Results for 'Substructural logics'

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  1.  1
    Substructural Logics: A Primer.Francesco Paoli - 2002 - Dordrecht, Netherland: Springer.
    The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.
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  2. Substructural Logics, Pluralism and Collapse.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2018 - Synthese 198 (Suppl 20):4991-5007.
    When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in (...)
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  3.  71
    An Introduction to Substructural Logics.Greg Restall - 1999 - Routledge.
    This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * (...)
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  4.  6
    Substructural Logics.Peter Joseph Schroeder-Heister & Kosta Došen - 1993 - Oxford, England: Clarendon Press.
    The new area of logic and computation is now undergoing rapid development. This has affected the social pattern of research in the area. A new topic may rise very quickly with a significant body of research around it. The community, however, cannot wait the traditional two years for a book to appear. This has given greater importance to thematic collections of papers, centred around a topic and addressing it from several points of view, usually as a result of a workshop, (...)
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  5.  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 (...)
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  6.  21
    Substructural Logics, Pragmatic Enrichment, and the Inferential Role of Logical Constants.Pilar Terrés Villalonga - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (6):628-654.
    ABSTRACT My aim in this paper is to present a pluralist thesis about the inferential role of logical constants, which embraces classical, relevant, linear and ordered logic. That is, I defend that a logical constant c has more than one correct inferential role. The thesis depends on a particular interpretation of substructural logics' vocabulary, according to which classical logic captures the literal meaning of logical constants and substructural logics encode a pragmatically enriched sense of those connectives. (...)
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  7. Substructural Logics.Peter Schroeder-Heister - 1996 - Erkenntnis 45 (1):115-118.
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  8.  67
    Craig Interpolation for Semilinear Substructural Logics.Enrico Marchioni & George Metcalfe - 2012 - Mathematical Logic Quarterly 58 (6):468-481.
    The Craig interpolation property is investigated for substructural logics whose algebraic semantics are varieties of semilinear pointed commutative residuated lattices. It is shown that Craig interpolation fails for certain classes of these logics with weakening if the corresponding algebras are not idempotent. A complete characterization is then given of axiomatic extensions of the “R-mingle with unit” logic that have the Craig interpolation property. This latter characterization is obtained using a model-theoretic quantifier elimination strategy to determine the varieties (...)
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  9.  21
    On Substructural Logics Preserving Degrees of Truth.Josep Maria Font - 2007 - Bulletin of the Section of Logic 36 (3/4):117-129.
  10.  11
    Synthesized Substructural Logics.Norihiro Kamide - 2007 - Mathematical Logic Quarterly 53 (3):219-225.
    A mechanism for combining any two substructural logics (e.g. linear and intuitionistic logics) is studied from a proof-theoretic point of view. The main results presented are cut-elimination and simulation results for these combined logics called synthesized substructural logics.
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  11.  31
    A Sahlqvist Theorem for Substructural Logic.Tomoyuki Suzuki - 2013 - Review of Symbolic Logic 6 (2):229-253.
    In this paper, we establish the first-order definability of sequents with consistent variable occurrence on bi-approximation semantics by means of the Sahlqvist–van Benthem algorithm. Then together with the canonicity results in Suzuki (2011), this allows us to establish a Sahlqvist theorem for substructural logic. Our result is not limited to substructural logic but is also easily applicable to other lattice-based logics.
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  12.  88
    Substructural Logics.Greg Restall - forthcoming - Stanford Encyclopedia of Philosophy.
    summary of work in relevant in the Anderson– tradition.]; Mares Troestra, Anne, 1992, Lectures on , CSLI Publications [A quick, easy-to.
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  13.  36
    Glivenko Theorems for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - Journal of Symbolic Logic 71 (4):1353 - 1384.
    It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the (...)
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  14.  70
    Modal Translations in Substructural Logics.Kosta Došen - 1992 - Journal of Philosophical Logic 21 (3):283 - 336.
    Substructural logics are logics obtained from a sequent formulation of intuitionistic or classical logic by rejecting some structural rules. The substructural logics considered here are linear logic, relevant logic and BCK logic. It is proved that first-order variants of these logics with an intuitionistic negation can be embedded by modal translations into S4-type extensions of these logics with a classical, involutive, negation. Related embeddings via translations like the double-negation translation are also considered. Embeddings (...)
