Journal articles: 'Logic in Computer Science'

1

Martin, Ursula. "Logic for computer science." Science of Computer Programming 11, no. 2 (December 1988): 176–78. http://dx.doi.org/10.1016/0167-6423(88)90006-8.

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Steingartner, William, Andrea Polakova, Peter Praznak, and Valerie Novitzka. "Linear logic in computer science." Journal of Applied Mathematics and Computational Mechanics 14, no. 1 (March 2015): 91–100. http://dx.doi.org/10.17512/jamcm.2015.1.09.

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Iashin, Boris Leonidovich. "Non-Classical Logics in Modern Science." Философская мысль, no. 1 (January 2023): 15–25. http://dx.doi.org/10.25136/2409-8728.2023.1.39350.

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Non-classical logicians have significantly expanded the traditional field of using logical methods. The first of them was the three-digit logic of Y. Lukasevich. Next came the three-digit logic of A. Bochvar, the "quantum logics" of G. Reichenbach and P. Detush-Fevrier, infinite-valued, probabilistic and other logics. The possibilities of non-classical logics have become widely used in various branches of scientific knowledge. Polysemantic, fuzzy, intuitionistic, modal, relevant and paranoherent, temporal and other non-classical logics are widely used today in physics, computational mathematics, computer science, linguistics, jurisprudence, ethics and other fields of natural science and socio-humanitarian knowledge. The recently increased interest in non-classical logics is explained, first of all, by the fact that various philosophical, syntactic, semantic and metalogical problems that were previously discussed in the scientific community are being replaced by practical interests. The main source of such interest is their wide application in computer science, artificial intelligence and programming. The logic of causality is used in the interpretation of the concepts of "law of nature", "ontological necessity" and "determinism"; temporal modal logics - for modeling, specification and verification of software systems of logical control; logics with vector semantics, combining the features of fuzzy and para-contradictory logics - in solving problems of dynamic verification of production knowledge bases and expert systems.

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Rota, Gian-Carlo. "Mathematical logic and theoretical computer science." Advances in Mathematics 72, no. 1 (November 1988): 168. http://dx.doi.org/10.1016/0001-8708(88)90023-0.

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Bringsjord, Selmer. "Computer Science as Immaterial Formal Logic." Philosophy & Technology 33, no. 2 (August 5, 2019): 339–47. http://dx.doi.org/10.1007/s13347-019-00366-7.

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Hoogewijs, Albert. "Partial-predicate logic in computer science." Acta Informatica 24, no. 4 (August 1987): 381–93. http://dx.doi.org/10.1007/bf00292109.

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Blass, Andreas. "Symbioses between mathematical logic and computer science." Annals of Pure and Applied Logic 167, no. 10 (October 2016): 868–78. http://dx.doi.org/10.1016/j.apal.2014.04.018.

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DeMol, Liesbeth. "Logic, Programming, and Computer Science: Local Perspectives." IEEE Annals of the History of Computing 43, no. 4 (October 1, 2021): 5–9. http://dx.doi.org/10.1109/mahc.2021.3121578.

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Vardi, Moshe Y. "Special selection in logic in computer science." Journal of Symbolic Logic 62, no. 2 (June 1997): 608. http://dx.doi.org/10.2307/2275549.

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Hamburger, Henry, and Dana Richards. "Logic and language models for computer science." ACM SIGACT News 33, no. 1 (March 2002): 67–70. http://dx.doi.org/10.1145/507457.507471.

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Gaboardi, Marco, and Igor Walukiewicz. "Report on Logic in Computer Science (LICS'23)." ACM SIGLOG News 10, no. 4 (October 2023): 44–45. http://dx.doi.org/10.1145/3636362.3636370.

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Th 38th Annual ACM/ IEEE Symposium on Logic in Computer Science (LICS), took place at Boston University, Boston, USA, from June 26 to June 29, 2023, with co-located events taking place on June 24 and June 25. Five workshops were co-located with LICS 2023: combinatorial games in finite model theory, the decision problem in first order logic, international workshop on quantitative logical method, structure meets power, and the logic mentoring workshop.

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Colburn, T. R., and G. M. Shute. "Metaphor in computer science." Journal of Applied Logic 6, no. 4 (December 2008): 526–33. http://dx.doi.org/10.1016/j.jal.2008.09.005.

