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Canonicity for Intensional Logics with Even Axioms

Published online by Cambridge University Press:  12 March 2014

Timothy J. Surendonk
Timothy J. Surendonk*
Affiliation:
Australian National University, Computer Sciences Laboratory, Research School of Information Sciences, C/O Automated Reasoning Group, Canberra, ACT 0200, Australia, E-mail: Timothy.Surendonk@scientist.com
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Abstract

This paper looks at the concept of neighborhood canonicity introduced by Brian Chellas [2]. We follow the lead of the author's paper [9] where it was shown that every non-iterative logic is neighborhood canonical and here we will show that all logics whose axioms have a simple syntactic form—no intensional operator is in boolean combination with a propositional letter—and which have the finite model property are neighborhood canonical. One consequence of this is that KMcK, the McKinsey logic, is neighborhood canonical, an interesting counterpoint to the results of Robert Goldblatt and Xiaoping Wang who showed, respectively, that KMcK is not relational canonical [5] and that KMcK is not relationally strongly complete [11].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1141 - 1156
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[1]Benton, R., Strong modal completeness with respect to neighborhood semantics, Department of Philosophy, The University of Michigan, 1975.Google Scholar
[2]Chellas, B. F., Modal Logic: An Introduction, Cambridge University Press, 1980.CrossRefGoogle Scholar
[3]Došen, K., Duality between modal algebras and neighbourhood frames, Studia Logica, vol. 48 (1989), no. 2, pp. 219–234.CrossRefGoogle Scholar
[4]Fine, K., Normal forms in modal logic, Notre Dame Journal of Formal Logic, vol. 16 (1975), no. 2, pp. 229–237.CrossRefGoogle Scholar
[5]Goldblatt, R., The McKinsey axiom is not canonical, this Journal, vol. 56 (1991), no. 2, pp. 554–562.Google Scholar
[6]Goldblatt, R., The mathematics of modality, CSLI Lecture Notes, Stanford, California, 1993.Google Scholar
[7]Grove, A., Two modellings for theory change, Journal of Philosophical Logic, vol. 17 (1988), pp. 157–170.CrossRefGoogle Scholar
[8]Surendonk, T., Neighborhoods, ultrafilters, and canonicity, Technical Report TR-ARP-04-96, Australian National University, Canberra, 1996, Automated Reasoning Project.Google Scholar
[9]Surendonk, T., Canonicity for intensional logics without iterative axioms, Journal of Philosophical Logic, vol. 26 (1997), pp. 391–409.CrossRefGoogle Scholar
[10]Surendonk, T., Canonicity for intensional logics, Ph.D. thesis, Australian National University, Canberra, 1998, Automated Reasoning Project.Google Scholar
[11]Wang, X., The McKinsey axiom is not compact, this Journal, vol. 57 (1992), no. 4, pp. 1230–1238.Google Scholar