Advertisement

Studia Logica

, Volume 48, Issue 1, pp 1–14 | Cite as

Completeness and conservative extension results for some boolean relevant logics

  • Steve Giambrone
  • Robert K. Meyer
Article

Abstract

This paper presents completeness and conservative extension results for the boolean extensions of the relevant logic T of Ticket Entailment, and for the contractionless relevant logics TW and RW. Some surprising results are shown for adding the sentential constant t to these boolean relevant logics; specifically, the boolean extensions with t are conservative of the boolean extensions without t, but not of the original logics with t. The special treatment required for the semantic normality of T is also shown along the way.

Keywords

Special Treatment Mathematical Logic Surprising Result Computational Linguistic Relevant Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. K. Meyer and R. Routley, Classical relevant logics I, Studia Logica 32 (1973), pp. 51–68.Google Scholar
  2. [2]
    R. K. Meyer and R. Routley, Classical relevant logics II, Studia Logica 33 (1974), pp. 183–94.Google Scholar
  3. [3]
    R. K. Meyer, New axiomatics for relevant logics I, Journal of Philosophical Logic 3 (1974), pp. 53–68.Google Scholar
  4. [4]
    N. D. Belnap Jr. and J. M. Dunn, Entailment and the disjunctive syllogism, in Contemporary Philosophy: A New Survey, eds. G. Floistad and G. H. von Wright, Martinus Nijhoff, The Hague, 1981.Google Scholar
  5. [5]
    R. K. Meyer, Why I Am Not a Relevantist, Research Paper No. 1, Logic Group, Australian National University, Canberra, 1979.Google Scholar
  6. [6]
    R. Routley, Relevantism and the Problem as to When Material Detachment and the Disjunctive Syllogism Can Be Correctly Used, Research Paper No. 12, Logic Group, Australian National University, Canberra, 1983.Google Scholar
  7. [7]
    R. K. Meyer, A Farewell to entailment, in Foundations of Logic and Linguistics: Selected Papers of the 7th International Congress on Logic, Methodology and the Philosophy of Science, Salzburg, 1983, pp. 577–636.Google Scholar
  8. [8]
    R. Routley, Ultralogic as universal, Relevance Logic Newsletter 2 (1977), pp. 50–90 and pp. 138–75. Reprinted as an appendix in Exploring Meinong's Jungle and Beyond, R. Routley, Research School of the Social Sciences, Australian National University, Canberra, 1980.Google Scholar
  9. [9]
    R. Routley, V. Plumwood, R. K. Meyer and R. T. Brady, Relevant Logics and Their Rivals. Ridgeview, Atascadero, CA, 1982.Google Scholar
  10. [10]
    S. Giambrone, Gentzen Systems and Decision Procedures for Relevant Logics, Australian National University Doctoral Dissertation, Canberra, 1982.Google Scholar
  11. [11]
    A. R. Anderson and N. D. Belnap, Jr., Entailment: The Logic of Relevance and Necessity, vol. 1. Princeton University Press, Princeton, 1975.Google Scholar
  12. [12]
    S. Giambrone, TW + and RW + are decidable, Journal of Philosophical Logic 14 (1985), pp. 235–54.Google Scholar
  13. [13]
    J.-Y. Girard, Linear Logic, Equipe de Logique Mathematique, Universite Paris, 1986.Google Scholar
  14. [14]
    A. Avron, The Semantics and Proof Theory of Linear Logic, Laboratory for Foundations of Computer Science Report Series, Department of Computer Science, University of Edinburgh, Edinburgh, 1987.Google Scholar
  15. [15]
    R. Routley and R. K. Meyer, The semantics of entailment, in Truth, Syntax and Modality, ed. Hughes Leblanc, North-Holland, Amsterdam, 1973, pp. 199–243.Google Scholar
  16. [16]
    A. Q. Abraham, The Semantics of Classical Relevant Logics, University of Canterbury Masters of Science Thesis, 1977.Google Scholar
  17. [17]
    R. Routley and R. K. Meyer, The semantics of entailment III, Journal of Philosophical Logic 1 (1972), pp. 192–208.Google Scholar
  18. [18]
    R. Routley and R. K. Meyer, The semantics of entailment IV: E, π′, π″, Appendix 1 of [9].Google Scholar
  19. [19]
    J. Slaney, A meta-completeness theorem for contraction-free relevant logics, Studia Logica 43 (1984), pp. 159–68.Google Scholar
  20. [20]
    R. K. Meyer, Metacompleteness, Notre Dame Journal of Formal Logic 17 (1976), pp. 501–516.Google Scholar
  21. [21]
    R. K. Meyer, S. Giambrone and R. T. Brady, Where gamma fails, Studia Logica 43 (1984), pp. 247–56.Google Scholar
  22. [22]
    R. Routley, Relevantism, material detachment and the disjunctive syllogism argument, Canadian Journal of Philosophy (1982).Google Scholar

Copyright information

© Polish Academy of Sciences 1989

Authors and Affiliations

  • Steve Giambrone
    • 1
    • 2
  • Robert K. Meyer
    • 1
    • 2
  1. 1.University of Southwestern LouisianaUSA
  2. 2.Australian National UniversityAustralia

Personalised recommendations