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Relevant bibliographies by topics / Algebra Logic. Algebraic logic

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Academic literature on the topic 'Algebra Logic. Algebraic logic'

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Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Algebra Logic. Algebraic logic"

1

Dai, Jianhua. "Generalized Rough Logics with Rough Algebraic Semantics." International Journal of Cognitive Informatics and Natural Intelligence 4, no. 2 (2010): 35–49. http://dx.doi.org/10.4018/jcini.2010040103.

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The collection of the rough set pairs <lower approximation, upper approximation> of an approximation (U, R) can be made into a Stone algebra by defining two binary operators and one unary operator on the pairs. By introducing a more unary operator, one can get a regular double Stone algebra to describe the rough set pairs of an approximation space. Sequent calculi corresponding to the rough algebras, including rough Stone algebras, Stone algebras, rough double Stone algebras, and regular double Stone algebras are proposed in this paper. The sequent calculi are called rough Stone logic (R

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Zhang, Xiaohong, Xiangyu Ma, and Xuejiao Wang. "Filters in Strong BI-Algebras and Residuated Pseudo-SBI-Algebras." Mathematics 8, no. 9 (2020): 1513. http://dx.doi.org/10.3390/math8091513.

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The concept of basic implication algebra (BI-algebra) has been proposed to describe general non-classical implicative logics (such as associative or non-associative fuzzy logic, commutative or non-commutative fuzzy logic, quantum logic). However, this algebra structure does not have enough characteristics to describe residual implications in depth, so we propose a new concept of strong BI-algebra, which is exactly the algebraic abstraction of fuzzy implication with pseudo-exchange principle (PEP). Furthermore, in order to describe the characteristics of the algebraic structure corresponding to

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Gehrke, Mai, Carol Walker, and Elbert Walker. "A Mathematical Setting for Fuzzy Logics." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 03 (1997): 223–38. http://dx.doi.org/10.1142/s021848859700021x.

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The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and -x=1-x for conjunction, disjunction and negation, respectively, is the standard propositional fuzzy logic. This is shown to be the same as three-valued logic. The propositional logic obtained when the algebra of truth values is the set {(a, b)|a≤ b and a,b∈[0,1]} of subintervals of the unit interval

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van Alten, C. J. "The finite model property for knotted extensions of propositional linear logic." Journal of Symbolic Logic 70, no. 1 (2005): 84–98. http://dx.doi.org/10.2178/jsl/1107298511.

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AbstractThe logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: . It is proved that the class of algebraic models for such a logic has the finite embeddability property, meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the finite model property with respect to its algebraic semantics and hence that the logic is decidable.

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Hirsch, Robin, and Ian Hodkinson. "Complete representations in algebraic logic." Journal of Symbolic Logic 62, no. 3 (1997): 816–47. http://dx.doi.org/10.2307/2275574.

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AbstractA boolean algebra is shown to be completely representable if and only if it is atomic, whereas it is shown that neither the class of completely representable relation algebras nor the class of completely representable cylindric algebras of any fixed dimension (at least 3) are elementary.

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Chajda, Ivan. "An algebra of quasiordered logic." Mathematica Bohemica 119, no. 2 (1994): 129–35. http://dx.doi.org/10.21136/mb.1994.126081.

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Biró, Balázs. "Non-finite-axiomatizability results in algebraic logic." Journal of Symbolic Logic 57, no. 3 (1992): 832–43. http://dx.doi.org/10.2307/2275434.

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This paper deals with relation, cylindric and polyadic equality algebras. First of all it addresses a problem of B. Jónsson. He asked whether relation set algebras can be expanded by finitely many new operations in a “reasonable” way so that the class of these expansions would possess a finite equational base. The present paper gives a negative answer to this problem: Our main theorem states that whenever Rs+ is a class that consists of expansions of relation set algebras such that each operation of Rs+ is logical in Jónsson's sense, i.e., is the algebraic counterpart of some (derived) connect

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DZIK, WOJCIECH, and PIOTR WOJTYLAK. "UNIFICATION IN SUPERINTUITIONISTIC PREDICATE LOGICS AND ITS APPLICATIONS." Review of Symbolic Logic 12, no. 1 (2018): 37–61. http://dx.doi.org/10.1017/s1755020318000011.

