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Published: 4 June 2021
Last updated: 25 January 2023

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1

Norman, Jean, and Richard Sylvan, eds. Directions in Relevant Logic. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-1005-8.

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2

Norman, Jean. Directions in Relevant Logic. Dordrecht: Springer Netherlands, 1989.

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3

Jean, Norman, and Sylvan Richard, eds. Directions in relevant logic. Dordrecht: Kluwer Academic Publishers, 1989.

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4

Relevant logic: A philosophical interpretation. Cambridge, UK: Cambridge Univeristy Press, 2004.

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5

Relevant logic: A philosophical examination of inference. Oxford, OX, UK: B. Blackwell, 1988.

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6

Shramko, Yaroslav. Intuitionismus und Relevanz. Berlin: Logos, 1999.

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7

Walton, Douglas N. Relevance in argumentation. Mahwah, NJ: L. Erlbaum Associates, 2002.

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8

Relevance in argumentation. Mahwah, N.J: L. Erlbaum Associates, 2004.

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9

Gabbay, Dov M. A practical logic of cognitive systems. Amsterdam: North Holland, 2003.

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10

Wright, Marie-Christine. A relevance logic for natural language. Manchester: University of Manchester, 1993.

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11

Bertrand Russell on modality and logical relevance. Aldershot, Hants, England: Ashgate, 1999.

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12

Hartmann, Dirk. On inferring: An enquiry into relevance and validity. Paderborn: Mentis, 2003.

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13

Hartmann, Dirk. On inferring: An enquiry into relevance and validity. Paderborn: Mentis, 2003.

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14

1930-, Belnap Nuel D., and Dunn J. Michael 1941-, eds. Entailment: The logic of relevance and necessity. 2nd ed. Princeton, N.J: Princeton University Press, 1990.

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15

Introduction à la logique pertinente. Paris: Presses universitaires de France, 2005.

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16

Heydrich, Wolfgang. Relevanzlogik und Situationssemantik. Berlin: W. de Gruyter, 1995.

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17

Tero, Tulenheimo, and Genot Emmanuel, eds. Unity, truth and the liar: The modern relevance of medieval solutions to the liar paradox. New York: Springer, 2008.

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18

The argument of the Tractatus: Its relevance to contemporary theories of logic, language, mind, and philosophical truth. Albany: State University of New York Press, 1986.

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19

Dániel, Varró, Varró Gergely, and SpringerLink (Online service), eds. Applications of Graph Transformations with Industrial Relevance: 4th International Symposium, AGTIVE 2011, Budapest, Hungary, October 4-7, 2011, Revised Selected and Invited Papers. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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20

Andrichenko, Lyudmila, A. Postnikov, L. Vasil'eva, Zh Gaunova, E. Nikitina, and Inna Plyugina. Reform of the organization of public power: the main directions of implementation. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1839416.

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The monograph examines topical issues of reforming the organization of public power in our country in connection with the adoption in 2020 of the Law on Amendments to the Constitution of the Russian Federation. The logic of changes in the organization of public power and the directions of concretization of constitutional values, taking into account the laws of the development of the constitutional system of Russia, are revealed. The most significant characteristics of the updated model of interaction of federal public authorities in accordance with the principle of separation of powers are identified, the trends of constitutional transformations in the spheres of federal relations and local self-government, ensuring the fulfillment by public authorities of international obligations of the Russian Federation are investigated. Particular attention is paid to the development of the legal mechanism of interaction between public authorities and civil society. The authors of the book take into account the results of legislative support for the reform of public power in 2020-2021, a forecast assessment of the implementation of the relevant constitutional and legislative novelties is given, including taking into account the existing legal risks. Solutions are proposed to a number of legal issues of legislative regulation of public power, which can increase the efficiency of its functioning. For researchers, teachers, students and postgraduates, deputies of representative authorities, state and municipal employees, as well as anyone interested in constitutional law issues.
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21

Muhaev, Rashid, Andrey Medushevskiy, Elena Shomina, and Alla Chernyh. Political theory. ru: INFRA-M Academic Publishing LLC., 2022. http://dx.doi.org/10.12737/1870568.