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Kamide, Norihiro. "Inconsistency-Tolerant Multi-Agent Calculus." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, no. 06 (December 2014): 815–29. http://dx.doi.org/10.1142/s0218488514500433.

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Verifying and specifying multi-agent systems in an appropriate inconsistency-tolerant logic are of growing importance in Computer Science since computer systems are generally used by or composed of inconsistency-tolerant multi-agents. In this paper, an inconsistency-tolerant logic for representing multi-agents is introduced as a Gentzen-type sequent calculus. This logic (or calculus) has multiple negation connectives that correspond to each agent, and these negation connectives have the property of paraconsistency that guarantees inconsistency-tolerance. The logic proposed is regarded as a modified generalization of trilattice logics, which are known to be useful for expressing fine-grained truth-values in computer networks. The completeness, cut-elimination and decidability theorems for the proposed logic (or sequent calculus) are proved as the main results of this paper.

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Goodman, Nicolas D. "R. E. Davis. Truth, deduction, and computation. Logic and semantics for computer science. Principles of computer science series. Computer Science Press, New York1989, xv + 265 pp." Journal of Symbolic Logic 57, no. 2 (June 1992): 760–61. http://dx.doi.org/10.2307/2275313.

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Turner, Raymond, and Amnon H. Eden. "The Philosophy of Computer Science." Journal of Applied Logic 6, no. 4 (December 2008): 459. http://dx.doi.org/10.1016/j.jal.2008.09.006.

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Gadducci, Fabio, and Ugo Montanari. "Comparing logics for rewriting: rewriting logic, action calculi and tile logic." Theoretical Computer Science 285, no. 2 (August 2002): 319–58. http://dx.doi.org/10.1016/s0304-3975(01)00362-0.

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Gorla, Daniele. "The 2021 experience of logic in computer science." ACM SIGLOG News 8, no. 4 (October 2021): 23–24. http://dx.doi.org/10.1145/3527372.3527376.

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I would have liked to start this report by saying that the 36th edition of the ACM/IEEE Symposium on Logic in Computer Science (LICS) took place in Rome, from June 29th to July 2nd, 2021. As general chair of the conference, I tried as hard as possible to have at least a hybrid event since, due to the COVID pandemic, it was clear that a fully-in-presence event was impossible. However, in February 2021, the Steering Committee and I had to give up and turn to a fully-online event (through Zoom), like what happened for LICS 2020 and for all conferences since March 2020 until today.

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Frias, Marcelo F., Gabriel A. Baum, and Armando M. Haeberer. "Fork Algebras in Algebra, Logic and Computer Science." Fundamenta Informaticae 32, no. 1 (1997): 1–25. http://dx.doi.org/10.3233/fi-1997-32101.

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HABIBALLA, Hashim, and Tibor KMET. "Mathematical Logic and Deduction in Computer Science Education." Informatics in Education 7, no. 1 (April 15, 2008): 75–90. http://dx.doi.org/10.15388/infedu.2008.05.

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Bottino, Rosa Maria, Paola Forcheri, and Maria Teresa Molfino. "Teaching computer science through a logic programming approach." Education and Computing 4, no. 2 (1988): 71–76. http://dx.doi.org/10.1016/s0167-9287(88)90535-3.

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Awwad, Mohamad. "FROM BOOLE’S LOGIC TO BOOLEAN APPLICATIONS IN COMPUTER SCIENCE." Educational Discourse: collection of scientific papers, no. 32(4) (May 5, 2021): 18–25. http://dx.doi.org/10.33930/ed.2019.5007.32(4)-2.

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The developments of an algebraic logical language of thoughts by G. Boole are considered using historical and theoretical perspectives. The technical implementations of Boolean logic in combinational circuits and in modern cryptography show strong influences of a 19th century logic on the latest technologies of computing.

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Copeland, B. Jack, and Zhao Fan. "Turing and Von Neumann: From Logic to the Computer." Philosophies 8, no. 2 (March 9, 2023): 22. http://dx.doi.org/10.3390/philosophies8020022.

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This article provides a detailed analysis of the transfer of a key cluster of ideas from mathematical logic to computing. We demonstrate the impact of certain of Turing’s logico-philosophical concepts from the mid-1930s on the emergence of the modern electronic computer—and so, in consequence, Turing’s impact on the direction of modern philosophy, via the computational turn. We explain why both Turing and von Neumann saw the problem of developing the electronic computer as a problem in logic, and we describe their joint journey from logic to electronic computation. While much has been written about Turing’s and von Neumann’s individual contributions to the development of the computer, this article investigates less well-known terrain: their interactions and mutual influences. Along the way we argue against ‘logic skeptics’ and ‘Turing skeptics’, who claim that neither logic nor Turing played any significant role in the creation of the modern computer.

