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Universal Algebra

Journal of Symbolic Logic 34 (1):113-114 (1969)

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  1. (1 other version)Logics Projectively Generated from [ℳ] = by a Set of Homomorphisms.Ventura Verdú - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (3):235-241.
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  • (1 other version)Quasi‐Boolean Algebras, Empirical Continuity and Three‐Valued Logic J. P. Cleave in Bristol (Great Britain).J. P. Cleave - 1976 - Mathematical Logic Quarterly 22 (1):481-500.
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  • (1 other version)Fuzzy propositional logic. Algebraic approach.Slava Meskhi - 1977 - Studia Logica 36 (3):189 - 194.
    The present paper contains some technical results on a many-valued logic with truth values from the interval of real numbers [0; 1]. This logic, discussed originally in [1], latter in [2] and [3], was called the logic of fuzzy concepts. Our aim is to give an algebraic axiomatics for fuzzy propositional logic. For this purpose the variety of L-algebras with signature en- riched with a unary operation { involution is stud- ied. A one-to-one correspondence between congruences on an LI-algebra and (...)
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  • The lattice of distributive closure operators over an algebra.Josep M. Font & Ventura Verdú - 1993 - Studia Logica 52 (1):1 - 13.
    In our previous paper Algebraic Logic for Classical Conjunction and Disjunction we studied some relations between the fragmentL of classical logic having just conjunction and disjunction and the varietyD of distributive lattices, within the context of Algebraic Logic. The central tool in that study was a class of closure operators which we calleddistributive, and one of its main results was that for any algebraA of type (2,2) there is an isomorphism between the lattices of allD-congruences ofA and of all distributive (...)
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  • Psychoneural Isomorphism: From Metaphysics to Robustness.Alfredo Vernazzani - 2020 - In Fabrizio Calzavarini & Marco Viola (eds.), Neural Mechanisms: New Challenges in the Philosophy of Neuroscience. Springer.
    At the beginning of the 20th century, Gestalt psychologists put forward the concept of psychoneural isomorphism, which was meant to replace Fechner’s obscure notion of psychophysical parallelism and provide a heuristics that may facilitate the search for the neural correlates of the mind. However, the concept has generated much confusion in the debate, and today its role is still unclear. In this contribution, I will attempt a little conceptual spadework in clarifying the concept of psychoneural isomorphism, focusing exclusively on conscious (...)
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  • Matrix approach in methodology of sentential calculi.Ryszard Wójcicki - 1973 - Studia Logica 32 (1):7 - 39.
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  • A Shared Framework for Consequence Operations and Abstract Model Theory.Christian Wallmann - 2013 - Logica Universalis 7 (2):125-145.
    In this paper we develop an abstract theory of adequacy. In the same way as the theory of consequence operations is a general theory of logic, this theory of adequacy is a general theory of the interactions and connections between consequence operations and its sound and complete semantics. Addition of axioms for the connectives of propositional logic to the basic axioms of consequence operations yields a unifying framework for different systems of classical propositional logic. We present an abstract model-theoretical semantics (...)
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  • (1 other version)Logics Projectively Generated from [ℳ︁] = (ℱ4, [{1}]) by a Set of Homomorphisms.Ventura Verdú - 1987 - Mathematical Logic Quarterly 33 (3):235-241.
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  • Algebraic study of Sette's maximal paraconsistent logic.Alexej P. Pynko - 1995 - Studia Logica 54 (1):89 - 128.
    The aim of this paper is to study the paraconsistent deductive systemP 1 within the context of Algebraic Logic. It is well known due to Lewin, Mikenberg and Schwarse thatP 1 is algebraizable in the sense of Blok and Pigozzi, the quasivariety generated by Sette's three-element algebraS being the unique quasivariety semantics forP 1. In the present paper we prove that the mentioned quasivariety is not a variety by showing that the variety generated byS is not equivalent to any algebraizable (...)
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  • Dynamic algebras: Examples, constructions, applications.Vaughan Pratt - 1991 - Studia Logica 50 (3-4):571 - 605.
    Dynamic algebras combine the classes of Boolean (B 0) and regular (R ; *) algebras into a single finitely axiomatized variety (B R ) resembling an R-module with scalar multiplication . The basic result is that * is reflexive transitive closure, contrary to the intuition that this concept should require quantifiers for its definition. Using this result we give several examples of dynamic algebras arising naturally in connection with additive functions, binary relations, state trajectories, languages, and flowcharts. The main result (...)
