Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Relevant logic and the theory of information


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 to check access.


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

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

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

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

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

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

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

  8. 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.

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

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

  11. 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.

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

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

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

  15. 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.

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

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

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

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

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

  21. 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.

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

Download references

Author information

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).

Download citation


  • Accessibility Relation
  • Relevant Logic
  • Ternary Accessibility Relation