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  1. Behavioral Algebraization of Logics.Carlos Caleiro, Ricardo Gonçalves & Manuel Martins - 2009 - Studia Logica 91 (1):63-111.
    We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of many-sorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL toward providing a meaningful algebraic counterpart also to logics with a many-sorted language, and possibly including non-truth-functional connectives. The proposed behavioral approach covers logics which are not algebraizable according to the standard approach, while also bringing a new (...)
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  • Selfextensional Logics with a Conjunction.Ramon Jansana - 2006 - Studia Logica 84 (1):63-104.
    A logic is selfextensional if its interderivability (or mutual consequence) relation is a congruence relation on the algebra of formulas. In the paper we characterize the selfextensional logics with a conjunction as the logics that can be defined using the semilattice order induced by the interpretation of the conjunction in the algebras of their algebraic counterpart. Using the charactrization we provide simpler proofs of several results on selfextensional logics with a conjunction obtained in [13] using Gentzen systems. We also obtain (...)
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  • Semantics without Toil? Brady and Rush Meet Halldén.Lloyd Humberstone - 2019 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 26 (3):340–404.
    The present discussion takes up an issue raised in Section 5 of Ross Brady and Penelope Rush’s paper ‘Four Basic Logical Issues’ concerning the (claimed) triviality – in the sense of automatic availability – of soundness and completeness results for a logic in a metalanguage employing at least as much logical vocabulary as the object logic, where the metalogical behaviour of the common logical vocabulary is as in the object logic. We shall see – in Propositions 4.5–4.7 – that this (...)
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  • Logical discrimination (2nd edition).Lloyd Humberstone - 2005 - In Jean-Yves Béziau (ed.), Logica Universalis: Towards a General Theory of Logic. Boston: Birkhäuser Verlog. pp. 225–246.
    We discuss conditions under which the following ‘truism’ does indeed express a truth: the weaker a logic is in terms of what it proves, the stronger it is as a tool for registering distinctions amongst the formulas in its language.
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  • On weakening the Deduction Theorem and strengthening of Modus Ponens.Félix Bou, Josep Maria Font & José Luis García Lapresta - 2004 - Mathematical Logic Quarterly 50 (3):303.
    This paper studies, with techniques ofAlgebraic Logic, the effects of putting a bound on the cardinality of the set of side formulas in the Deduction Theorem, viewed as a Gentzen-style rule, and of adding additional assumptions inside the formulas present in Modus Ponens, viewed as a Hilbert-style rule. As a result, a denumerable collection of new Gentzen systems and two new sentential logics have been isolated. These logics are weaker than the positive implicative logic. We have determined their algebraic models (...)
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  • (1 other version)Categorical Abstract Algebraic Logic: More on Protoalgebraicity.George Voutsadakis - 2006 - Notre Dame Journal of Formal Logic 47 (4):487-514.
    Protoalgebraic logics are characterized by the monotonicity of the Leibniz operator on their theory lattices and are at the lower end of the Leibniz hierarchy of abstract algebraic logic. They have been shown to be the most primitive among those logics with a strong enough algebraic character to be amenable to algebraic study techniques. Protoalgebraic π-institutions were introduced recently as an analog of protoalgebraic sentential logics with the goal of extending the Leibniz hierarchy from the sentential framework to the π-institution (...)
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  • Constructible models of orthomodular quantum logics.Piotr Wilczek - unknown
    We continue in this article the abstract algebraic treatment of quantum sentential logics Wil. The Notions borrowed from the field of Model Theory and Abstract Algebraic Logic - AAL (i.e., consequence relation, variety, logical matrix, deductive filter, reduced product, ultraproduct, ultrapower, Frege relation, Leibniz congruence, Suszko congruence, Leibniz operator) are applied to quantum logics. We also proved several equivalences between state property systems (Jauch-Piron-Aerts line of investigations) and AAL treatment of quantum logics (corollary 18 and 19). We show that there (...)
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  • Restricted Rules of Inference and Paraconsistency.Sankha S. Basu & Mihir K. Chakraborty - 2022 - Logic Journal of the IGPL 30 (3):534-560.
    In this paper, we study two companions of a logic, viz., the left variable inclusion companion and the restricted rules companion, their nature and interrelations, especially in connection with paraconsistency. A sufficient condition for the two companions to coincide has also been proved. Two new logical systems—intuitionistic paraconsistent weak Kleene logic (IPWK) and paraconsistent pre-rough logic (PPRL)—are presented here as examples of logics of left variable inclusion. IPWK is the left variable inclusion companion of intuitionistic propositional logic and is also (...)
