Skip to main content
SpringerLink
Log in

Relevant logic and the theory of information

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

This paper provides an interpretation of the Routley-Meyer semantics for a weak negation-free relevant logic using Israel and Perry's theory of information. In particular, Routley and Meyer's ternary accessibility relation is given an interpretation in information-theoretic terms.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, A. R. and N. D. Belnap Jr.: 1975, Entailment: Logic of Relevance and Necessity, Vol. 1, Princeton University Press, Princeton.

    Google Scholar 

  • Anderson, A. R., N. D. Belnap, Jr., and J. M. Dunn: 1992, Entailment: Logic of Relevance and Necessity, Vol. 2, Princeton University Press, Princeton.

    Google Scholar 

  • Barwise, J.: 1989, The Situation in Logic, CSLI, Stanford.

  • Barwise, J.: 1989a, ‘On the Model Theory of Common Knowledge’, in Barwise 1989, pp. 203–220.

  • Barwise, J., J. M. Gawron, G. Plotkin, and S. Tutiya: 1981, Situation Theory and its Applications, Vol. 2, Stanford.

  • Barwise, J. and J. Perry: 1983, Situations and Attitudes, MIT Press, Cambridge, MA.

    Google Scholar 

  • Barwise, J. and J. Perry: 1985, ‘Shifting Situations and Shaken Attitudes: An Interview with Barwise and Perry’, Linguistics and Philosophy 8, 105–161.

    Google Scholar 

  • Copeland, B. J.: 1979, ‘When is a Semantics Not a Semantics: Some Reasons for Disliking the Routley-Meyer Semantics for Relevance Logic’, Journal of Philosophical Logic 8, 399–413.

    Google Scholar 

  • Cooper, R.: 1991, ‘Persistence and Structural Determination’, in Barwise et al. 1991, pp. 295–309.

  • Cooper, R. and J. Kamp: 1991, ‘Negation in Situation Semantics and Discourse Representation Theory’, in Barwise et al. 1991, pp. 311–33.

  • Cresswell, M. J.: 1988, ‘The World Situation (It's a Small World After All)’, in Semantical Essays. Possible Worlds and Their Rivals, Kluwer, Reidel, pp. 65–77.

    Google Scholar 

  • Devlin, K.: 1991, Logic and Information, Cambridge University Press, Cambridge.

    Google Scholar 

  • Dretske, F.: 1981, Knowledge and the Flow of Information, MIT Press, Cambridge, MA.

    Google Scholar 

  • Fine, K.: 1974, ‘Models for Entailment’, Journal of Philosophical Logic 3, 347–72.

    Google Scholar 

  • Israel, D. and J. Perry: 1990, ‘What is Information?’, in P. P. Hanson (ed.), Information, Language, and Cognition, University of British Columbia Press, Vancouver, pp. 1–19.

    Google Scholar 

  • Israel, D. and J. Perry: 1991, ‘Information and Architecture’, in Barwise et al. 1991, pp. 147–59.

  • Restall, G.: 1994, On Logics Without Contraction, University of Queensland Dissertation, Brisbane.

    Google Scholar 

  • Restall, G.: 1996, ‘Information Flow and Relevant Logics’, in J. Seligman and D. Westerstahl (eds.), Logic, Language and Computation, CSLI, Stanford, pp. 463–77.

    Google Scholar 

  • Routley, F. R and R. K. Meyer: 1972, ‘The Semantics of Entailment II’, Journal of Philosophical Logic 1, 53–73.

    Google Scholar 

  • Routley, F. R. and R. K. Meyer: 1972, ‘The Semantics of Entailment III’, Journal of Philosophical Logic 1, 192–208.

    Google Scholar 

  • Routley, F. R. and R. K. Meyer: 1973, ‘The Semantics of Entailment (I)’, in H. Leblanc (ed.), Truth, Syntax and Modality, North Holland, Amsterdam, pp. 199–243.

    Google Scholar 

  • Routley, F. R. and R. K. Meyer: 1976, ‘Every Sentential Logc Has a Two-Valued Semantics’, Logique et analyse n.s. 19, 345–65.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Philosophy Department, Victoria University of Wellington, Wellington, New Zealand

    Edwin D. Mares

Authors
  1. Edwin D. Mares
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

I am indebted to Max Cresswell for invariable conversations relating to the topic and encouraging me to provide a philosophical explanation of the ternary semantics for relevant logic and to Errol Martin also for useful discussions and encouragement. I am also grateful to Greg Restall who made his work available to me while I was finishing this project. While working on this project, I was supported by a grant from the Centre for Information Science Research at The Australian National University. I am grateful to John Slaney and Michael McRobbie for securing this grant. I gave an earlier version of this paper to the Basser School of Computer Science at the University of Sydney and to the philosophy department at Victoria University of Wellington. I thank all those in attendance especially John Bacon, Norman Foo, Abhaya Nayak, Kim Sterelny, and James Maclaurin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mares, E.D. Relevant logic and the theory of information. Synthese 109, 345–360 (1996). https://doi.org/10.1007/BF00413865

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00413865

Keywords

Search

Navigation