..

[36]  Günter Asser,et al.  Zeitschrift für mathematische Logik und Grundlagen der Mathematik , 1955 .

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