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Oliveira, Kleidson Êglicio Carvalho da Silva. "Paraconsistent Logic Programming in Three and Four-Valued Logics." Bulletin of Symbolic Logic 28, no. 2 (June 2022): 260. http://dx.doi.org/10.1017/bsl.2021.34.

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AbstractFrom the interaction among areas such as Computer Science, Formal Logic, and Automated Deduction arises an important new subject called Logic Programming. This has been used continuously in the theoretical study and practical applications in various fields of Artificial Intelligence. After the emergence of a wide variety of non-classical logics and the understanding of the limitations presented by first-order classical logic, it became necessary to consider logic programming based on other types of reasoning in addition to classical reasoning. A type of reasoning that has been well studied is the paraconsistent, that is, the reasoning that tolerates contradictions. However, although there are many paraconsistent logics with different types of semantics, their application to logic programming is more delicate than it first appears, requiring an in-depth study of what can or cannot be transferred directly from classical first-order logic to other types of logic.Based on studies of Tarcisio Rodrigues on the foundations of Paraconsistent Logic Programming (2010) for some Logics of Formal Inconsistency (LFIs), this thesis intends to resume the research of Rodrigues and place it in the specific context of LFIs with three- and four-valued semantics. This kind of logics are interesting from the computational point of view, as presented by Luiz Silvestrini in his Ph.D. thesis entitled “A new approach to the concept of quase-truth” (2011), and by Marcelo Coniglio and Martín Figallo in the article “Hilbert-style presentations of two logics associated to tetravalent modal algebras” [Studia Logica (2012)]. Based on original techniques, this study aims to define well-founded systems of paraconsistent logic programming based on well-known logics, in contrast to the ad hoc approaches to this question found in the literature.Abstract prepared by Kleidson Êglicio Carvalho da Silva Oliveira.E-mail: kecso10@yahoo.com.brURL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/322632

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Bezerra, Edson Vinícius. "Society semantics for four-valued Łukasiewicz logic." Logic Journal of the IGPL 28, no. 5 (November 29, 2018): 892–911. http://dx.doi.org/10.1093/jigpal/jzy066.

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AbstractWe argue that many-valued logics (MVLs) can be useful in analysing informational conflicts by using society semantics (SSs). This work concentrates on four-valued Łukasiewicz logic. SSs were proposed by Carnielli and Lima-Marques (1999, Advances in Contemporary Logic and Computer Science, 235, 33–52) to deal with conflicts of information involving rational agents that make judgements about propositions according to a given logic within a society, where a society is understood as a collection $\mathcal{A}$ of agents. The interesting point of such semantics is that a new logic can be obtained by combining the logic of the agents under some appropriate rules. Carnielli and Lima-Marques (1999, Advances in Contemporary Logic and Computer Science, 235, 33–52) defined SSs for the three-valued logics $I^{1}$ and $P^{1}$. In this kind of semantics, all the agents reason according to classical logic (CL) and the molecular formulas behave in the same way as in CL (the non-classical character of these logics only appears at the propositional level). Marcos (unpublished data) provided SSs with classical agents for the three-valued Łukasiewicz logic Ł$_{3}$, but in this case, the molecular formulas do not behave classically. We prove here that one can characterize Ł$_{4}^{\prime}$, a conservative extension of Ł$_{4}$ obtained by adding a connective $\blacktriangledown$, by means of a closed society where the agents reason according to Ł$_{3}$. We shall emphasize the importance of recovery operators in the construction of this class of societies. Moreover, we shall relate this semantics to Suszko’s view on the ‘two-valuedness’ of logic.

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VALDERRAMA GARRIDO, YUDELKIS, and WALFREDO GONZÁLEZ HERNÁNDEZ. "LA LÓGICA MATEMÁTICA DESDE LAS DISCIPLINAS CIENTÍFICAS DE INFORMÁTICA." Revista Ingeniería, Matemáticas y Ciencias de la Información 6, no. 12 (July 19, 2019): 37–48. http://dx.doi.org/10.21017/rimci.2019.v6.n12.a65.