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  • (1 other version)Proof systems for the coalgebraic cover modality.Marta Bílková, Alessandra Palmigiano & Yde Venema - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 1-21.
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  • Constructing Natural Extensions of Propositional Logics.Adam Přenosil - 2016 - Studia Logica 104 (6):1179-1190.
    The proofs of some results of abstract algebraic logic, in particular of the transfer principle of Czelakowski, assume the existence of so-called natural extensions of a logic by a set of new variables. Various constructions of natural extensions, claimed to be equivalent, may be found in the literature. In particular, these include a syntactic construction due to Shoesmith and Smiley and a related construction due to Łoś and Suszko. However, it was recently observed by Cintula and Noguera that both of (...)
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  • The Semi Heyting–Brouwer Logic.Juan Manuel Cornejo - 2015 - Studia Logica 103 (4):853-875.
    In this paper we introduce a logic that we name semi Heyting–Brouwer logic, \, in such a way that the variety of double semi-Heyting algebras is its algebraic counterpart. We prove that, up to equivalences by translations, the Heyting–Brouwer logic \ is an axiomatic extension of \ and that the propositional calculi of intuitionistic logic \ and semi-intuitionistic logic \ turn out to be fragments of \.
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  • Update to “A Survey of Abstract Algebraic Logic”.Josep Maria Font, Ramon Jansana & Don Pigozzi - 2009 - Studia Logica 91 (1):125-130.
    A definition and some inaccurate cross-references in the paper A Survey of Abstract Algebraic Logic, which might confuse some readers, are clarified and corrected; a short discussion of the main one is included. We also update a dozen of bibliographic references.
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  • Cut elimination and strong separation for substructural logics: an algebraic approach.Nikolaos Galatos & Hiroakira Ono - 2010 - Annals of Pure and Applied Logic 161 (9):1097-1133.
    We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on substructural logics over the full Lambek Calculus [34], Galatos and Ono [18], Galatos et al. [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated (...)
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  • On the infinite-valued Łukasiewicz logic that preserves degrees of truth.Josep Maria Font, Àngel J. Gil, Antoni Torrens & Ventura Verdú - 2006 - Archive for Mathematical Logic 45 (7):839-868.
    Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate (...)
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  • On an axiomatic system for the logic of linearly ordered BCI-matrices.San-min Wang & Dao-Wu Pei - 2012 - Archive for Mathematical Logic 51 (3-4):285-297.
    The logic FBCI given by linearly ordered BCI-matrices is known not to be an axiomatic extension of the well-known BCI logic. In this paper we axiomatize FBCI by adding a recursively enumerable set of schemes of inference rules to BCI and show that there is no finite axiomatization for FBCI.
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  • Leibniz-linked Pairs of Deductive Systems.Josep Maria Font & Ramon Jansana - 2011 - Studia Logica 99 (1-3):171-202.
    A pair of deductive systems (S,S’) is Leibniz-linked when S’ is an extension of S and on every algebra there is a map sending each filter of S to a filter of S’ with the same Leibniz congruence. We study this generalization to arbitrary deductive systems of the notion of the strong version of a protoalgebraic deductive system, studied in earlier papers, and of some results recently found for particular non-protoalgebraic deductive systems. The necessary examples and counterexamples found in the (...)
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  • The Lattice of Super-Belnap Logics.Adam Přenosil - 2023 - Review of Symbolic Logic 16 (1):114-163.
    We study the lattice of extensions of four-valued Belnap–Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. We describe the global structure of this lattice by splitting it into several subintervals, and prove some new completeness theorems for super-Belnap logics. The crucial technical tool for this purpose will be the so-called antiaxiomatic (or explosive) part operator. The antiaxiomatic (or explosive) extensions of Belnap–Dunn logic turn out to be of particular interest owing to their connection to graph theory: the lattice (...)
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  • Supervenience, Dependence, Disjunction.Lloyd Humberstone - forthcoming - Logic and Logical Philosophy:1.
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  • The semantic isomorphism theorem in abstract algebraic logic.Tommaso Moraschini - 2016 - Annals of Pure and Applied Logic 167 (12):1298-1331.
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  • Behavioral equivalence of hidden k -logics: An abstract algebraic approach.Sergey Babenyshev & Manuel A. Martins - 2016 - Journal of Applied Logic 16:72-91.
