Order:
  1.  50
    Is Multiset Consequence Trivial?Petr Cintula & Francesco Paoli - forthcoming - Synthese:1-25.
    Dave Ripley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction—whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to a closure operator in (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  2.  32
    Distinguished Algebraic Semantics for T -Norm Based Fuzzy Logics: Methods and Algebraic Equivalencies.Petr Cintula, Francesc Esteva, Joan Gispert, Lluís Godo, Franco Montagna & Carles Noguera - 2009 - Annals of Pure and Applied Logic 160 (1):53-81.
    This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  3.  61
    Weakly Implicative (Fuzzy) Logics I: Basic Properties. [REVIEW]Petr Cintula - 2006 - Archive for Mathematical Logic 45 (6):673-704.
    This paper presents two classes of propositional logics (understood as a consequence relation). First we generalize the well-known class of implicative logics of Rasiowa and introduce the class of weakly implicative logics. This class is broad enough to contain many “usual” logics, yet easily manageable with nice logical properties. Then we introduce its subclass–the class of weakly implicative fuzzy logics. It contains the majority of logics studied in the literature under the name fuzzy logic. We present many general theorems for (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   22 citations  
  4.  19
    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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  5.  42
    The Proof by Cases Property and its Variants in Structural Consequence Relations.Petr Cintula & Carles Noguera - 2013 - Studia Logica 101 (4):713-747.
    This paper is a contribution to the study of the rôle of disjunction inAlgebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this paper), (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  6.  38
    On Theories and Models in Fuzzy Predicate Logics.Petr Hájek & Petr Cintula - 2006 - Journal of Symbolic Logic 71 (3):863 - 880.
    In the last few decades many formal systems of fuzzy logics have been developed. Since the main differences between fuzzy and classical logics lie at the propositional level, the fuzzy predicate logics have developed more slowly (compared to the propositional ones). In this text we aim to promote interest in fuzzy predicate logics by contributing to the model theory of fuzzy predicate logics. First, we generalize the completeness theorem, then we use it to get results on conservative extensions of theories (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   24 citations  
  7.  42
    Structural Completeness in Fuzzy Logics.Petr Cintula & George Metcalfe - 2009 - Notre Dame Journal of Formal Logic 50 (2):153-182.
    Structural completeness properties are investigated for a range of popular t-norm based fuzzy logics—including Łukasiewicz Logic, Gödel Logic, Product Logic, and Hájek's Basic Logic—and their fragments. General methods are defined and used to establish these properties or exhibit their failure, solving a number of open problems.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   14 citations  
  8.  29
    Implicational (Semilinear) Logics I: A New Hierarchy. [REVIEW]Petr Cintula & Carles Noguera - 2010 - Archive for Mathematical Logic 49 (4):417-446.
    In abstract algebraic logic, the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this process one considers the Leibniz relation of indiscernible formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper performs an analogous abstract study of non-classical logics based on the kind of generalized implication connectives they possess. It yields a new classification of logics expanding Leibniz (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   13 citations  
  9.  41
    Product Ł Ukasiewicz Logic.Rostislav Horčík & Petr Cintula - 2004 - Archive for Mathematical Logic 43 (4):477-503.
    Łu logic plays a fundamental role among many-valued logics. However, the expressive power of this logic is restricted to piecewise linear functions. In this paper we enrich the language of Łu logic by adding a new connective which expresses multiplication. The resulting logic, PŁ, is defined, developed, and put into the context of other well-known many-valued logics. We also deal with several extensions of this propositional logic. A predicate version of PŁ logic is introduced and developed too.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  10.  56
    Nonassociative Substructural Logics and Their Semilinear Extensions: Axiomatization and Completeness Properties: Nonassociative Substructural Logics.Petr Cintula, Rostislav Horčík & Carles Noguera - 2013 - Review of Symbolic Logic 6 (3):394-423.
    Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a nonassociative generalization of FL has been studied by Galatos and Ono as the logic of lattice-ordered residuated unital groupoids. This paper is based on an alternative Hilbert-style presentation for SL which is almost MP -based. This presentation is then used to obtain, in a uniform way applicable to most substructural logics, a form (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  11.  13
    A Note on Natural Extensions in Abstract Algebraic Logic.Petr Cintula & Carles Noguera - 2015 - Studia Logica 103 (4):815-823.
    Transfer theorems are central results in abstract algebraic logic that allow to generalize properties of the lattice of theories of a logic to any algebraic model and its lattice of filters. Their proofs sometimes require the existence of a natural extension of the logic to a bigger set of variables. Constructions of such extensions have been proposed in particular settings in the literature. In this paper we show that these constructions need not always work and propose a wider setting in (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  12.  18
    Logics with Disjunction and Proof by Cases.San-min Wang & Petr Cintula - 2008 - Archive for Mathematical Logic 47 (5):435-446.
    This paper is a contribution to the general study of consequence relations which contain (definable) connective of “disjunction”. Our work is centered around the “proof by cases property”, we present several of its equivalent definitions, and show some interesting applications, namely in constructing axiomatic systems for intersections of logics and recognizing weakly implicative fuzzy logics among the weakly implicative ones.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  13.  9
