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.
Similar content being viewed by others
References
R. K. Meyer and R. Routley, Classical relevant logics I, Studia Logica 32 (1973), pp. 51–68.
R. K. Meyer and R. Routley, Classical relevant logics II, Studia Logica 33 (1974), pp. 183–94.
R. K. Meyer, New axiomatics for relevant logics I, Journal of Philosophical Logic 3 (1974), pp. 53–68.
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.
R. K. Meyer, Why I Am Not a Relevantist, Research Paper No. 1, Logic Group, Australian National University, Canberra, 1979.
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.
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.
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.
R. Routley, V. Plumwood, R. K. Meyer and R. T. Brady, Relevant Logics and Their Rivals. Ridgeview, Atascadero, CA, 1982.
S. Giambrone, Gentzen Systems and Decision Procedures for Relevant Logics, Australian National University Doctoral Dissertation, Canberra, 1982.
A. R. Anderson and N. D. Belnap, Jr., Entailment: The Logic of Relevance and Necessity, vol. 1. Princeton University Press, Princeton, 1975.
S. Giambrone, TW + and RW + are decidable, Journal of Philosophical Logic 14 (1985), pp. 235–54.
J.-Y. Girard, Linear Logic, Equipe de Logique Mathematique, Universite Paris, 1986.
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.
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.
A. Q. Abraham, The Semantics of Classical Relevant Logics, University of Canterbury Masters of Science Thesis, 1977.
R. Routley and R. K. Meyer, The semantics of entailment III, Journal of Philosophical Logic 1 (1972), pp. 192–208.
R. Routley and R. K. Meyer, The semantics of entailment IV: E, π′, π″, Appendix 1 of [9].
J. Slaney, A meta-completeness theorem for contraction-free relevant logics, Studia Logica 43 (1984), pp. 159–68.
R. K. Meyer, Metacompleteness, Notre Dame Journal of Formal Logic 17 (1976), pp. 501–516.
R. K. Meyer, S. Giambrone and R. T. Brady, Where gamma fails, Studia Logica 43 (1984), pp. 247–56.
R. Routley, Relevantism, material detachment and the disjunctive syllogism argument, Canadian Journal of Philosophy (1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Giambrone, S., Meyer, R.K. Completeness and conservative extension results for some boolean relevant logics. Stud Logica 48, 1–14 (1989). https://doi.org/10.1007/BF00370629
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00370629