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  • Almost structural completeness; an algebraic approach.Wojciech Dzik & Michał M. Stronkowski - 2016 - Annals of Pure and Applied Logic 167 (7):525-556.
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  • On the Deductive System of the Order of an Equationally Orderable Quasivariety.Ramon Jansana - 2016 - Studia Logica 104 (3):547-566.
    We consider the equationally orderable quasivarieties and associate with them deductive systems defined using the order. The method of definition of these deductive systems encompasses the definition of logics preserving degrees of truth we find in the research areas of substructural logics and mathematical fuzzy logic. We prove several general results, for example that the deductive systems so defined are finitary and that the ones associated with equationally orderable varieties are congruential.
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  • Taking Degrees of Truth Seriously.Josep Maria Font - 2009 - Studia Logica 91 (3):383-406.
    This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying these in the (...)
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  • Categorical Abstract Algebraic Logic: Models of π-Institutions.George Voutsadakis - 2005 - Notre Dame Journal of Formal Logic 46 (4):439-460.
    An important part of the theory of algebraizable sentential logics consists of studying the algebraic semantics of these logics. As developed by Czelakowski, Blok, and Pigozzi and Font and Jansana, among others, it includes studying the properties of logical matrices serving as models of deductive systems and the properties of abstract logics serving as models of sentential logics. The present paper contributes to the development of the categorical theory by abstracting some of these model theoretic aspects and results from the (...)
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  • A Logic for Dually Hemimorphic Semi-Heyting Algebras and its Axiomatic Extensions.Juan Manuel Cornejo & Hanamantagouda P. Sankappanavar - 2022 - Bulletin of the Section of Logic 51 (4):555-645.
    The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion of semi-Heyting algebras by a dual hemimorphism. In this paper, we focus on the variety \(\mathbb{DHMSH}\) from a logical point of view. The paper presents an extensive investigation of the logic corresponding to the variety of dually hemimorphic semi-Heyting algebras and of its axiomatic extensions, along with an equally extensive universal algebraic study of their corresponding algebraic semantics. Firstly, we present a (...)
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  • Wansing's bi-intuitionistic logic: semantics, extension and unilateralisation.Juan C. Agudelo-Agudelo - 2024 - Journal of Applied Non-Classical Logics 34 (1):31-54.
    The well-known algebraic semantics and topological semantics for intuitionistic logic (Int) is here extended to Wansing's bi-intuitionistic logic (2Int). The logic 2Int is also characterised by a quasi-twist structure semantics, which leads to an alternative topological characterisation of 2Int. Later, notions of Fregean negation and of unilateralisation are proposed. The logic 2Int is extended with a ‘Fregean negation’ connective ∼, obtaining 2Int∼, and it is showed that the logic N4⋆ (an extension of Nelson's paraconsistent logic) results to be the unilateralisation (...)
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  • Algebraic logic for the negation fragment of classical logic.Luciano J. González - forthcoming - Logic Journal of the IGPL.
    The general aim of this article is to study the negation fragment of classical logic within the framework of contemporary (Abstract) Algebraic Logic. More precisely, we shall find the three classes of algebras that are canonically associated with a logic in Algebraic Logic, i.e. we find the classes |$\textrm{Alg}^*$|⁠, |$\textrm{Alg}$| and the intrinsic variety of the negation fragment of classical logic. In order to achieve this, firstly, we propose a Hilbert-style axiomatization for this fragment. Then, we characterize the reduced matrix (...)
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  • A comparison between monoidal and substructural logics.Clayton Peterson - 2016 - Journal of Applied Non-Classical Logics 26 (2):126-159.
    Monoidal logics were introduced as a foundational framework to analyse the proof theory of deontic logic. Building on Lambek’s work in categorical logic, logical systems are defined as deductive systems, that is, as collections of equivalence classes of proofs satisfying specific rules and axiom schemata. This approach enables the classification of deductive systems with respect to their categorical structure. When looking at their proof theory, however, one can see that there are similarities between monoidal and substructural logics. The purpose of (...)
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  • Gentzen-Style Sequent Calculus for Semi-intuitionistic Logic.Diego Castaño & Juan Manuel Cornejo - 2016 - Studia Logica 104 (6):1245-1265.