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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 (October 26, 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 pure and applied mathematical sciences (=mathematical logic), and the “intensional” modal logics of the philosophical disciplines (=philosophical logic). It is particularly significant in this categorical framework the possibility of extending the operator algebra formalism from (quantum and classical) physics to logic, via the so-called “Boolean algebras with operators” (BAOs), with this extension being the core of our formal ontology. In this context, I discuss the relevance of the algebraic Hopf coproduct and colimit operations, and then of the category of coalgebras in the computations over lattices of quantum numbers in the quantum field theory (QFT), interpreted as the fundamental physics. This coalgebraic formalism is particularly relevant for modeling the notion of the “quantum vacuum foliation” in QFT of dissipative systems, as a foundation of the notion of “complexity” in physics, and “memory” in biological and neural systems, using the powerful “colimit” operators. Finally, I suggest that in the CT logic, the relational semantics of BAOs, applied to the modal coalgebraic relational logic of the “possible worlds” in Kripke’s model theory, is the proper logic of the formal ontology and epistemology of the natural realism, as a formalized philosophy of nature and sciences.

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Wagner-D�bler, Roland. "Science-technology coupling: The case of mathematical logic and computer science." Journal of the American Society for Information Science 48, no. 2 (February 1997): 171–83. http://dx.doi.org/10.1002/(sici)1097-4571(199702)48:2<171::aid-asi7>3.0.co;2-v.

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Bala, Romi, and Hemant Pandey. "Mathematical Logic: Foundations and Beyond." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9, no. 3 (December 17, 2018): 1405–11. http://dx.doi.org/10.61841/turcomat.v9i3.14599.

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Mathematical logic serves as the cornerstone of formal reasoning, providing precise tools for analyzing the structure and validity of arguments. This paper offers a comprehensive exploration of key topics in mathematical logic, spanning from classical propositional and predicate logic to modal logic and non-classical logics. It examines the syntactic and semantic aspects of various logical systems, delves into proof theory and computational complexity, and explores applications in diverse fields such as mathematics, computer science, philosophy, and linguistics. By elucidating the fundamental principles and practical implications of mathematical logic, this paper highlights its pivotal role in advancing knowledge and addressing complex challenges across disciplines.

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Kuznetsov, Stepan. "Action Logic is Undecidable." ACM Transactions on Computational Logic 22, no. 2 (May 15, 2021): 1–26. http://dx.doi.org/10.1145/3445810.

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Action logic is the algebraic logic (inequational theory) of residuated Kleene lattices. One of the operations of this logic is the Kleene star, which is axiomatized by an induction scheme. For a stronger system that uses an -rule instead (infinitary action logic), Buszkowski and Palka (2007) proved -completeness (thus, undecidability). Decidability of action logic itself was an open question, raised by Kozen in 1994. In this article, we show that it is undecidable, more precisely, -complete. We also prove the same undecidability results for all recursively enumerable logics between action logic and infinitary action logic, for fragments of these logics with only one of the two lattice (additive) connectives, and for action logic extended with the law of distributivity.

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Normann, Dag. "Computing with Functionals—Computability Theory or Computer Science?" Bulletin of Symbolic Logic 12, no. 1 (March 2006): 43–59. http://dx.doi.org/10.2178/bsl/1140640943.

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AbstractWe review some of the history of the computability theory of functionals of higher types, and we will demonstrate how contributions from logic and theoretical computer science have shaped this still active subject.

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Halpern, Joseph Y., Robert Harper, Neil Immerman, Phokion G. Kolaitis, Moshe Y. Vardi, and Victor Vianu. "On the Unusual Effectiveness of Logic in Computer Science." Bulletin of Symbolic Logic 7, no. 2 (March 2001): 213–36. http://dx.doi.org/10.2307/2687775.

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In 1960, E. P. Wigner, a joint winner of the 1963 Nobel Prize for Physics, published a paper titled On the Unreasonable Effectiveness of Mathematics in the Natural Sciences [61]. This paper can be construed as an examination and affirmation of Galileo's tenet that “The book of nature is written in the language of mathematics”. To this effect, Wigner presented a large number of examples that demonstrate the effectiveness of mathematics in accurately describing physical phenomena. Wigner viewed these examples as illustrations of what he called the empirical law of epistemology, which asserts that the mathematical formulation of the laws of nature is both appropriate and accurate, and that mathematics is actually the correct language for formulating the laws of nature. At the same time, Wigner pointed out that the reasons for the success of mathematics in the natural sciences are not completely understood; in fact, he went as far as asserting that “… the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.”

