Relevant bibliographies by topics / Algebraic category of LM-logic algebras

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Academic literature on the topic 'Algebraic category of LM-logic algebras'

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Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Algebraic category of LM-logic algebras"

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Ciungu, Lavinia Corina. "Convergence with a fixed regulator in perfect MV-algebras." Demonstratio Mathematica 41, no. 1 (2008): 1–10. http://dx.doi.org/10.1515/dema-2013-0044.

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AbstractMV-algebras were introduced by Chang as an algebraic counterpart of the Łukasiewicz infinite-valued logic. D. Mundici proved that the category of MV-algebras is equivalent to the category of abelian
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Ion, C. Baianu, Georgescu George, F. Glazebrook James, and Brown Ronald. "BRAIN Journal - Lukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems." Brain Journal 1, SPECIAL ISSUE ON COMPLEXITY IN SCIENCES AND ARTIFICIAL INTELLIGENCE (2010): 1–11. https://doi.org/10.5281/zenodo.1037321.

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ABSTRACT The fundamentals of ÃLukasiewicz-Moisil logic algebras and their applications to complex genetic network dynamics and highly complex systems are presented in the context of a categorical ontology theory of levels, Medical Bioinformatics and self-organizing, highly complex systems. Quantum Automata were defined in refs.[2] and [3] as generalized, probabilistic automata with quantum state spaces [1]. Their next-state functions operate through transitions between quantum states defined by the quantum equations of motions in the Schr¨odinger representation, with both initial and boundary
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Adámek, Jiří, Liang-Ting Chen, Stefan Milius, and Henning Urbat. "Reiterman’s Theorem on Finite Algebras for a Monad." ACM Transactions on Computational Logic 22, no. 4 (2021): 1–48. http://dx.doi.org/10.1145/3464691.

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Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman’s theorem states that they precisely specify pseudovarieties, i.e., classes of finite algebras closed under finite products, subalgebras and quotients. In this article, Reiterman’s theorem is generalized to finite Eilenberg-Moore algebras for a monad T on a category D: we prove that a class of finite T -algebras is a pseudovariety iff it is presentable by profinite equations. As a key technical tool, we introduce the concept of a profinite monad T ^ associated to the monad T , which gi
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Coniglio, Marcelo E., Aldo Figallo-Orellano, and Ana Claudia Golzio. "Non-deterministic algebraization of logics by swap structures1." Logic Journal of the IGPL 28, no. 5 (2018): 1021–59. http://dx.doi.org/10.1093/jigpal/jzy072.

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Abstract Multialgebras (or hyperalgebras or non-deterministic algebras) have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency (or LFIs) that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are
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PAVLOVIĆ, DUšKO. "Categorical logic of names and abstraction in action calculi." Mathematical Structures in Computer Science 7, no. 6 (1997): 619–37. http://dx.doi.org/10.1017/s0960129597002296.

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Milner's action calculus implements abstraction in monoidal categories, so that familiar λ-calculi can be subsumed together with the π-calculus and the Petri nets. Variables are generalised to names, which allow only a restricted form of substitution.In the present paper, the well-known categorical semantics of the λ-calculus is generalised to the action calculus. A suitable functional completeness theorem for symmetric monoidal categories is proved: we determine the conditions under which the abstraction is definable. Algebraically, the distinction between the variables and the names boils do
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Basti, Gianfranco. "The Philosophy of Nature of the Natural Realism. The Operator Algebra from Physics to Logic." Philosophies 7, no. 6 (2022): 121. http://dx.doi.org/10.3390/philosophies7060121.

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This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern mathematical, natural, and artificial sciences, the theoretical computer science included. I present the formal philosophy in the framework of the category theory (CT) as an axiomatic metalanguage—in many senses “wider” than set theory (ST)—of mathematics and logic, both of the “extensional” logics of the pur
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Grosu, Radu, Dorel Lucanu, and Gheorghe Stefanescu. "Mixed Relations as Enriched Semiringal Categories." JUCS - Journal of Universal Computer Science 6, no. (1) (2000): 112–29. https://doi.org/10.3217/jucs-006-01-0112.

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A study of the classes of finite relations as enriched strict monoidal categories is presented in [CaS91]. The relations there are interpreted as connections in flowchart schemes, hence an angelic theory of relations is used. Finite relations may be used to model the connections between the components of dataflow networks [BeS98, BrS96], as well. The corresponding algebras are slightly different enriched strict monoidal categories modeling a forward-demonic theory of relations. In order to obtain a full model for parallel programs one needs to mix control and reactive parts, hence a richer the
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Corradini, Andrea, Hartmut Ehrig, Grzegorz Rozenberg, and Gabriele Taentzer. "Introduction." Mathematical Structures in Computer Science 12, no. 2 (2002): 111. http://dx.doi.org/10.1017/s0960129501003504.

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This special issue of Mathematical Structures in Computer Science is devoted to the theory and applications of graph transformations. This research area dates back to the early seventies and is based on mathematical techniques from graph theory, algebra, logic and category theory. The theory of graph transformations has become attractive as a modelling and programming paradigm for complex graphical structures in a large variety of areas in computer science and for applications to other fields. During the Joint APPLIGRAPH/GETGRATS Workshop on Graph Transformation Systems (GRATRA 2000) – a satel
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Sharma, Amit. "On the Left Properness of the Model Category of Permutative Categories." Axioms 12, no. 1 (2023): 87. http://dx.doi.org/10.3390/axioms12010087.

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In this paper, we introduce a notion of free cofibrations of permutative categories. We show that each cofibration of permutative categories is a retract of a free cofibration. The main goal of this paper is to show that the natural model category of permutative categories is a left proper model category.
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Gu, Aihua, Zhongzhen Yan, Xixi Zhang, and Yongsheng Xiang. "Research on the Modeling of Automatic Pricing and Replenishment Strategies for Perishable Goods with Time-Varying Deterioration Rates." Axioms 13, no. 1 (2024): 62. http://dx.doi.org/10.3390/axioms13010062.

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This paper focuses on the modeling of automatic pricing and replenishment strategies for perishable products with time-varying deterioration rates based on an improved SVR-LSTM-ARIMA hybrid model. This research aims to support supermarkets in planning future strategies, optimizing category structure, reducing loss rates, and improving profit margins and service quality. Specifically, the paper selects perishable vegetables as the research category and calculates the cost-plus ratio for each vegetable category. Correlation analysis is conducted with total sales, and a non-parametric relationshi
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Dissertations / Theses on the topic "Algebraic category of LM-logic algebras"

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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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Söderberg, Christoffer. "Category O for Takiff sl2." Thesis, Uppsala universitet, Algebra och geometri, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-385982.

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Fong, Brendan. "The algebra of open and interconnected systems." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:79a23c8c-81a5-4cf1-a108-29ba7dfd8850.

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Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes, automata, Petri nets, chemical reaction networks, and so on. The key feature is that the language is comprised of a number of components with multiple (input/output) terminals, each possibly labelled with some type, that may then be connected together along these terminals to form a larger network. The components form hyperedges between labelled vertices, a
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Steele, Hugh Paul. "Combinatorial arguments for linear logic full completeness." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/combinatorial-arguments-for-linear-logic-full-completeness(274c6b87-dc58-4dc3-86bc-8c29abc2fc34).html.

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We investigate categorical models of the unit-free multiplicative and multiplicative-additive fragments of linear logic by representing derivations as particular structures known as dinatural transformations. Suitable categories are considered to satisfy a property known as full completeness if all such entities are the interpretation of a correct derivation. It is demonstrated that certain Hyland-Schalk double glueings [HS03] are capable of transforming large numbers of degenerate models into more accurate ones. Compact closed categories with finite biproducts possess enough structure that th
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Carissimi, Nicola. "Reconstruction of schemes via the tensor triangulated category of perfect complexes." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23343/.

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This elaborate consists of a detailed presentation of the construction introduced for the first time by Paul Balmer and aimed to define a locally ringed space associated to a given tensor triangulated category, the so called spectrum of the category. The focus of this thesis is the case of the tensor triangulated category of perfect complexes on a noetherian scheme X, the full triangulated subcategory of the derived category of sheaves of modules consisting of complexes of sheaves locally quasi-isomorphic to complexes of locally free sheaves. This category inherits the structure of derived ten
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Forsberg, Love. "Semigroups, multisemigroups and representations." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-327270.

