Skip to main content
SpringerLink
Log in

The Relevance of Relevance to Relevance Logic

  • Conference paper
Logic and Its Applications (ICLA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8923))

Included in the following conference series:

Abstract

I explore the question of whether the concept of relevance is relevant to the study of what Anderson and Belnap call “relevance logic.” The answer should be “Of course!” But there are some twists and turns, as is shown by the fact that it has taken over 50 years to get here. Despite protests by R. K. Meyer that the concept of relevance is not part of what he calls “relevant logic,” I suggest and defend interpreting the Routley–Meyer ternary accessibility relation using information states a, b, c, so Rabc means “in the context a, b is relevant to c.” Motivations are provided from Sperber and Wilson’s work in linguistics on relevance.

This is part of a larger joint project with Katalin Bimbó, supported by an Insight Grant from the Social Sciences and Humanities Research Council of Canada: “The Third Place is the Charm: The Emergence, the Development and the Future of the Ternary Relational Semantics for Relevance and Some Other Non-classical Logics.” I thank Kata for reading the manuscript and for her corrections/suggestions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderson, A., Belnap, N.: Entailment: The Logic of Relevance and Necessity, vol. I. Princeton University Press (1975)

    Google Scholar 

  • Anderson, A., Belnap, N., Dunn, J.M.: Entailment: The Logic of Relevance and Necessity, vol. II. Princeton University Press (1992)

    Google Scholar 

  • Beall, J.C., Brady, R., Dunn, J.M., Hazen, A.P., Mares, E., Meyer, R.K., Priest, G., Restall, G., Ripley, R., Slaney, J., Sylvan (formerly Routley, R.): On the Ternary Relation and Conditionality. The Journal of Philosophical Logic 41, 595–612 (2012)

    Google Scholar 

  • Belnap, N.D.: A Useful Four-valued Logic. In: Dunn, J.M., Epstein, G. (eds.) Modern Uses of Multiple-Valued Logic, pp. 8–37. D. Reidel, Dordrecht (1977a)

    Google Scholar 

  • Belnap, N.D.: How a Computer Should Think. In: Ryle, G. (ed.) Contemporary Aspects of Philosophy, pp. 30–55. Oriel Press Ltd., Stocksfield (1977b)

    Google Scholar 

  • van Benthem, J.: Review of “On when a semantics is not a semantics” by B. J. Copeland. The Journal of Symbolic Logic 49, 994–995 (1984)

    Article  Google Scholar 

  • Białynicki, A., Rasiowa, H.: On the Representation of Quasi-Boolean Algebras. Bulletin de l’Académie Polonaize des Sciences 5, 259–261

    Google Scholar 

  • Copeland, B.J.: On When a Semantics Is Not a Semantics: Some Reasons for Disliking the Routley–Meyer Semantics for Relevance Logic. Journal of Philosophical Logic 8, 399–413 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  • Dunn, J.M.: The Algebra of Intensional Logics, Ph.D. Dissertation, University of Pittsburgh, University Microfilms (1966)

    Google Scholar 

  • Dunn, J.M.: Natural Language versus Formal Language. In: Joint Symposium of the Association for Symbolic Logic and the American Philosophical Association (December 1969), On-line with historical introduction at http://www.philosophy.indiana.edu/people/papers/natvsformal.pdf

  • Dunn, J.M.: Intuitive Semantics for First Degree Entailments and Coupled Trees. Philosophical Studies 29, 149–168 (1976)

    Article  MathSciNet  Google Scholar 

  • Dunn, J.M.: Relevance Logic and Entailment. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 3, pp. 117–224. D. Reidel, Dordrecht (1986); Updated as Dunn, J.M., Restall, G.: Relevance Logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 6, pp. 1–128. Kluwer Academic Publishers (2002)

    Google Scholar 

  • Dunn, J.M.: Star and Perp: Two Treatments of Negation. In: Tomberlin, J. (ed.) Philosophical Perspectives. Language and Logic, vol. 7, pp. 331–357 (1993)

    Google Scholar 

  • Dunn, J.M.: A Comparative Study of Various Semantical Treatments of Negation: A History of Formal Negation. In: Gabbay, D., Wansing, H. (eds.) What is Negation, pp. 23–61. Kluwer Academic Publishers (1999)

    Google Scholar 

  • Dunn, J.M.: The Concept of Information and the Development of Modern Logic. In: Stelzner, W., Stöckler, M. (eds.) Zwischen traditioneller und moderner Logik: Nichtklassische Ansatze (Non-classical Approaches in the Transition from Traditional to Modern Logic), pp. 423–447. Mentis-Verlag, Paderborn (2001a)

    Google Scholar 

  • Dunn, J.M.: Ternary Relational Semantics and Beyond: Programs as Data and Programs as Instructions. Logical Studies 7, 1–20 (2001b), http://www.logic.ru/LogStud/

  • Dunn, J.M.: Representation of Relation Algebras Using Routley–Meyer Frames. In: Anderson, C.A., Zelëny, M. (eds.) Logic, Meaning and Computation: Essays in Memory of Alonzo Church. Draft in Indiana Univ. Logic Group Preprint Series, IULG-93-28, pp. 77–108. Kluwer, Dordrecht (2001c)