    The variety \ of semi-Heyting algebras was introduced by H. P. Sankappanavar [13] as an abstraction of the variety of Heyting algebras. Semi-Heyting algebras are the algebraic models for a logic HsH, known as semi-intuitionistic logic, which is equivalent to the one defined by a Hilbert style calculus in Cornejo :9–25, 2011) [6]. In this article we introduce a Gentzen style sequent calculus GsH for the semi-intuitionistic logic whose associated logic GsH is the same as HsH. The advantage of this (...)
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  • 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 (...)
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  • On Some Semi-Intuitionistic Logics.Juan M. Cornejo & Ignacio D. Viglizzo - 2015 - Studia Logica 103 (2):303-344.
    Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Heyting algebras. We present a new, more streamlined set of axioms for semi-intuitionistic logic, which we prove translationally equivalent to the original one. We then study some formulas that define a semi-Heyting implication, and specialize this study to the case in which the formulas use only the lattice operators and the intuitionistic implication. We prove then that all the logics thus (...)
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  • Order algebraizable logics.James G. Raftery - 2013 - Annals of Pure and Applied Logic 164 (3):251-283.
    This paper develops an order-theoretic generalization of Blok and Pigozziʼs notion of an algebraizable logic. Unavoidably, the ordered model class of a logic, when it exists, is not unique. For uniqueness, the definition must be relativized, either syntactically or semantically. In sentential systems, for instance, the order algebraization process may be required to respect a given but arbitrary polarity on the signature. With every deductive filter of an algebra of the pertinent type, the polarity associates a reflexive and transitive relation (...)
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  • The simplest protoalgebraic logic.Josep Maria Font - 2013 - Mathematical Logic Quarterly 59 (6):435-451.
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  • Categorical abstract algebraic logic: Gentzen π ‐institutions and the deduction‐detachment property.George Voutsadakis - 2005 - Mathematical Logic Quarterly 51 (6):570-578.
    Given a π -institution I , a hierarchy of π -institutions I is constructed, for n ≥ 1. We call I the n-th order counterpart of I . The second-order counterpart of a deductive π -institution is a Gentzen π -institution, i.e. a π -institution associated with a structural Gentzen system in a canonical way. So, by analogy, the second order counterpart I of I is also called the “Gentzenization” of I . In the main result of the paper, it (...)
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  • On Barrio, Lo Guercio, and Szmuc on Logics of Evidence and Truth.Abilio Rodrigues & Walter Carnielli - forthcoming - Logic and Logical Philosophy:1-26.
    The aim of this text is to reply to criticisms of the logics of evidence and truth and the epistemic approach to paraconsistency advanced by Barrio [2018], and Lo Guercio and Szmuc [2018]. We also clarify the notion of evidence that underlies the intended interpretation of these logics and is a central point of Barrio’s and Lo Guercio & Szmuc’s criticisms.
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  • The Poset of All Logics I: Interpretations and Lattice Structure.R. Jansana & T. Moraschini - 2021 - Journal of Symbolic Logic 86 (3):935-964.
    A notion of interpretation between arbitrary logics is introduced, and the poset$\mathsf {Log}$of all logics ordered under interpretability is studied. It is shown that in$\mathsf {Log}$infima of arbitrarily large sets exist, but binary suprema in general do not. On the other hand, the existence of suprema of sets of equivalential logics is established. The relations between$\mathsf {Log}$and the lattice of interpretability types of varieties are investigated.
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  • The Poset of All Logics III: Finitely Presentable Logics.Ramon Jansana & Tommaso Moraschini - 2020 - Studia Logica 109 (3):539-580.
    A logic in a finite language is said to be finitely presentable if it is axiomatized by finitely many finite rules. It is proved that binary non-indexed products of logics that are both finitely presentable and finitely equivalential are essentially finitely presentable. This result does not extend to binary non-indexed products of arbitrary finitely presentable logics, as shown by a counterexample. Finitely presentable logics are then exploited to introduce finitely presentable Leibniz classes, and to draw a parallel between the Leibniz (...)
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  • On the complexity of the Leibniz hierarchy.Tommaso Moraschini - 2019 - Annals of Pure and Applied Logic 170 (7):805-824.
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  • Algebraic Analysis of Demodalised Analytic Implication.Antonio Ledda, Francesco Paoli & Michele Pra Baldi - 2019 - Journal of Philosophical Logic 48 (6):957-979.
    The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn as a variation on a time-honoured logical system by C.I. Lewis’ student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is “analytically contained” in its antecedent. DAI has been investigated both proof-theoretically and model-theoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several different algebraic semantics for DAI, (...)