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If you want to know what role politics plays in society and how it affects you, read this textbook. In it you will find answers to questions that concern everyone. What is politics: science, art or technology of domination in the hands of the elect? Are there laws in politics, is it possible to know them and use them in the interests of society, and not just the ruling class? Why has power always been a bone of contention, what is its attractive power? Does the theory of politics have the right to claim the status of a science about the laws of the functioning of power, if all knowledge about politics is situational, relative and changeable? Why are the conclusions and recommendations of political science relevant to society often ignored by the elite? These and many other questions are answered based on the analysis of the political practices of foreign countries and Russia. The author interprets politics as a mechanism of volitional distribution of public goods, revealing its laws, exposing the hidden logic of the struggle for power, However, politics is presented not only as a mechanism for coordinating heterogeneous interests, but also as a set of beliefs, ideas, meanings that determine technologies and structures of symbolic domination and behavior patterns in the information society. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of philosophical, political science, law faculties and faculties of world politics and public and municipal administration, as well as for anyone interested in theoretical and applied problems of politics.
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22

Borzyh, Stanislav. Pananthropea. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1218149.

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The monograph is dedicated to the supercontinent Pananthropea, which was created by the efforts of people, and therefore is named in his honor. It consists of all purely geographical continents, as well as all land areas, representing a single organism that functions exactly as a whole, but at the same time divided by nature itself. The relevance of this approach is shown as follows, as described in the three chapters of the text. First, it demonstrates the physical connectivity of all regions of our planet with each other, which is expressed in a change in the logic of the topology, today planted and controlled by man. Secondly, the presence of this huge and unbroken array is evidenced by the biological component of the world economy, which we have also transformed to suit our needs, thereby redrawing the natural course of affairs in this area and turning it into a global one. Third, the same is true of the cultural domain of our life, which at some point became universal, which again was achieved for the sake of our goals and interests, as a result of which we are all now members of a single interconnected association. It is of interest to both specialists and a wide audience and will be useful for us to understand both ourselves and the reality that we have constructed.
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23

Mares, Edwin D. Relevant Logic: A Philosophical Interpretation. Cambridge University Press, 2009.

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24

Mares, Edwin D. Relevant Logic: A Philosophical Interpretation. Cambridge University Press, 2011.

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25

Mares, Edwin D. Relevant Logic: A Philosophical Interpretation. Cambridge University Press, 2004.

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26

Mares, Edwin D. Relevant Logic: A Philosophical Interpretation. Cambridge University Press, 2007.

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27

Read, Stephen. Relevant Logic: A Philosophical Examination of Inference. Blackwell Pub, 1989.

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28

(Editor), Richard Sylvan, and Ross Brady (Editor), eds. Relevant Logics and Their Rivals (Western Philosophy Series, 2). Ridgeview Publishing Company, 2003.

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29

Burgess, John P. Logic and Philosophical Methodology. Edited by Herman Cappelen, Tamar Szabó Gendler, and John Hawthorne. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199668779.013.30.

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This article explores the role of logic in philosophical methodology, as well as its application in philosophy. The discussion gives a roughly equal coverage to the seven branches of logic: elementary logic, set theory, model theory, recursion theory, proof theory, extraclassical logics, and anticlassical logics. Mathematical logic comprises set theory, model theory, recursion theory, and proof theory. Philosophical logic in the relevant sense is divided into the study of extensions of classical logic, such as modal or temporal or deontic or conditional logics, and the study of alternatives to classical logic, such as intuitionistic or quantum or partial or paraconsistent logics. The nonclassical consists of the extraclassical and the anticlassical, although the distinction is not clearcut.
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30

Tennant, Neil. Core Logic. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198777892.001.0001.