    A Henkin-Style Proof of Completeness for First-Order Algebraizable Logics.Petr Cintula & Carles Noguera - 2015 - Journal of Symbolic Logic 80 (1):341-358.
  14.  9
    Formal Systems of Fuzzy Logic and Their Fragments.Petr Cintula, Petr Hájek & Rostislav Horčík - 2007 - Annals of Pure and Applied Logic 150 (1-3):40-65.
    Formal systems of fuzzy logic are well-established logical systems and respected members of the broad family of the so-called substructural logics closely related to the famous logic BCK. The study of fragments of logical systems is an important issue of research in any class of non-classical logics. Here we study the fragments of nine prominent fuzzy logics to all sublanguages containing implication. However, the results achieved in the paper for those nine logics are usually corollaries of theorems with much wider (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  15.  14
    Implicational Logics II: Additional Connectives and Characterizations of Semilinearity.Petr Cintula & Carles Noguera - 2016 - Archive for Mathematical Logic 55 (3-4):353-372.
    This is the continuation of the paper :417–446, 2010). We continue the abstract study of non-classical logics based on the kind of generalized implication connectives they possess and we focus on semilinear logics, i.e. those that are complete with respect to the class of models where the implication defines a linear order. We obtain general characterizations of semilinearity in terms of the intersection-prime extension property, the syntactical semilinearity metarule and the class of finitely subdirectly irreducible models. Moreover, we consider extensions (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  16.  12
    Implicational Logics III: Completeness Properties.Petr Cintula & Carles Noguera - 2018 - Archive for Mathematical Logic 57 (3-4):391-420.
    This paper presents an abstract study of completeness properties of non-classical logics with respect to matricial semantics. Given a class of reduced matrix models we define three completeness properties of increasing strength and characterize them in several useful ways. Some of these characterizations hold in absolute generality and others are for logics with generalized implication or disjunction connectives, as considered in the previous papers. Finally, we consider completeness with respect to matrices with a linear dense order and characterize it in (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  17.  28
    A Logical Framework for Graded Predicates.Petr Cintula, Carles Noguera & Nicholas J. J. Smith - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction: LORI 2017. Berlin: Springer. pp. 3-16.
    In this position paper we present a logical framework for modelling reasoning with graded predicates. We distinguish several types of graded predicates and discuss their ubiquity in rational interaction and the logical challenges they pose. We present mathematical fuzzy logic as a set of logical tools that can be used to model reasoning with graded predicates, and discuss a philosophical account of vagueness that makes use of these tools. This approach is then generalized to other kinds of graded predicates. Finally, (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  18.  13
    Advances in the ŁΠ and Logics.Petr Cintula - 2003 - Archive for Mathematical Logic 42 (5):449-468.
    The ŁΠ and logics were introduced by Godo, Esteva and Montagna. These logics extend many other known propositional and predicate logics, including the three mainly investigated ones (Gödel, product and Łukasiewicz logic). The aim of this paper is to show some advances in this field. We will see further reduction of the axiomatic systems for both logics. Then we will see many other logics contained in the ŁΠ family of logics (namely logics induced by the continuous finitely constructed t-norms and (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  19.  15
    Residuated Logics Based on Strict Triangular Norms with an Involutive Negation.Petr Cintula, Erich Peter Klement, Radko Mesiar & Mirko Navara - 2006 - Mathematical Logic Quarterly 52 (3):269-282.
    In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t-norms and their dual t-conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t-norms which are different from the product logic.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  20.  6
    Towards Evaluation Games for Fuzzy Logics.Petr Cintula & Ondrej Majer - 2009 - In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Springer Verlag. pp. 117--138.
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  21.  24
    Note on Deduction Theorems in Contraction‐Free Logics.Karel Chvalovský & Petr Cintula - 2012 - Mathematical Logic Quarterly 58 (3):236-243.
    This paper provides a finer analysis of the well-known form of the Local Deduction Theorem in contraction-free logics . An infinite hierarchy of its natural strengthenings is introduced and studied. The main results are the separation of its initial four members and the subsequent collapse of the hierarchy.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  22.  12
    Advances in the and [Mathematical Formula] Logics.Petr Cintula - 2003 - Archive for Mathematical Logic 42 (5):449-468.
  23.  17
    How Much Propositional Logic Suffices for Rosser’s Essential Undecidability Theorem?Guillermo Badia, Petr Cintula, Petr Hajek & Andrew Tedder - forthcoming - Review of Symbolic Logic:1-18.
    In this paper we explore the following question: how weak can a logic be for Rosser's essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson's Q is essentially undecidable in intuitionistic logic, and P. Hajek proved it in the fuzzy logic BL for Grzegorczyk's variant of Q which interprets the arithmetic operations as non-total non-functional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  24. How Much Propositional Logic Suffices for Rosser's Essential Undecidability Theorem?Guillermo Badia, Petr Cintula, Petr Hajek & Andrew Tedder - forthcoming - Review of Symbolic Logic.
    In this paper we explore the following question: how weak can a logic be for Rosser’s essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson’s Q is essentially undecidable in intuitionistic logic, and P. Hájek proved it in the fuzzy logic BL for Grzegorczyk’s variant of Q which interprets the arithmetic operations as nontotal nonfunctional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...)
     