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AbstractWe introduce unification in first-order logic. In propositional logic, unification was introduced by S. Ghilardi, see Ghilardi (1997, 1999, 2000). He successfully applied it in solving systematically the problem of admissibility of inference rules in intuitionistic and transitive modal propositional logics. Here we focus on superintuitionistic predicate logics and apply unification to some old and new problems: definability of disjunction and existential quantifier, disjunction and existential quantifier under implication, admissible rules, a basis for the passive rules, (almost) struc

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Hirsch, Robin, and Ian Hodkinson. "Step by step – Building representations in algebraic logic." Journal of Symbolic Logic 62, no. 1 (1997): 225–79. http://dx.doi.org/10.2307/2275740.

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AbstractWe consider the problem of finding and classifying representations in algebraic logic. This is approached by letting two players build a representation using a game. Homogeneous and universal representations are characterized according to the outcome of certain games. The Lyndon conditions defining representable relation algebras (for the finite case) and a similar schema for cylindric algebras are derived. Finte relation algebras with homogeneous representations are characterized by first order formulas. Equivalence games are defined, and are used to establish whether an algebra is ω-

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Bancerek, Grzegorz. "Algebraic Approach to Algorithmic Logic." Formalized Mathematics 22, no. 3 (2014): 225–55. http://dx.doi.org/10.2478/forma-2014-0025.

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Summary We introduce algorithmic logic - an algebraic approach according to [25]. It is done in three stages: propositional calculus, quantifier calculus with equality, and finally proper algorithmic logic. For each stage appropriate signature and theory are defined. Propositional calculus and quantifier calculus with equality are explored according to [24]. A language is introduced with language signature including free variables, substitution, and equality. Algorithmic logic requires a bialgebra structure which is an extension of language signature and program algebra. While-if algebra of ge

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Dissertations / Theses on the topic "Algebra Logic. Algebraic logic"

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Engstrom, Ronald W. Retzer Kenneth A. "The effects of logic on achievement in intermediate algebra." Normal, Ill. : Illinois State University, 1988. http://www.mlb.ilstu.edu/articles/dissertations/8818710.PDF.

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Thesis (D.A.)--Illinois State University, 1988.<br>Title from title page screen, viewed Oct. 13, 2004. Dissertation Committee: Kenneth A. Retzer (chair), Lynn H. Brown, John A. Dossey, Lotus D. Hershberger, Albert D. Otto, Walter D. Pierce. Includes bibliographical references (leaves 97-102) and abstract. Also available in print.

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Townsend, Brian E. "Examining secondary students algebraic reasoning flexibility and strategy use /." Diss., Columbia, Mo. : University of Missouri-Columbia, 2005. http://hdl.handle.net/10355/4131.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2005.<br>The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (November 14, 2006) Vita. Includes bibliographical references.

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Lu, Weiyun. "Topics in Many-valued and Quantum Algebraic Logic." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35173.

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Introduced by C.C. Chang in the 1950s, MV algebras are to many-valued (Łukasiewicz) logics what boolean algebras are to two-valued logic. More recently, effect algebras were introduced by physicists to describe quantum logic. In this thesis, we begin by investigating how these two structures, introduced decades apart for wildly different reasons, are intimately related in a mathematically precise way. We survey some connections between MV/effect algebras and more traditional algebraic structures. Then, we look at the categorical structure of effect algebras in depth, and in particular see how

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Akishev, Galym. "Monadic bounded algebras : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics /." ResearchArchive@Victoria e-Thesis, 2009. http://hdl.handle.net/10063/915.

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Albuquerque, Hugo Cardoso. "Operators and strong versions of sentential logics in Abstract Algebraic Logic." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/394003.

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This dissertation presents the results of our research on some recent devel-opments in Abstract Algebraic Logic (AAL), namely on the Suszko operator, the Leibniz filters, and truth-equational logics. Part I builts and develops an abstract framework which unifies under a common treatment the study of the Leibniz, Suszko, and Frege operators in AAL. Part II generalizes the theory of the strong version of protoalgebraic logics, started in, to arbitrary sentential logics. The interplay between several Leibniz- and Suszko-related notions led us to consider a general framework based upon the noti

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Esteban, María. "Duality Theory and Abstract Algebraic Logic." Doctoral thesis, Universitat de Barcelona, 2013. http://hdl.handle.net/10803/125336.