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This thesis consists of four papers about the intersection between semigroup theory, category theory and representation theory. We say that a representation of a semigroup by a matrix semigroup is effective if it is injective and define the effective dimension of a semigroup S as the minimal n such that S has an effective representation by square matrices of size n. A multisemigroup is a generalization of a semigroup where the multiplication is set-valued, but still associative. A 2-category consists of objects, 1-morphisms and 2-morphisms. A finitary 2-category has finite dimensional vector s
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de, Boer Menno. "A Proof and Formalization of the Initiality Conjecture of Dependent Type Theory." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-181640.

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In this licentiate thesis we present a proof of the initiality conjecture for Martin-Löf’s type theory with 0, 1, N, A+B, ∏AB, ∑AB, IdA(u,v), countable hierarchy of universes (Ui)iєN closed under these type constructors and with type of elements (ELi(a))iєN. We employ the categorical semantics of contextual categories. The proof is based on a formalization in the proof assistant Agda done by Guillaume Brunerie and the author. This work was part of a joint project with Peter LeFanu Lumsdaine and Anders Mörtberg, who are developing a separate formalization of this conjecture with respect to cate
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Ugolini, Matteo. "K3 surfaces." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18774/.

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Ferreira, Rodrigo Costa. "Semântica proposicional categórica." Universidade Federal da Paraí­ba, 2010. http://tede.biblioteca.ufpb.br:8080/handle/tede/5678.

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Made available in DSpace on 2015-05-14T12:11:59Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 891353 bytes, checksum: 2d056c7f53fdfb7c20586b64874e848d (MD5) Previous issue date: 2010-12-01<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The basic concepts of what later became called category theory were introduced in 1945 by Samuel Eilenberg and Saunders Mac Lane. In 1940s, the main applications were originally in the fields of algebraic topology and algebraic abstract. During the 1950s and 1960s, this theory became an important conceptual framework in other many areas of
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Malakhovski, Ian. "Sur le pouvoir expressif des structures applicatives et monadiques indexées." Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30118.

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Il est bien connu que des constructions théoriques très simples telles que les structures Either (équivalent type théorique de l'opérateur logique "ou"), State (représentant des transformateurs d'état composables), Applicative (application des fonctions généralisée) et Monad (composition de programmes séquentielles généralisée), nommés structures en Haskell, couvrent une grande partie de ce qui est habituellement nécessaire pour exprimer avec élégance la plupart des idiomes informatiques utilisés dans les programmes classiques. Cependant, il est usuellement admis qu'il existe plusieurs classes
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Books on the topic "Algebraic category of LM-logic algebras"

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Argentina) Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry (3rd 2010 Buenos Aires. Topics in noncommutative geometry: Third Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry, Universidad de Buenos Aires, Buenos Aires, Argentina, July 26-August 6, 2010. Edited by Cortiñas, Guillermo, editor of compilation. American Mathematical Society, 2012.

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Hinkis, Arie. Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion. Springer Basel, 2013.

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Makkai, Mihály. Models, logics, and higher-dimensional categories: A tribute to the work of Mihaly Makkai. American Mathematical Society, 2011.

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Ghilardi, Silvio. Sheaves, games, and model completions: A categorical approach to nonclassical propositional logics. Kluwer Academic Publishers, 2002.

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Ghilardi, Silvio. Sheaves, games, and model completions: A categorical approach to nonclassical propositional logics. Kluwer Academic Publishers, 2002.

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Tulane University. Dept. of Mathematics, ed. Mathematical foundations of information flow: Clifford lectures on information flow in physics, geometry and logic and computation, March 12-15, 2008, Tulane University, New Orleans, Louisiana. American Mathematical Society, 2012.

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Papers in Honour of Bernhard Banaschewski: Proceedings Of The Bb Fest 96, A Conference Held At The University Of Cape Town, 15-20 July 1996, On . . . Applications To Topology, Order And Algebra. Brummer Guillaume Gilmour Christopher, 2010.

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Marquis, Jean-Pierre. From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory. Springer, 2010.

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Heunen, Chris, and Jamie Vicary. Categories for Quantum Theory. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198739623.001.0001.

