Skip to main content Accessibility help
×
Home

CONSERVATIVITY OF HEYTING IMPLICATION OVER RELEVANT QUANTIFICATION

  • ROBERT GOLDBLATT (a1)

Abstract

It is known that propositional relevant logics can be conservatively extended by the addition of a Heyting (intuitionistic) implication connective. We show that this same conservativity holds for a range of first-order relevant logics with strong identity axioms, using an adaptation of Fine’s stratified model theory. For systems without identity, the question of conservatively adding Heyting implication is thereby reduced to the question of conservatively adding the axioms for identity. Some results in this direction are also obtained. The conservative presence of Heyting implication allows the development of an alternative model theory for quantified relevant logics.

Copyright

Corresponding author

*CENTRE FOR LOGIC, LANGUAGE AND COMPUTATION, VICTORIA UNIVERSITY OF WELLINGTON, P.O. BOX 600 WELLINGTON, NEW ZEALAND. E-mail: rob.goldblatt@vuw.ac.nz

References

Hide All
Anderson, A. R., Belnap, N. D. Jr, & Dunn, J. M. (1992). Entailment: The Logic of Relevance and Necessity, Vol. II. Princeton University Press.
Birkhoff, G. (1967). Lattice Theory (third edition). American Mathematical Society, Providence, Rhode Island.
Dunn, J. M. (1993). Star and perp: Two treatments of negation. Philosophical Perspectives, 7, 331357.
Fine, K. (1974). Models for entailment. Journal of Philosophical Logic, 3, 347372. Reprinted in Anderson et al. (1992, §51).
Fine, K. (1988). Semantics for quantified relevance logic. Journal of Philosophical Logic, 17, 2259. Reprinted in Anderson et al. (1992, §53).
Goldblatt, R. I. (1974). Semantic analysis of orthologic. Journal of Philosophical Logic, 3, 1935.
Mares, E. D. (1992). Semantics for relevance logic with identity. Studia Logica, 51(1), 120.
Restall, G. (1998). Displaying and deciding substructural logics 1: Logics with contraction. Journal of Philosophical Logic, 27, 179216.
Restall, G. (2000). An Introduction to Substructural Logics. Routledge, London.
Routley, R., & Meyer, R. K. (1973). The semantics of entailment. In Leblanc, H., editor. Truth, Syntax and Modality. North-Holland, Amsterdam, pp. 199243.

Related content

Powered by UNSILO

CONSERVATIVITY OF HEYTING IMPLICATION OVER RELEVANT QUANTIFICATION

  • ROBERT GOLDBLATT (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.