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In this thesis we present the results of our research on duality theory for non-classical logics under the point of view of Abstract Algebraic Logic (AAL). Firstly, we propose an abstract Spectral-like duality and an abstract Priestley-style duality for every filter distributive finitary congruential logic with theorems. This proposal aims to unify the various dualities for concrete logics that we find in the literature, by showing the abstract template in which all of them fit. Secondly, the dual correspondence of some logical properties is examined. This serves to reveal the connection betwe

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Spinks, Matthew (Matthew James) 1970. "Contributions to the theory of pre-BCK-algebras." Monash University, Gippsland School of Computing and Information Technology, 2002. http://arrow.monash.edu.au/hdl/1959.1/7947.

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Amrhein, Beatrice. "Universal algebra in combinatory logic /." [S.l.] : [s.n.], 1992. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10005.

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Seres, Silvija. "The algebra of logic programming." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365466.

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Stroiński, Mateusz. "Homological Algebra for Quiver Representations." Thesis, Uppsala universitet, Algebra och geometri, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354756.

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Books on the topic "Algebra Logic. Algebraic logic"

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Algebras of logic as BCK algebras. Editura ASE, 2008.

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Plotkin, B. I. Universal algebra, algebraic logic, and databases. Kluwer Academic Publishers, 1994.

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Plotkin, B. Universal Algebra, Algebraic Logic, and Databases. Springer Netherlands, 1994.

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Plotkin, B. Universal Algebra, Algebraic Logic, and Databases. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0820-1.

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Algebraic logic. Springer-Verlag, 1985.

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Gindikin, S. G. Algebraic Logic. Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1877-5.

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Andréka, Hajnal, Miklós Ferenczi, and István Németi, eds. Cylindric-like Algebras and Algebraic Logic. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35025-2.

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Hailperin, Theodore. Boole's logic and probability: A critical exposition from the standpoint of contemporary algebra, logic, and probability theory. 2nd ed. North-Holland Pub. Co., 1986.

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The algebra of logic. Dover Publications, 2005.

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Bergman, Clifford H., Roger D. Maddux, and Don L. Pigozzi, eds. Algebraic Logic and Universal Algebra in Computer Science. Springer-Verlag, 1990. http://dx.doi.org/10.1007/bfb0043074.

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Book chapters on the topic "Algebra Logic. Algebraic logic"

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Plotkin, B. "Category Algebra and Algebraic Theories." In Universal Algebra, Algebraic Logic, and Databases. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0820-1_7.

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Kempf, George R. "Logic." In Algebraic Structures. Vieweg+Teubner Verlag, 1995. http://dx.doi.org/10.1007/978-3-322-80278-1_19.

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Andréka, H., I. Németi, and I. Sain. "Algebraic Logic." In Handbook of Philosophical Logic. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-017-0452-6_3.

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Plotkin, B. "The Categorial Approach to Algebraic Logic." In Universal Algebra, Algebraic Logic, and Databases. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0820-1_12.

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Hsu, John Y. "Boolean Algebra." In Computer Logic. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0047-2_2.

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Gindikin, S. G. "Predicate Logic." In Algebraic Logic. Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1877-5_12.

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Ono, Hiroakira. "Basics of Algebraic Logic." In Proof Theory and Algebra in Logic. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-7997-0_7.

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Plotkin, B. "Algebraic Model of a Database." In Universal Algebra, Algebraic Logic, and Databases. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0820-1_13.

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Dang, Han-Hing, Peter Höfner, and Bernhard Möller. "Towards Algebraic Separation Logic." In Relations and Kleene Algebra in Computer Science. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04639-1_5.

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Andréka, Hajnal, István Németi, and Ildikó Sain. "Applying Algebraic Logic to Logic." In Algebraic Methodology and Software Technology (AMAST’93). Springer London, 1994. http://dx.doi.org/10.1007/978-1-4471-3227-1_3.