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Martin, Ursula. "Panelist position statement: logic and models in computer science." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, no. 1835 (September 6, 2005): 2397–99. http://dx.doi.org/10.1098/rsta.2005.1654.

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Brown, Mark A., and Jose Carno. "Third international workshop on deontic logic in computer science." Knowledge Engineering Review 11, no. 3 (September 1996): 289–92. http://dx.doi.org/10.1017/s0269888900007931.

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The Third International Workshop on Deontic Logic in Computer Science (ΔEON'96) took place in Sesimbra, Portugal, from 11–13 January 1996. It consisted of 12 refereed technical presentations and four invited talks. The invited speakers were Nuel Belnap (Pittsburgh University, USA), Andrew Jones (Oslo University, Norway), Krister Segerberg (Uppsala University, Sweden) and Marek Sergot (Imperial College, UK).

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Myers, J. Paul. "The central role of mathematical logic in computer science." ACM SIGCSE Bulletin 22, no. 1 (February 1990): 22–26. http://dx.doi.org/10.1145/319059.319071.

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Goranko, Valentin. "Logic in Computer Science: Modelling and Reasoning About Systems." Journal of Logic, Language and Information 16, no. 1 (September 30, 2006): 117–20. http://dx.doi.org/10.1007/s10849-006-9017-y.

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KIKOT, STANISLAV, AGI KURUCZ, YOSHIHITO TANAKA, FRANK WOLTER, and MICHAEL ZAKHARYASCHEV. "KRIPKE COMPLETENESS OF STRICTLY POSITIVE MODAL LOGICS OVER MEET-SEMILATTICES WITH OPERATORS." Journal of Symbolic Logic 84, no. 02 (April 3, 2019): 533–88. http://dx.doi.org/10.1017/jsl.2019.22.

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AbstractOur concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same consequence relations for a given spi-logic.

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Purser, David. "SIGLOG Monthly 230." ACM SIGLOG News 9, no. 4 (October 2022): 44–49. http://dx.doi.org/10.1145/3583660.3583667.

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The ACM Special Interest Group on Logic (SIGLOG), the European Association for Theoretical Computer Science (EATCS), the European Association for Computer Science Logic (EACSL), and the Kurt Goedel Society (KGS) are pleased to announce that

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Krajíček, Jan. "Hardness assumptions in the foundations of theoretical computer science." Archive for Mathematical Logic 44, no. 6 (May 3, 2005): 667–75. http://dx.doi.org/10.1007/s00153-005-0279-x.

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Gasarch, William I. "Eitan Gurari. An introduction to the theory of computation. Principles of computer science series. Computer Science Press, Rockville, Md., 1989, xii + 314 pp." Journal of Symbolic Logic 56, no. 1 (March 1991): 338–39. http://dx.doi.org/10.2307/2274932.

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Kupke, Clemens, Dirk Pattinson, and Lutz Schröder. "Coalgebraic Reasoning with Global Assumptions in Arithmetic Modal Logics." ACM Transactions on Computational Logic 23, no. 2 (April 30, 2022): 1–34. http://dx.doi.org/10.1145/3501300.

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We establish a generic upper bound ExpTime for reasoning with global assumptions (also known as TBoxes) in coalgebraic modal logics. Unlike earlier results of this kind, our bound does not require a tractable set of tableau rules for the instance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that potentially avoids building the entire exponential-sized space of candidate states, and thus offers a basis for practical reasoning. This algorithm still involves frequent fixpoint computations; we show how these can be handled efficiently in a concrete algorithm modelled on Liu and Smolka’s linear-time fixpoint algorithm. Finally, we show that the upper complexity bound is preserved under adding nominals to the logic, i.e., in coalgebraic hybrid logic.

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Robinson, J. A. "Logic and logic programming." Communications of the ACM 35, no. 3 (March 1992): 40–65. http://dx.doi.org/10.1145/131295.131296.

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YUEN, TIMOTHY T., MARITZA REYES, and YUANLIN ZHANG. "Introducing Computer Science to High School Students Through Logic Programming." Theory and Practice of Logic Programming 19, no. 2 (November 14, 2018): 204–28. http://dx.doi.org/10.1017/s1471068418000431.

