Switch to: Citations

Add references

You must login to add references.
  1. On the admissible rules of intuitionistic propositional logic.Rosalie Iemhoff - 2001 - Journal of Symbolic Logic 66 (1):281-294.
    We present a basis for the admissible rules of intuitionistic propositional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility.
    Download  
     
    Export citation  
     
    Bookmark   60 citations  
  • Unification in intuitionistic logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.
    We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras.
    Download  
     
    Export citation  
     
    Bookmark   66 citations  
  • (1 other version)Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
    Download  
     
    Export citation  
     
    Bookmark   394 citations  
  • Introduction to Lattices and Order.B. A. Davey & H. A. Priestley - 2002 - Cambridge University Press.
    This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...)
    Download  
     
    Export citation  
     
    Bookmark   101 citations  
  • Stable canonical rules.Guram Bezhanishvili, Nick Bezhanishvili & Rosalie Iemhoff - 2016 - Journal of Symbolic Logic 81 (1):284-315.
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • Modal logic.Alexander Chagrov - 1997 - New York: Oxford University Press. Edited by Michael Zakharyaschev.
    For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators. It starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantic and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. A specialist (...)
    Download  
     
    Export citation  
     
    Bookmark   88 citations  
  • One hundred and two problems in mathematical logic.Harvey Friedman - 1975 - Journal of Symbolic Logic 40 (2):113-129.
    Download  
     
    Export citation  
     
    Bookmark   63 citations  
  • Admissibility of logical inference rules.Vladimir Vladimir Rybakov - 1997 - New York: Elsevier.
    The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and special (...)
    Download  
     
    Export citation  
     
    Bookmark   39 citations  
  • Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus.V. V. Rybakov - 1990 - Annals of Pure and Applied Logic 50 (1):71-106.
    Questions connected with the admissibility of rules of inference and the solvability of the substitution problem for modal and intuitionistic logic are considered in an algebraic framework. The main result is the decidability of the universal theory of the free modal algebra imageω extended in signature by adding constants for free generators. As corollaries we obtain: there exists an algorithm for the recognition of admissibility of rules with parameters in the modal system Grz, the substitution problem for Grz and for (...)
    Download  
     
    Export citation  
     
    Bookmark   16 citations  
  • Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
    This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.
    Download  
     
    Export citation  
     
    Bookmark   295 citations  
  • Multiple-conclusion Rules, Hypersequents Syntax and Step Frames.Nick Bezhanishvili & Silvio Ghilardi - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10: Papers From the Tenth Aiml Conference, Held in Groningen, the Netherlands, August 2014. London, England: CSLI Publications. pp. 54-73.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Unification and admissible rules for paraconsistent minimal Johanssonsʼ logic J and positive intuitionistic logic IPC.Sergei Odintsov & Vladimir Rybakov - 2013 - Annals of Pure and Applied Logic 164 (7-8):771-784.
    We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking just unifiability (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • Admissible rules in the implication–negation fragment of intuitionistic logic.Petr Cintula & George Metcalfe - 2010 - Annals of Pure and Applied Logic 162 (2):162-171.
    Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic and its consistent axiomatic extensions . A Kripke semantics characterization is given for the structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of form a PSPACE-complete set and have no finite basis.
    Download  
     
    Export citation  
     
    Bookmark   24 citations  
  • Construction of an Explicit Basis for Rules Admissible in Modal System S4.Vladimir V. Rybakov - 2001 - Mathematical Logic Quarterly 47 (4):441-446.
    We find an explicit basis for all admissible rules of the modal logic S4. Our basis consists of an infinite sequence of rules which have compact and simple, readable form and depend on increasing set of variables. This gives a basis for all quasi-identities valid in the free modal algebra ℱS4 of countable rank.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Canonical Rules.Emil Jeřábek - 2009 - Journal of Symbolic Logic 74 (4):1171 - 1205.
    We develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of the Blok–Esakia (...)
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • Rules of inference with parameters for intuitionistic logic.Vladimir V. Rybakov - 1992 - Journal of Symbolic Logic 57 (3):912-923.
    An algorithm recognizing admissibility of inference rules in generalized form (rules of inference with parameters or metavariables) in the intuitionistic calculus H and, in particular, also in the usual form without parameters, is presented. This algorithm is obtained by means of special intuitionistic Kripke models, which are constructed for a given inference rule. Thus, in particular, the direct solution by intuitionistic techniques of Friedman's problem is found. As a corollary an algorithm for the recognition of the solvability of logical equations (...)
    Download  
     
    Export citation  
     
    Bookmark   27 citations  
  • Cofinal Stable Logics.Guram Bezhanishvili, Nick Bezhanishvili & Julia Ilin - 2016 - Studia Logica 104 (6):1287-1317.
    We generalize the \}\)-canonical formulas to \}\)-canonical rules, and prove that each intuitionistic multi-conclusion consequence relation is axiomatizable by \}\)-canonical rules. This yields a convenient characterization of stable superintuitionistic logics. The \}\)-canonical formulas are analogues of the \}\)-canonical formulas, which are the algebraic counterpart of Zakharyaschev’s canonical formulas for superintuitionistic logics. Consequently, stable si-logics are analogues of subframe si-logics. We introduce cofinal stable intuitionistic multi-conclusion consequence relations and cofinal stable si-logics, thus answering the question of what the analogues of cofinal (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Continuity, freeness, and filtrations.Silvio Ghilardi - 2010 - Journal of Applied Non-Classical Logics 20 (3):193-217.
    The role played by continuous morphisms in propositional modal logic is investigated: it turns out that they are strictly related to filtrations and to suitable variants of the notion of a free algebra. We also employ continuous morphisms in incremental constructions of (standard) finitely generated free ????4-algebras.
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Canonical formulas for k4. part I: Basic results.Michael Zakharyaschev - 1992 - Journal of Symbolic Logic 57 (4):1377-1402.
    Download  
     
    Export citation  
     
    Bookmark   30 citations  
  • Best solving modal equations.Silvio Ghilardi - 2000 - Annals of Pure and Applied Logic 102 (3):183-198.
    We show that some common varieties of modal K4-algebras have finitary unification type, thus providing effective best solutions for equations in free algebras. Applications to admissible inference rules are immediate.
    Download  
     
    Export citation  
     
    Bookmark   53 citations  
  • Tools and techniques in modal logic.Marcus Kracht - 1999 - New York: Elsevier.
    This book treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory and transfer theory and is intended as a course in modal logic for students who have had prior contact with modal logic and who wish to study it more deeply. It presupposes training in mathematical or logic. Very little specific knowledge is presupposed, most results which are needed are proved in this book.
    Download  
     
    Export citation  
     
    Bookmark   56 citations  
  • Consequence Relations and Admissible Rules.Rosalie Iemhoff - 2016 - Journal of Philosophical Logic 45 (3):327-348.
    This paper contains a detailed account of the notion of admissibility in the setting of consequence relations. It is proved that the two notions of admissibility used in the literature coincide, and it provides an extension to multi–conclusion consequence relations that is more general than the one usually encountered in the literature on admissibility. The notion of a rule scheme is introduced to capture rules with side conditions, and it is shown that what is generally understood under the extension of (...)
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • Independent bases of admissible rules.Emil Jerábek - 2008 - Logic Journal of the IGPL 16 (3):249-267.
    We show that IPC, K4, GL, and S4, as well as all logics inheriting their admissible rules, have independent bases of admissible rules.
    Download  
     
    Export citation  
     
    Bookmark   18 citations