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  15.  89
    Relevant and Substructural Logics.Greg Restall - unknown
    This essay is structured around the bifurcation between proofs and models: The first section discusses Proof Theory of relevant and substructural logics, and the second covers the Model Theory of these logics. This order is a natural one for a history of relevant and substructural logics, because much of the initial work — especially in the Anderson–Belnap tradition of relevant logics — started by developing proof theory. The model theory of relevant logic came some (...)
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  16.  21
    Structural Completeness in Substructural Logics.J. S. Olson, J. G. Raftery & C. J. Van Alten - 2008 - Logic Journal of the IGPL 16 (5):453-495.
    Hereditary structural completeness is established for a range of substructural logics, mainly without the weakening rule, including fragments of various relevant or many-valued logics. Also, structural completeness is disproved for a range of systems, settling some previously open questions.
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  17.  42
    Substructural Logics with Mingle.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (2):227-249.
    We introduce structural rules mingle, and investigatetheorem-equivalence, cut- eliminability, decidability, interpolabilityand variable sharing property for sequent calculi having the mingle.These results include new cut-elimination results for the extendedlogics: FLm (full Lambek logic with the mingle), GLm(Girard's linear logic with the mingle) and Lm (Lambek calculuswith restricted mingle).
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  18.  63
    Algebraic Proof Theory for Substructural Logics: Cut-Elimination and Completions.Agata Ciabattoni, Nikolaos Galatos & Kazushige Terui - 2012 - Annals of Pure and Applied Logic 163 (3):266-290.
  19. Displaying and Deciding Substructural Logics 1: Logics with Contraposition.Greg Restall - 1998 - Journal of Philosophical Logic 27 (2):179-216.
    Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic. However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modified proof theory which more closely models relevant logics. In addition, we use this proof theory to show decidability for a large range of substructural logics.
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  20.  86
    Kripke Semantics for Modal Substructural Logics.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (4):453-470.
    We introduce Kripke semantics for modal substructural logics, and provethe completeness theorems with respect to the semantics. Thecompleteness theorems are proved using an extended Ishihara's method ofcanonical model construction (Ishihara, 2000). The framework presentedcan deal with a broad range of modal substructural logics, including afragment of modal intuitionistic linear logic, and modal versions ofCorsi's logics, Visser's logic, Méndez's logics and relevant logics.
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  21.  9
    Modal Translation of Substructural Logics.Chrysafis Hartonas - 2020 - Journal of Applied Non-Classical Logics 30 (1):16-49.
    ABSTRACTIn an article dating back in 1992, Kosta Došen initiated a project of modal translations in substructural logics, aiming at generalising the well-known Gödel–McKinsey–Tarski translation of intuitionistic logic into S4. Došen's translation worked well for BCI and stronger systems, but not for systems below BCI. Dropping structural rules results in logic systems without distribution. In this article, we show, via translation, that every substructural logic is a fragment of a corresponding sorted, residuated modal logic. At the conceptual (...)
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  22.  7
    Variable Sharing in Substructural Logics: An Algebraic Characterization.Guillermo Badia - 2018 - Bulletin of the Section of Logic 47 (2):107-115.
    We characterize the non-trivial substructural logics having the variable sharing property as well as its strong version. To this end, we find the algebraic counterparts over varieties of these logical properties. -/- .
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  23.  34
    An Introduction to Substructural Logics (Review).Kosta Dosen - 2001 - Bulletin of Symbolic Logic 7 (4):527-530.
  24.  64
    Proper Semantics for Substructural Logics, From a Stalker Theoretic Point of View.Sato Kentaro - 2008 - Studia Logica 88 (2):295-324.
    We study filters in residuated structures that are associated with congruence relations (which we call -filters), and develop a semantical theory for general substructural logics based on the notion of primeness for those filters. We first generalize Stone’s sheaf representation theorem to general substructural logics and then define the primeness of -filters as being “points” (or stalkers) of the space, the spectrum, on which the representing sheaf is defined. Prime FL-filters will turn out to coincide with (...)
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  25.  54
    Current Trends in Substructural Logics.Katalin Bimbó - 2015 - Journal of Philosophical Logic 44 (6):609-624.
    This paper briefly overviews some of the results and research directions. In the area of substructural logics from the last couple of decades. Substructural logics are understood here to include relevance logics, linear logic, variants of Lambek calculi and some other logics that are motivated by the idea of omitting some structural rules or making other structural changes in LK, the original sequent calculus for classical logic.
