Number of Extensions of Non-Fregean Logics
- 52 Downloads
We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality relation), and only countably many lie between WH and WF.
Keywordsdenotation non-classical propositional logic sense sentential calculus with identity situation
Unable to display preview. Download preview PDF.
- 1.Bloom, S. L. and Suszko, R.: Investigations into the sentential calculus with identity, Notre Dame J. Formal Logic 13/3 (1972), 289–308. Google Scholar
- 2.Omyła, M.: Zarys Logiki Niefregowskiej, Państwowe Wydawnicztwo Naukowe, Warszawa, 1986. Google Scholar
- 3.Suszko, R.: Non-Fregean logic and theories, An. Univ. Bucuresti, Acta Logica 9 (1968), 105–125. Google Scholar
- 4.Suszko, R.: Identity connective and modality, Studia Logica 27 (1971), 7–39. Google Scholar
- 5.Suszko, R.: Abolition of the Fregean axiom, in A. Dold and B. Eckmann (eds.), Logic Colloquium 1972–73, Springer-Verlag, Berlin, 1975, pp. 169–239. Google Scholar
- 6.Suszko, R.: A note on modal systems and SCI, Bull. Sect. Logic 1(4) (1972), 42–45. Google Scholar
- 7.Suszko, R.: Adequate models for the non-Fregean sentential calculus SCI, in Logic, Language and Probability. A selection of papers of the 4th International Congress for Logic, Methodology and Philosophy, Reidel Publ. Company, Dordrecht, 1973, pp. 49–54. Google Scholar
- 8.Zachorowski, S.: Proof of a conjecture of R. Suszko, Studia Logica 34(3) (1975), 253–256. Google Scholar