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Core Logic has unusual philosophical, proof-theoretic, metalogical, computational, and revision-theoretic virtues. It is an elegant kernel lying deep within Classical Logic, a canon for constructive and relevant deduction furnishing faithful formalizations of informal constructive mathematical proofs. Its classicized extension provides likewise for non-constructive mathematical reasoning. Confining one’s search to core proofs affords automated reasoners great gains in efficiency. All logico-semantical paradoxes involve only core reasoning. Core proofs are in normal form, and relevant in a highly exigent ‘vocabulary-sharing’ sense never attained before. Essential advances on the traditional Gentzenian treatment are that core natural deductions are isomorphic to their corresponding sequent proofs, and make do without the structural rules of Cut and Thinning. This ensures relevance of premises to conclusions of proofs, without loss of logical completeness. Every core proof converts any verifications of its premises into a verification of its conclusion. Core Logic makes one reassess the dogma of ‘unrestricted’ transitivity of deduction, because any core ‘restriction’ of transitivity ensures a more than compensatory payoff of epistemic gain: A core proof of A from X and one of B from {A}∪Y effectively determine a proof of B or of absurdity from some subset of X∪Y. The primitive introduction and elimination rules governing the logical operators in Core Logic are subtly different from Gentzen’s. They are obtained by smoothly extrapolating protean rules for determining truth values of sentences under interpretations. Core rules are inviolable: One needs all of them in order to revise beliefs rationally in light of new evidence.
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31

Brady, Ross. Relevant Logics and Their Rivals: Volume II - a Continuation of the Work of Richard Sylvan, Robert Meyer, Val Plumwood and Ross Brady. Taylor & Francis Group, 2023.

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32

Brady, Ross. Relevant Logics and Their Rivals: Volume II - a Continuation of the Work of Richard Sylvan, Robert Meyer, Val Plumwood and Ross Brady. Taylor & Francis Group, 2023.

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33

Brady, Ross. Relevant Logics and Their Rivals: Volume II - a Continuation of the Work of Richard Sylvan, Robert Meyer, Val Plumwood and Ross Brady. Taylor & Francis Group, 2023.

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34

Brady, Ross. Relevant Logics and Their Rivals: Volume II - a Continuation of the Work of Richard Sylvan, Robert Meyer, Val Plumwood and Ross Brady. Taylor & Francis Group, 2023.

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35

Brady, Ross. Relevant Logics and Their Rivals: Volume II - a Continuation of the Work of Richard Sylvan, Robert Meyer, Val Plumwood and Ross Brady. Taylor & Francis Group, 2023.

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36

Bělohlávek, Radim, Joseph W. Dauben, and George J. Klir. Fuzzy Logic in the Narrow Sense. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780190200015.003.0004.

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The chapter examines the various propositional and predicate many-valued logics that were studied prior to the emergence of the concept of a fuzzy set in the mid-1960s, which led to the genesis of fuzzy logic in broad and narrow senses. Early ideas regarding formal systems of fuzzy logic allowed for deduction from partially true premises to partially true consequences, as suggested first by Goguen in the 1960s and further developed by Pavelka in the 1970s, and these ideas were developed from the 1990s onward. The systematic development of fuzzy logics based on t-norms and their residua, pursued under the leadership of Hájek in the 1990s, is discussed in some detail. An overview is presented of fuzzy logics that are not truth-functional, such as probabilistic, possibilistic and modal fuzzy logic. The chapter concludes by reviewing relevant additional issues, such as issues of computational complexity for fuzzy logic or higher-order fuzzy logics.
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37

Tennant, Neil. The Logic of Number. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780192846679.001.0001.