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Conference papers on the topic "Algebra Logic. Algebraic logic"

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Liang, Fei, and Zhe Lin. "On the Decidability of Intuitionistic Tense Logic without Disjunction." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/249.

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Implicative semi-lattices (also known as Brouwerian semi-lattices) are a generalization of Heyting algebras, and have been already well studied both from a logical and an algebraic perspective. In this paper, we consider the variety ISt of the expansions of implicative semi-lattices with tense modal operators, which are algebraic models of the disjunction-free fragment of intuitionistic tense logic. Using methods from algebraic proof theory, we show that the logic of tense implicative semi-lattices has the finite model property. Combining with the finite axiomatizability of the logic, it follo

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Gomes, Joel Felipe Ferreira, and Vitor Rodrigues Greati. "Notes on the Logic of Perfect Paradefinite Algebras." In Workshop Brasileiro de Lógica. Sociedade Brasileira de Computação, 2021. http://dx.doi.org/10.5753/wbl.2021.15777.

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This work introduces the variety of perfect paradefinite algebras (PPalgebras), consisting of De Morgan algebras enriched with a perfect operator o, which turns out to be equivalent to the variety of involutive Stone algebras (IS-algebras). The corresponding order-preserving logic PP≤ is a Logic of Formal Inconsistency, a Logic of Formal Undeterminedness, a C-system and a D-system, some of these features being evident in the proposed axiomatization of PP-algebras. After proving the mentioned algebraic equivalence, we show how to axiomatize, by means of Hilbert-style calculi, certain extensions

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Plotkin, Gordon, and Matija Pretnar. "A Logic for Algebraic Effects." In 2008 23rd Annual IEEE Symposium on Logic in Computer Science (LICS 2008). IEEE, 2008. http://dx.doi.org/10.1109/lics.2008.45.

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DOWNEY, ROD. "COMPUTABILITY, DEFINABILITY AND ALGEBRAIC STRUCTURES." In 7th and 8th Asian Logic Conferences. CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS, 2003. http://dx.doi.org/10.1142/9789812705815_0004.

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PAL'CHUNOV, D. E., and G. E. YAKHYAEVA. "INTERVAL FUZZY ALGEBRAIC SYSTEMS." In Proceedings of the 9th Asian Logic Conference. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772749_0014.

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Leustean, Ioana. "The Tensor PMV-algebra of an MV-algebra." In 2011 IEEE 41st International Symposium on Multiple-Valued Logic (ISMVL). IEEE, 2011. http://dx.doi.org/10.1109/ismvl.2011.37.

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Honglan Liu, Qingshi Gao, and Weidong Hao. "Probabilistic logic system is Boolean algebra homomorphic with set algebra." In 2010 International Conference on Progress in Informatics and Computing (PIC). IEEE, 2010. http://dx.doi.org/10.1109/pic.2010.5687410.

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YUUICHI, KAWAGUCHI. "A COMMON STRUCTURE OF LOGICAL AND ALGEBRAIC ALGORITHMS." In 7th and 8th Asian Logic Conferences. CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS, 2003. http://dx.doi.org/10.1142/9789812705815_0009.

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Bonchi, Filippo, Robin Piedeleu, Pawel Sobocinski, and Fabio Zanasi. "Graphical Affine Algebra." In 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2019. http://dx.doi.org/10.1109/lics.2019.8785877.

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Flax, L. "Cognitive modelling using a logic-based algebra." In Fourth IEEE Conference on Cognitive Informatics, 2005. (ICCI 2005). IEEE, 2005. http://dx.doi.org/10.1109/coginf.2005.1532613.

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Reports on the topic "Algebra Logic. Algebraic logic"

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IOWA STATE UNIV AMES DEPT OF MATHEMATICS. Applications of Algebraic Logic and Universal Algebra to Computer Science. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada210556.

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Barnett, Janet Heine. Origins of Boolean Algebra in the Logic of Classes: George Boole, John Venn and C. S. Peirce. The MAA Mathematical Sciences Digital Library, 2013. http://dx.doi.org/10.4169/loci003997.

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