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Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition and a conceptual way to understand many high-level quantum phenomena. Here, we lay the foundations for this categorical quantum mechanics, with an emphasis on the graphical calculus that makes computation intuitive. We describe superposition and entanglement using biproducts and dual objects, and show how quantum teleportation can be studied abstractly using these structures. We investigate monoids, Frobenius structures an
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Tarlecki, Andrzej, and Donald Sannella. Foundations of Algebraic Specification and Formal Software Development. Springer, 2014.

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Book chapters on the topic "Algebraic category of LM-logic algebras"

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Birkmann, Fabian, Henning Urbat, and Stefan Milius. "Monoidal Extended Stone Duality." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57228-9_8.

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AbstractExtensions of Stone-type dualities have a long history in algebraic logic and have also been instrumental for proving results in algebraic language theory. We show how to extend abstract categorical dualities via monoidal adjunctions, subsuming various incarnations of classical extended Stone and Priestley duality as a special case. Guided by these categorical foundations, we investigate residuation algebras, which are algebraic models of language derivatives, and show the subcategory of derivation algebras to be dually equivalent to the category of profinite ordered monoids, restricti
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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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Plotkin, B. "The Category of Sets. Topoi. Fuzzy Sets." In Universal Algebra, Algebraic Logic, and Databases. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0820-1_5.

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Goguen, Joseph A., and Răzvan Diaconescu. "An introduction to category-based equational logic." In Algebraic Methodology and Software Technology. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60043-4_48.

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Gratzer, Daniel, Mathias Adam Møller, and Lars Birkedal. "Idempotent Resources in Separation Logic." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-90897-2_3.

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Abstract We revisit the foundational notion of “resources” used by separation logics from a categorical and algebraic viewpoint. In particular, we show that the cameras used by concurrent, higher-order, impredicative separation logics like Iris as a generalization of partial commutative monoids can be simplified and clarified and we introduce a category of cameras in which many vital cameras exhibit simple universal properties. We do this by observing that an important structure on cameras (the core operator) can be uniquely constrained and replaced by the property governing the idempotent ele
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More, Anuj Kumar, and Mohua Banerjee. "New Algebras and Logic from a Category of Rough Sets." In Rough Sets. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-60837-2_8.

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Sazonov, V. Yu. "A category of many-sorted algebraic theories which is equivalent to the category of categories with finite products." In Logic at Botik '89. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51237-3_19.

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Fukihara, Yōji, and Shin-ya Katsumata. "Generalized Bounded Linear Logic and its Categorical Semantics." In Lecture Notes in Computer Science. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71995-1_12.

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AbstractWe introduce a generalization of Girard et al.’s called (and its affine variant ). It is designed to capture the core mechanism of dependency in , while it is also able to separate complexity aspects of . The main feature of is to adopt a multi-object pseudo-semiring as a grading system of the !-modality. We analyze the complexity of cut-elimination in , and give a translation from with constraints to with positivity axiom. We then introduce indexed linear exponential comonads (ILEC for short) as a categorical structure for interpreting the $${!}$$ ! -modality of . We give an elementar
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Marti-Oliet, Narciso, and Jose Meseguer. "An algebraic axiomatization of linear logic models." In Topology and Category Theory in Computer Science. Oxford University PressOxford, 1991. http://dx.doi.org/10.1093/oso/9780198537601.003.0013.

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Abstract There are many notions of type in computing. The most classical notion is ‘types as sets’, which has been extended to cover many features of modern programming languages. This chapter shows that such features are handled perhaps even more naturally by an extension of the ‘types as algebras’ notion to a ‘types as theories’ notion. This notion naturally supports object-oriented concepts, including inheritance and local state, as well as generic modules and dependent types. Moreover, it explains why polymorphic operations are natural transformations and provides a systematic foundation f
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Loeckx, J., and H. D. Ehrich. "Algebraic specification of abstract data types." In Handbook of Logic in Computer Science: Volume 5. Algebraic and Logical Structures. Oxford University Press, 2001. http://dx.doi.org/10.1093/oso/9780198537816.003.0007.

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It is widely accepted that the quality of software can be improved if its design is systematically based on the principles of modularization and formalization. Modularization consists in replacing a problem by several “smaller” ones. Formalization consists in using a formal language; it obliges the software designer to be precise and principally allows a mechanical treatment. One may distinguish two modularization techniques for the software design. The first technique consists in a modularization on the basis of the control structures. It is used in classical programming languages where it le
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