    Chapter  Google Scholar 

  • Dunn, J.M.: Ternary Semantics for Dynamic Logic, Hoare Logic, Action Logic, etc. In: Smirnov’s Readings, vol. 4, pp. 70–71. Institute of Logic, Russian Academy of Sciences (2003)

    Google Scholar 

  • Dunn, J.M.: Information in Computer Science. In: van Benthem, J., Adriaans, P. (eds.) Handbook of the Philosophy of Information, pp. 581–608. Elsievier, Amsterdam (2008)

    Chapter  Google Scholar 

  • Dunn, J.M., Meyer, R.K.: Combinatory Logic and Structurally Free Logic. Journal of the Interest Group in Pure and Applied Logic 5, 505–537 (1997)

    MATH  MathSciNet  Google Scholar 

  • Fine, K.: Models for Entailment. Journal of Philosophical Logic 3, 347–372 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  • Gabbay, D.M., Woods, J.: Agenda Relevance: A Study in Formal Pragmatics in their A Practical Logic of Cognitive Systems, vol. 1. Elsevier, Amsterdam (2003)

    Google Scholar 

  • Girard, J.-Y.: Linear Logic. Theoretical Computer Science 50, 1–102 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • Grice, P.: Logic and Conversation, pp. 3–143. Harvard University, William James Lectures (1967) (In Grice (1989))

    Google Scholar 

  • Grice, P.: Studies in the Way of Words. Harvard University Press, Cambridge (1989)

    Google Scholar 

  • Maksimova, L.: A Semantics for the System E of Entailment. Bulletin of the Section of Logic, Polish Academy of Sciences, Institute of Philosophy and Sociology 2, 18–21 (1973)

    Google Scholar 

  • Mares, E.D.: Relevant Logic and the Theory of Information. Synthese 109, 345–360 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  • Mares, E.D.: ‘Four-valued’ Semantics for the Relevant Logic R. Journal of Philosophical Logic 33, 327–341 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Mares, E.D.: Relevant Logic: A Philosophical Interpretation. Cambridge University Press (2004)

    Google Scholar 

  • Meyer, R.K.: Why I Am Not a Relevantist, Research paper, no. 1, Australian National University Logic Group, Research School of Social Sciences, Canberra (1978)

    Google Scholar 

  • Meyer, R.K.: A Farewell to Entailment. In: Dorn, G., Weingartner, P. (eds.) Foundations of Logic and Linguistics: Problems and Solutions, pp. 577–636. Plenum Press, New York (1985)

    Chapter  Google Scholar 

  • Morris, C.W.: Foundations of the Theory of Signs. In: Neurath, O. (ed.) International Encyclopedia of Unified Science, vol. 1(2). University of Chicago Press, Chicago (1938)

    Google Scholar 

  • Restall, G.: Relevant and Substructural Logics. In: Gabbay, D.M., Woods, J. (eds.) Handbook of the History of Logic. Logic and Modalities in the Twentieth Century, vol. 7, pp. 289–398. Elsevier, Amsterdam (2006)

    Google Scholar 

  • Routley, R., Meyer, R.K.: The Semantics of Entailment, II, III. Journal of Philosophical Logic 1, 53–73, 192–208 (1972)

    Google Scholar 

  • Routley, R., Meyer, R.K.: The Semantics of Entailment. In: Leblanc, H. (ed.) Truth, Syntax and Modality, Proceedings of the Temple University Conference on Alternative Semantics. North-Holland, Amsterdam (1973)

    Google Scholar 

  • Routley, R., Meyer, R.K., Plumwood, V., Brady, R.: Relevant Logics and their Rivals. In: Part I, The Basic Philosophical and Semantic Theory. Ridgeview Publishing Company, Atascadero (1983)

    Google Scholar 

  • Routley, R., Routley, V.: Semantics of First Degree Entailment. Noûs 6, 335–359 (1972)

    Article  MathSciNet  Google Scholar 

  • Sperber, D., Wilson, D.: Postface to the second edition of Relevance: Communication and Cognition. Blackwell, Oxford (1995)

    Google Scholar 

  • Urquhart, A.: Semantics for Relevant Logics. The Journal of Symbolic Logic 37, 159–169 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  • Wilson, D., Sperber, D.: On Defining Relevance. In: Grandy, R., Warner, R. (eds.) Philosophical Grounds of Rationality: Intentions, Categories, Ends, pp. 143–158. Oxford University Press (1986)

    Google Scholar 

  • Wilson, D., Sperber, D.: Relevance Theory. In: Horn, L.R., Ward, G. (eds.) The Handbook of Pragmatics, pp. 607–632. Blackwell, Oxford (2004)

    Google Scholar 

  • Wilson, D., Sperber, D.: Meaning and Relevance. Cambridge University Press (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Informatics and Computing, and Department of Philosophy, Indiana University, Bloomington, USA

    J. Michael Dunn

Authors
  1. J. Michael Dunn
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Mohua Banerjee

  2. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Powai, 400076, Mumbai, India

    Shankara Narayanan Krishna

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dunn, J.M. (2015). The Relevance of Relevance to Relevance Logic. In: Banerjee, M., Krishna, S.N. (eds) Logic and Its Applications. ICLA 2015. Lecture Notes in Computer Science, vol 8923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45824-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-45824-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-45823-5

  • Online ISBN: 978-3-662-45824-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation