A logical matrix (A, D) is finite (tabular) if A is finite. If C = K ⊧, for a finite set K of finite matrices, C is called strongly finite, S F. A syntactical test of S F-ness provides Theorem 4.1.4. All axiomatic strengthenings of an S F-logic are S F (Corollary 4.1.6). All S F-logics are finitary (Theorem 4.1.7).
KeywordsSequential Consequence Logical System Heyting Algebra Simple Sentence Consequence Operation
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- 1.This need not be exactly so. As a matter of fact, there is a remarkable revival of many-valued (and thus strongly finite) logic these days. The usefulness of many-valued logic as well as philosophical significance of the idea of many-valnedness have been strongly advocated by many writers — by the Russian logician and specialist in computer science Viktor. K. Finn (cf. e.g. Fian by the Canadian mathematician an philosopher of physics Robin Giles (cf. e.g. Giles ), various aspects of the idea of many-valnedness have been studied by J. van Bentham, S. Blamney, J. P. Cleave, S. Feferman, B. C. van Flraassen, D. Scott, S. K. Thomason, A. Urqnhart, P. Woodruff and many others.Google Scholar
- 8.The idea of the aame-theoretic semsntics is due to P. Lorentzen who proposed a gametheoretic interpretation for intnitionistic logic. Some further work in this direction was done by K. Lorentz, see Lorentzen and LorentzGoogle Scholar