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This book defines and develops the program of Natural Logicism for the natural, rational, and real numbers. The central method is to formulate rules of natural deduction governing variable-binding number-abstraction operators and other logico-mathematical expressions such as zero and successor. The introduction and elimination rules for a number-abstraction operator @ allow one to infer to, and away from, identity statements in the canonical form ‘t=@xΦ‎(x)’. These enable ‘single-barreled’ abstraction, in contrast with the ‘double-barreled’ abstraction effected by principles such as Frege's Basic Law V, or Hume's Principle. The logical system used for the foundational reasoning is free Core Logic. It handles non-denoting singular terms and allows only constructive and relevant reasoning. Natural Logicism imposes upon its account of the numbers four conditions of adequacy. First, one must show how it is that the various kinds of number are applicable in our wider thought and talk about the world. One does this by deriving all instances of three respective schemas: Schema N for the naturals, Schema Q for the rationals, and Schema R for the reals. These provide truth-conditions for statements deploying terms referring to numbers of the kind in question. Second, one must show how it is that the naturals sit among the rationals as themselves again, and the rationals likewise among the reals. Third, one should reveal enough of the metaphysical nature of the numbers to be able to derive the mathematician's basic laws governing them. Fourth, one should be able to demonstrate that there are uncountably many reals.
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38

Walton, Douglas. Relevance in Argumentation. Lawrence Erlbaum, 2003.

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39

Walton, Douglas. Relevance in Argumentation. Taylor & Francis Group, 2003.

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40

Walton, Douglas. Relevance in Argumentation. Taylor & Francis Group, 2003.

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41

Walton, Douglas. Relevance in Argumentation. Taylor & Francis Group, 2003.

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42

Walton, Douglas. Relevance in Argumentation. Taylor & Francis Group, 2003.

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43

Walton, Douglas. Relevance in Argumentation. Lawrence Erlbaum, 2003.

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44

Walton, Douglas. Relevance in Argumentation. Taylor & Francis Group, 2003.

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45

Fine, Kit. The World of Truth-Making. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198792161.003.0003.

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This chapter considers a number of different ways to develop a semantics in which statements are evaluated at partial possibilities rather than possible worlds. These include the exact version of truth-maker semantics in which truth-makers are wholly relevant to the statements they make true, the inexact version in which they are relevant, but not necessarily wholly relevant, to the statements they make true, and the loose version, in which they need only necessitate the statements they make true, regardless of relevance. The chapter explores the question of how these different semantical schemes are related; and it argues for the surprising conclusion that classical logic can only be properly accommodated within the ‘relevantist’ version of these approaches by allowing possible worlds to be among the partial possibilities. Thus, whatever reasons there might be for adopting such a semantics, they should not include a distaste for possible worlds.
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46

Tennant, Neil. The Relevance Properties of Core Logic. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198777892.003.0010.

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Ironically Anderson and Belnap argue for the rejection of Disjunctive Syllogism by means of an argument that appears to employ it. We aim to establish a ‘variable-sharing’ result for Classical Core Logic that is stronger than any such result for any other system. We define an exigent relevance condition R(X,A) on the premise-set X and the conclusion A of any proof, exploiting positive and negative occurrences of subformulae. This treatment includes first-order proofs. Our main result on relevance is that for every proof of A from X in Classical Core Logic, we have R(X,A). R(X,A) is a best possible explication of the sought notion of relevance. Our result is optimal, and challenges relevantists in the Anderson–Belnap tradition to identify any strengthening of the relation R(X,A) that can be shown to hold for some subsystem of Anderson–Belnap R but that can be shown to fail for Classical Core Logic.
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47

Woods, John, and Dov M. Gabbay. A Practical Logic of Cognitive Systems, Volume 2: The Reach of Abduction: Insight and Trial. Elsevier Science, 2005.

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48

Bertrand Russell on Modality and Logical Relevance. Taylor & Francis Group, 2018.

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49

Dejnozka, Jan. Bertrand Russell on Modality and Logical Relevance. Taylor & Francis Group, 2018.

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50

Dejnozka, Jan. Bertrand Russell on Modality and Logical Relevance. Taylor & Francis Group, 2018.

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