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AbstractThis paper investigates how high school students in an introductory computer science (CS) course approach computing in the logic programming (LP) paradigm. This qualitative study shows how novice students operate within the LP paradigm while engaging in foundational computing concepts and skills: students are engaged in a cyclical process of abstraction, reasoning, and creating representations of their ideas in code while also being informed by the (procedural) requirements and the revision/debugging process. As these computing concepts and skills are also expected in traditional approaches to introductory K-12 CS courses, this paper asserts that LP is a viable paradigm choice for high school novices.

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Kneuper, Ralf. "Truth, deduction and computation: Logic and semantics for computer science." Science of Computer Programming 15, no. 2-3 (December 1990): 249–51. http://dx.doi.org/10.1016/0167-6423(90)90089-v.

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Basti, Gianfranco, Antonio Capolupo, and Giuseppe Vitiello. "Quantum field theory and coalgebraic logic in theoretical computer science." Progress in Biophysics and Molecular Biology 130 (November 2017): 39–52. http://dx.doi.org/10.1016/j.pbiomolbio.2017.04.006.

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Sajid, Naseer Ahmed, Muhammad Tanvir Afzal, and Muhammad Abdul Qadir. "Multi-label classification of computer science documents using fuzzy logic." Journal of the National Science Foundation of Sri Lanka 44, no. 2 (June 30, 2016): 155. http://dx.doi.org/10.4038/jnsfsr.v44i2.7996.

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Clavel, Manuel. "Reflection in General Logics, Rewriting Logic, and Maude." Electronic Notes in Theoretical Computer Science 15 (1998): 71–82. http://dx.doi.org/10.1016/s1571-0661(05)82553-8.

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Zantema, Hans, and Jan Friso Groote. "Transforming equality logic to propositional logic." Electronic Notes in Theoretical Computer Science 86, no. 1 (May 2003): 162–73. http://dx.doi.org/10.1016/s1571-0661(04)80661-3.

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Clavel, Manuel, José Meseguer, and Miguel Palomino. "Reflection in Membership Equational Logic, Many-Sorted Equational Logic, Horn Logic with Equality, and Rewriting Logic." Electronic Notes in Theoretical Computer Science 71 (April 2004): 110–26. http://dx.doi.org/10.1016/s1571-0661(05)82531-9.

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Clavel, Manuel, José Meseguer, and Miguel Palomino. "Reflection in membership equational logic, many-sorted equational logic, Horn logic with equality, and rewriting logic." Theoretical Computer Science 373, no. 1-2 (March 2007): 70–91. http://dx.doi.org/10.1016/j.tcs.2006.12.009.

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Grädel, Erich, and Richard Wilke. "Logics with Multiteam Semantics." ACM Transactions on Computational Logic 23, no. 2 (April 30, 2022): 1–30. http://dx.doi.org/10.1145/3487579.

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Team semantics is the mathematical basis of modern logics of dependence and independence. In contrast to classical Tarski semantics, a formula is evaluated not for a single assignment of values to the free variables, but on a set of such assignments, called a team. Team semantics is appropriate for a purely logical understanding of dependency notions, where only the presence or absence of data matters, but being based on sets, it does not take into account multiple occurrences of data values. It is therefore insufficient in scenarios where such multiplicities matter, in particular for reasoning about probabilities and statistical independencies. Therefore, an extension from teams to multiteams (i.e. multisets of assignments) has been proposed by several authors. In this paper we aim at a systematic development of logics of dependence and independence based on multiteam semantics. We study atomic dependency properties of finite multiteams and discuss the appropriate meaning of logical operators to extend the atomic dependencies to full-fledged logics for reasoning about dependence properties in a multiteam setting. We explore properties and expressive power of a wide spectrum of different multiteam logics and compare them to second-order logic and to logics with team semantics. In many cases the results resemble what is known in team semantics, but there are also interesting differences. While in team semantics, the combination of inclusion and exclusion dependencies leads to a logic with the full power of both independence logic and existential second-order logic, independence properties of multiteams are not definable by any combination of properties that are downwards closed or union closed and thus are strictly more powerful than inclusion-exclusion logic. We also study the relationship of logics with multiteam semantics with existential second-order logic for a specific class of metafinite structures. It turns out that inclusion-exclusion logic can be characterised in a precise sense by the Presburger fragment of this logic, but for capturing independence, we need to go beyond it and add some form of multiplication. Finally, we also consider multiteams with weights in the reals and study the expressive power of formulae by means of topological properties.

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Journal articles on the topic 'Logic in Computer Science'

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