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  26. Substructural Logics, Combinatory Logic, and Lambda-Calculus.Katalin Bimbo - 1999 - Dissertation, Indiana University
    The dissertation deals with problems in "logic", more precisely, it deals with particular formal systems aiming at capturing patterns of valid reasoning. Sequent calculi were proposed to characterize logical connectives via introduction rules. These systems customarily also have structural rules which allow one to rearrange the set of premises and conclusions. In the "structurally free logic" of Dunn and Meyer the structural rules are replaced by combinatory rules which allow the same reshuffling of formulae, and additionally introduce an explicit marker (...)
     
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  27.  37
    Substructural Logics.Heinrich Wansing - 1996 - Erkenntnis 45 (1):115-118.
  28.  17
    Meeting Strength in Substructural Logics.Yde Venema - 1995 - Studia Logica 54 (1):3-32.
    This paper contributes to the theory of hybrid substructural logics, i.e. weak logics given by a Gentzen-style proof theory in which there is only a limited possibility to use structural rules. Following the literature, we use an operator to mark formulas to which the extra structural rules may be applied. New in our approach is that we do not see this ▽ as a modality, but rather as the meet of the marked formula with a special type (...)
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  29.  14
    Algebraic Perspectives on Substructural Logics.Davide Fazio, Antonio Ledda & Francesco Paoli (eds.) - 2020 - Springer International Publishing.
    This volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics. -/- Substructural logics are usually formulated as Gentzen systems that lack one or more (...)
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  30.  4
    Bi-Approximation Semantics for Substructural Logic at Work.Tomoyuki Suzuki - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 411-433.
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  31.  36
    Normal Modal Substructural Logics with Strong Negation.Norihiro Kamide - 2003 - Journal of Philosophical Logic 32 (6):589-612.
    We introduce modal propositional substructural logics with strong negation, and prove the completeness theorems (with respect to Kripke models) for these logics.
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  32. Distributive Substructural Logics as Coalgebraic Logics Over Posets.Marta Bílková, Rostislav Horčik & Jiří Velebil - 2012 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 119-142.
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  33.  72
    Meeting Strength in Substructural Logics.Yde Venema - 1995 - Studia Logica 54 (1):3 - 32.
    This paper contributes to the theory of hybrid substructural logics, i.e. weak logics given by a Gentzen-style proof theory in which there is only alimited possibility to use structural rules. Following the literture, we use an operator to mark formulas to which the extra structural rules may be applied. New in our approach is that we do not see this as a modality, but rather as themeet of the marked formula with a special typeQ. In this way (...)
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  34.  21
    An Algebraic Approach to the Disjunction Property of Substructural Logics.Daisuke Souma - 2007 - Notre Dame Journal of Formal Logic 48 (4):489-495.
    Some of the basic substructural logics are shown by Ono to have the disjunction property (DP) by using cut elimination of sequent calculi for these logics. On the other hand, this syntactic method works only for a limited number of substructural logics. Here we show that Maksimova's criterion on the DP of superintuitionistic logics can be naturally extended to one on the DP of substructural logics over FL. By using this, we show (...)
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  35.  67
    Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - Studia Logica 83 (1-3):279-308.
    Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.
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  36.  22
    Finite Models of Some Substructural Logics.Wojciech Buszkowski - 2002 - Mathematical Logic Quarterly 48 (1):63-72.
    We give a proof of the finite model property of some fragments of commutative and noncommutative linear logic: the Lambek calculus, BCI, BCK and their enrichments, MALL and Cyclic MALL. We essentially simplify the method used in [4] for proving fmp of BCI and the Lambek ca culus and in [5] for proving fmp of MALL. Our construction of finite models also differs from that used in Lafont [8] in his proof of fmp of MALL.
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  37.  36
    Metacompleteness of Substructural Logics.Takahiro Seki - 2012 - Studia Logica 100 (6):1175-1199.
    Metacompleteness is used to prove properties such as the disjunction property and the existence property in the area of relevant logics. On the other hand, the disjunction property of several basic propositional substructural logics over FL has been proved using the cut elimination theorem of sequent calculi and algebraic characterization. The present paper shows that Meyer’s metavaluational technique and Slaney’s metavaluational technique can be applied to basic predicate intuitionistic substructural logics and basic predicate involutive (...) logics, respectively. As a corollary of metacompleteness, the disjunction property, the existence property, and the admissibility of certain rules in such logics can be proved. (shrink)
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  38.  5
    A Useful Substructural Logic.Greg Restall - 1994 - Logic Journal of the IGPL 2 (2):137-148.