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  • Judgment aggregation in nonmonotonic logic.Xuefeng Wen - 2018 - Synthese 195 (8):3651-3683.
    Judgment aggregation studies how to aggregate individual judgments on logically correlated propositions into collective judgments. Different logics can be used in judgment aggregation, for which Dietrich and Mongin have proposed a generalized model based on general logics. Despite its generality, however, all nonmonotonic logics are excluded from this model. This paper argues for using nonmonotonic logic in judgment aggregation. Then it generalizes Dietrich and Mongin’s model to incorporate a large class of nonmonotonic logics. This generalization broadens the theoretical boundaries of (...)
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  • Willem Blok's Contribution to Abstract Algebraic Logic.Ramon Jansana - 2006 - Studia Logica 83 (1-3):31-48.
    Willem Blok was one of the founders of the field Abstract Algebraic Logic. The paper describes his research in this field.
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  • The Beth Property in Algebraic Logic.W. J. Blok & Eva Hoogland - 2006 - Studia Logica 83 (1-3):49-90.
    The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics.
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  • 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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  • Beyond Rasiowan Systems: Unital Deductive Systems.Alexei Y. Muravitsky - 2014 - Logica Universalis 8 (1):83-102.
    We deal with monotone structural deductive systems in an unspecified propositional language \ . These systems fall into several overlapping classes, forming a hierarchy. Along with well-known classes of deductive systems such as those of implicative, Fregean and equivalential systems, we consider new classes of unital and weakly implicative systems. The latter class is auxiliary, while the former is central in our discussion. Our analysis of unital systems leads to the concept of Lindenbaum–Tarski algebra which, under some natural conditions, is (...)
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  • Relation Formulas for Protoalgebraic Equality Free Quasivarieties; Pałasińska’s Theorem Revisited.Anvar M. Nurakunov & Michał M. Stronkowski - 2013 - Studia Logica 101 (4):827-847.
    We provide a new proof of the following Pałasińska's theorem: Every finitely generated protoalgebraic relation distributive equality free quasivariety is finitely axiomatizable. The main tool we use are ${\mathcal{Q}}$ Q -relation formulas for a protoalgebraic equality free quasivariety ${\mathcal{Q}}$ Q . They are the counterparts of the congruence formulas used for describing the generation of congruences in algebras. Having this tool in hand, we prove a finite axiomatization theorem for ${\mathcal{Q}}$ Q when it has definable principal ${\mathcal{Q}}$ Q -subrelations. This (...)
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  • Contextual Deduction Theorems.J. G. Raftery - 2011 - Studia Logica 99 (1-3):279-319.
    Logics that do not have a deduction-detachment theorem (briefly, a DDT) may still possess a contextual DDT —a syntactic notion introduced here for arbitrary deductive systems, along with a local variant. Substructural logics without sentential constants are natural witnesses to these phenomena. In the presence of a contextual DDT, we can still upgrade many weak completeness results to strong ones, e.g., the finite model property implies the strong finite model property. It turns out that a finitary system has a contextual (...)
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  • Free Spectra of Linear Equivalential Algebras.Katarzyna Slomczyńska - 2005 - Journal of Symbolic Logic 70 (4):1341 - 1358.
    We construct the finitely generated free algebras and determine the free spectra of varieties of linear equivalential algebras and linear equivalential algebras of finite height corresponding. respectively, to the equivalential fragments of intermediate Gödel-Dummett logic and intermediate finite-valued logics of Gödel. Thus we compute the number of purely equivalential propositional formulas in these logics in n variables for an arbitrary n ∈ N.
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  • Leo Esakia on Duality in Modal and Intuitionistic Logics.Guram Bezhanishvili (ed.) - 2014 - Dordrecht, Netherland: Springer.
    This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations (...)
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  • 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 (...)
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  • Admissible Rules and the Leibniz Hierarchy.James G. Raftery - 2016 - Notre Dame Journal of Formal Logic 57 (4):569-606.
    This paper provides a semantic analysis of admissible rules and associated completeness conditions for arbitrary deductive systems, using the framework of abstract algebraic logic. Algebraizability is not assumed, so the meaning and significance of the principal notions vary with the level of the Leibniz hierarchy at which they are presented. As a case study of the resulting theory, the nonalgebraizable fragments of relevance logic are considered.
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