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  • Problems of equivalence, categoricity of axioms and states description in databases.Tatjana L. Plotkin, Sarit Kraus & Boris I. Plotkin - 1998 - Studia Logica 61 (3):347-366.
    The paper is devoted to applications of algebraic logic to databases. In databases a query is represented by a formula of first order logic. The same query can be associated with different formulas. Thus, a query is a class of equivalent formulae: equivalence here being similar to that in the transition to the Lindenbaum-Tarski algebra. An algebra of queries is identified with the corresponding algebra of logic. An algebra of replies to the queries is also associated with algebraic logic. These (...)
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  • Logic and Natural Selection.Jaroslav Peregrin - 2010 - Logica Universalis 4 (2):207-223.
    Is logic, feasibly, a product of natural selection? In this paper we treat this question as dependent upon the prior question of where logic is founded. After excluding other possibilities, we conclude that logic resides in our language, in the shape of inferential rules governing the logical vocabulary of the language. This means that knowledge of (the laws of) logic is inseparable from the possession of the logical constants they govern. In this sense, logic may be seen as a product (...)
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  • Algebraization of quantifier logics, an introductory overview.István Németi - 1991 - Studia Logica 50 (3-4):485 - 569.
    This paper is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics. The paper has a survey character, too. The most frequently used algebras like cylindric-, relation-, polyadic-, and quasi-polyadic algebras are carefully introduced and intuitively explained for the nonspecialist. Their variants, connections with logic, abstract model theory, and further algebraic logics are also reviewed. Efforts were made to make the review part relatively comprehensive. In some (...)
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  • On three-valued implicative systems.Marian Maduch - 1978 - Studia Logica 37 (4):351 - 385.
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  • (1 other version)Products of Closure Algebras and Their Dual Spaces.G. J. Logan - 1977 - Mathematical Logic Quarterly 23 (27-30):439-441.
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  • (1 other version)Closure Algebras and T1‐Spaces.G. J. Logan - 1976 - Mathematical Logic Quarterly 23 (1‐6):91-92.
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  • (1 other version)Closure Algebras and T 1 ‐Spaces.G. J. Logan - 1977 - Mathematical Logic Quarterly 23 (1-6):91-92.
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  • A semantic approach to nonmonotonic reasoning: Inference operations and choice.Sten Lindström - 2022 - Theoria 88 (3):494-528.
    Theoria, Volume 88, Issue 3, Page 494-528, June 2022.
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  • Minimally generated abstract logics.Steffen Lewitzka & Andreas B. M. Brunner - 2009 - Logica Universalis 3 (2):219-241.
    In this paper we study an alternative approach to the concept of abstract logic and to connectives in abstract logics. The notion of abstract logic was introduced by Brown and Suszko —nevertheless, similar concepts have been investigated by various authors. Considering abstract logics as intersection structures we extend several notions to their κ -versions, introduce a hierarchy of κ -prime theories, which is important for our treatment of infinite connectives, and study different concepts of κ -compactness. We are particularly interested (...)
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  • Über eine verallgemeinerung der robinsonschen modellvervollständigung I.Klaus Kaiser - 1969 - Mathematical Logic Quarterly 15 (1‐3):37-48.
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  • (2 other versions)Über eine verallgemeinerung der robinsonschen modellvervollständigung I.Klaus Kaiser - 1969 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (1-3):37-48.
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  • Nonstandard Methods and Finiteness Conditions in Algebra.Matt Insall - 1991 - Mathematical Logic Quarterly 37 (33-35):525-532.
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  • Embedding semigroups in groups: not as simple as it might seem.Christopher Hollings - 2014 - Archive for History of Exact Sciences 68 (5):641-692.
    We consider the investigation of the embedding of semigroups in groups, a problem which spans the early-twentieth-century development of abstract algebra. Although this is a simple problem to state, it has proved rather harder to solve, and its apparent simplicity caused some of its would-be solvers to go awry. We begin with the analogous problem for rings, as dealt with by Ernst Steinitz, B. L. van der Waerden and Øystein Ore. After disposing of A. K. Sushkevich’s erroneous contribution in this (...)
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  • (1 other version)Algebraic logic for classical conjunction and disjunction.Josep M. Font & Ventura Verdú - 1991 - Studia Logica 50 (3-4):391 - 419.