    Formal systems seem to come in two general kinds: useful and useless. This is painting things starkly, but the point is important. Formal structures can either be used in interesting and important ways, or they can languish unused and irrelevant. Lewis' modal logics are good examples. The systems S4 and S5 are useful in many different ways. They map out structures that are relevant to a number of different applications. S1, S2 and S3 however, are not so lucky. They (...)
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  39.  4
    Distributive Substructural Logics as Coalgebraic Logics Over Posets.Marta Bílková, Rostislav Horčik & Jiří Velebil - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 119-142.
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  40. LP, K3, and FDE as Substructural Logics.Lionel Shapiro - 2017 - In Pavel Arazim & Tomáš Lavička (eds.), The Logica Yearbook 2016. London: College Publications.
    Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.
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  41.  63
    Context and Consequence. An Intercontextual Substructural Logic.Elia Zardini - 2014 - Synthese 191 (15):3473-3500.
    Some apparently valid arguments crucially rely on context change. To take a kind of example first discussed by Frege, ‘Tomorrow, it’ll be sunny’ taken on a day seems to entail ‘Today, it’s sunny’ taken on the next day, but the first sentence taken on a day sadly does not seem to entail the second sentence taken on the second next day. Mid-argument context change has not been accounted for by the tradition that has extensively studied the distinctive logical properties of (...)
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  42.  40
    Residuated Lattices: An Algebraic Glimpse at Substructural Logics.Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski & Hiroakira Ono - 2007 - Elsevier.
    This is also where we begin investigating lattices of logics and varieties, rather than particular examples.
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  43.  79
    Constructive Logic with Strong Negation is a Substructural Logic. I.Matthew Spinks & Robert Veroff - 2008 - Studia Logica 88 (3):325-348.
    The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the substructural logic FL ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL ew (namely, a certain variety of FL ew -algebras) are term equivalent. This answers a longstanding question of Nelson (...)
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  44.  37
    Radical Anti-Realism and Substructural Logics.Jacques Dubucs & Mathieu Marion - 2003 - In A. Rojszczak, J. Cachro & G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science. Kluwer Academic Publishers. pp. 235--249.
  45.  43
    Uniform Interpolation in Substructural Logics.Majid Alizadeh, Farzaneh Derakhshan & Hiroakira Ono - 2014 - Review of Symbolic Logic 7 (3):455-483.
  46.  6
    Inter-Model Connectives and Substructural Logics.Igor Sedlár - 2014 - In Roberto Ciuni, Heinrich Wansing & Caroline Willkommen (eds.), Recent Trends in Philosophical Logic (Proceedings of Trends in Logic XI). Springer. pp. 195-209.
    The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. (...)
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  47.  52
    Constructive Logic with Strong Negation is a Substructural Logic. II.M. Spinks & R. Veroff - 2008 - Studia Logica 89 (3):401-425.
    The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the substructural logic FL ew. The main result of Part I of this series [41] shows that the equivalent variety semantics of N and the equivalent variety semantics of NFL ew are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of (...)
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  48.  17
    Generalized Quantification as Substructural Logic.Natasha Alechina & Michiel Van Lambalgen - 1996 - Journal of Symbolic Logic 61 (3):1006 - 1044.
    We show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables. In the case of generalized quantifiers, explicit attention to relations of dependence becomes indispensible for setting up proof systems. It is shown that this can be done by turning variables into structured objects, governed by various types of (...)
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  49.  4
    Information, Awareness and Substructural Logics.Igor Sedlár - 2013 - In Leonid Libkin, Ulrich Kohlenbach & Ruy de Queiroz (eds.), Logic, Language, Information and Computation (Lecture Notes in Computer Science 8071). Springer. pp. 266-281.
    The paper outlines a generalisation of the awareness-based epistemic semantics by Fagin and Halpern. Awareness is construed as a relation between agents and pieces of information instead of formulas. The main motive for introducing the generalisation is that it shows substructural logics to be a natural component of information-based epistemic logic: substructural logics can be seen as describing the logical behaviour of pieces of information. Substructural epistemic logics are introduced and some of their properties (...)
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  50.  49
    Quantifiers, Propositions and Identity: Admissible Semantics for Quantified Modal and Substructural Logics.Robert Goldblatt - 2011 - Cambridge University Press.
    Machine generated contents note: Introduction and overview; 1. Logics with actualist quantifiers; 2. The Barcan formulas; 3. The existence predicate; 4. Propositional functions and predicate substitution; 5. Identity; 6. Cover semantics for relevant logic; References; Index.
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