    Export citation  
     
    Bookmark  
  25.  8
    Representing Strategic Games and Their Equilibria in Many-Valued Logics.Libor Běhounek, Petr Cintula, Chris Fermüller & Tomáš Kroupa - 2016 - Logic Journal of the IGPL 24 (3):238-267.
  26.  23
    An Abstract Approach to Consequence Relations.Petr Cintula, José Gil-férez, Tommaso Moraschini & Francesco Paoli - 2019 - Review of Symbolic Logic 12 (2):331-371.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  27.  4
    Advances in the ŁΠ And.Petr Cintula - 2003 - Archive for Mathematical Logic 42 (5).
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  28.  7
    Editors’ Introduction: Special Issue on Non-Classical Modal and Predicate Logics.Petr Cintula, Z. Weber & S. Ju - 2019 - Logic Journal of the IGPL 27 (4):385-386.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  29. Handbook of Mathematical Fuzzy Logic - Volume 3.Petr Cintula, Christian Fermüller & Carles Noguera (eds.) - 2015 - College Publications.
     
    Export citation  
     
    Bookmark  
  30. Logical Models of Reasoning with Vague Information.Petr Cintula, Chris Fermüller, Lluis Godo & Petr Hájek (eds.) - forthcoming
    Translate
     
     
    Export citation  
     
    Bookmark  
  31.  53
    Normal Forms for Fuzzy Logics: A Proof-Theoretic Approach. [REVIEW]Petr Cintula & George Metcalfe - 2007 - Archive for Mathematical Logic 46 (5-6):347-363.
    A method is described for obtaining conjunctive normal forms for logics using Gentzen-style rules possessing a special kind of strong invertibility. This method is then applied to a number of prominent fuzzy logics using hypersequent rules adapted from calculi defined in the literature. In particular, a normal form with simple McNaughton functions as literals is generated for łukasiewicz logic, and normal forms with simple implicational formulas as literals are obtained for Gödel logic, Product logic, and Cancellative hoop logic.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  32. Reasoning Under Vagueness.Petr Cintula, Christian Fermuller, Lluis Godo & Petr Hajek (eds.) - forthcoming - College Publications.
    Translate
     
     
    Export citation  
     
    Bookmark  
  33.  24
    Two Notions of Compactness in Gödel Logics.Petr Cintula - 2005 - Studia Logica 81 (1):99-123.
    Compactness is an important property of classical propositional logic. It can be defined in two equivalent ways. The first one states that simultaneous satisfiability of an infinite set of formulae is equivalent to the satisfiability of all its finite subsets. The second one states that if a set of formulae entails a formula, then there is a finite subset entailing this formula as well. In propositional many-valued logic, we have different degrees of satisfiability and different possible definitions of entailment, hence (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  34. Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives.Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.) - 2011 - College Publications.
     
    Export citation  
     
    Bookmark  
  35.  8
    Product Ukasiewicz Logic.Rostislav Hork & Petr Cintula - 2004 - Archive for Mathematical Logic 43 (4):477-503.
    Direct download  
     
    Export citation  
     
    Bookmark