    In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...)
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  • (1 other version)Hyperidentities of Dyadic Algebras.Klaus Denecke - 1989 - Mathematical Logic Quarterly 35 (4):303-310.
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  • (1 other version)Hyperidentities of Dyadic Algebras.Klaus Denecke - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (4):303-310.
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  • (3 other versions)Equivalential logics (II).Janusz Czelakowski - 1981 - Studia Logica 40 (4):355 - 372.
    In the first section logics with an algebraic semantics are investigated. Section 2 is devoted to subdirect products of matrices. There, among others we give the matrix counterpart of a theorem of Jónsson from universal algebra. Some positive results concerning logics with, finite degrees of maximality are presented in Section 3.
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  • (1 other version)Quasi-Boolean Algebras, Empirical Continuity and Three-Valued Logic J. P. Cleave in Bristol.J. P. Cleave - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):481-500.
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  • From Curry to Haskell.Felice Cardone - 2020 - Philosophy and Technology 34 (1):57-74.
    We expose some basic elements of a style of programming supported by functional languages like Haskell by relating them to a coherent set of notions and techniques from Curry’s work in combinatory logic and formal systems, and their algebraic and categorical interpretations. Our account takes the form of a commentary to a simple fragment of Haskell code attempting to isolate the conceptual sources of the linguistic abstractions involved.
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  • A conceptual construction of complexity levels theory in spacetime categorical ontology: Non-Abelian algebraic topology, many-valued logics and dynamic systems. [REVIEW]R. Brown, J. F. Glazebrook & I. C. Baianu - 2007 - Axiomathes 17 (3-4):409-493.
    A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...)
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  • Varieties of monadic Heyting algebras. Part I.Guram Bezhanishvili - 1998 - Studia Logica 61 (3):367-402.
    This paper deals with the varieties of monadic Heyting algebras, algebraic models of intuitionistic modal logic MIPC. We investigate semisimple, locally finite, finitely approximated and splitting varieties of monadic Heyting algebras as well as varieties with the disjunction and the existence properties. The investigation of monadic Heyting algebras clarifies the correspondence between intuitionistic modal logics over MIPC and superintuitionistic predicate logics and provides us with the solutions of several problems raised by Ono [35].
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  • Varieties of monadic Heyting algebras part II: Duality theory.Guram Bezhanishvili - 1999 - Studia Logica 62 (1):21-48.
    In this paper we continue the investigation of monadic Heyting algebras which we started in [2]. Here we present the representation theorem for monadic Heyting algebras and develop the duality theory for them. As a result we obtain an adequate topological semantics for intuitionistic modal logics over MIPC along with a Kripke-type semantics for them. It is also shown the importance and the effectiveness of the duality theory for further investigation of monadic Heyting algebras and logics over MIPC.
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  • An abstract, logical approach to characterizing strong equivalence in non-monotonic knowledge representation formalisms.Ringo Baumann & Hannes Strass - 2022 - Artificial Intelligence 305 (C):103680.
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  • A Semantic Approach to Nonmonotonic Reasoning: Inference Operations and Choice, Uppsala Prints and Preprints in Philosophy, 1994, no 10.Sten Lindström - manuscript
    This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premises. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. A (...)
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  • Categorical ontology of levels and emergent complexity: an introduction. [REVIEW]Ion C. Baianu - 2007 - Axiomathes 17 (3-4):209-222.
    An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first (...)
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  • A Novel Tendency in Philosophical Logic.Andrew Schumann - 2008 - Studies in Logic, Grammar and Rhetoric 14 (27).
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  • Logika a logiky.Jaroslav Peregrin - manuscript
    Kniha, jako je tato, nemůže být tak docela dílem jediného člověka. Dovést ji do podoby koherentního celku bych nedokázal bez pomoci svých kolegů, kteří po mně text četli a upozornili mě na spoustu chyb a nedůsledností, které se v něm vyskytovaly. Můj dík v tomto směru patří zejména Vojtěchu Kolmanovi, Liboru Běhounkovi a Martě Bílkové. Za připomínky k různým částem rukopisu jsem vděčen i Pavlu Maternovi, Milanu Matouškovi, Prokopu Sousedíkovi, Vladimíru Svobodovi, Petru Hájkovi a Grahamu Priestovi. Kniha vznikla v rámci (...)
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