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There exists an uncountable set of pretabular extensions of the relevant logic R and each logic of this set is generated by a variety of finite height

Published online by Cambridge University Press:  12 March 2014

Kazimierz Swirydowicz
Kazimierz Swirydowicz*
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznan, Poland, E-mail: [email protected]
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Abstract

In Handbook of Philosophical Logic M. Dunn formulated a problem of describing pretabular extensions of relevant logics (cf. M. Dunn [1984], p. 211; M. Dunn, G. Restall [2002], p. 79). The main result of this paper is described in the title.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 4 , December 2008 , pp. 1249 - 1270
Copyright
Copyright © Association for Symbolic Logic 2008

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References

REFERENCES

Anderson, A. R. A. and Belnap, N. D. Jr. [1975], Entailment, vol. 1, Princeton University Press, Princeton.Google Scholar
Blok, J. W. [1980], Pretabular varieties of modal algebras, Studia Logica, vol. 39, pp. 101–124.CrossRefGoogle Scholar
Blok, J. W. and Dziobiak, W. [1986], On the lattice of quasivarieties of Sugihara algebras, Studia Logica, vol. 45, no. 3, pp. 275–280.CrossRefGoogle Scholar
Blok, J. W. and Pigozzi, D. [1989], Algebraizable logics, Memoirs of the American Mathematical Society, vol. 77, no. 396, American Mathematical Society, Providence, R.I.Google Scholar
Dunn, J. M. [1970], Algebraic completeness results for R-mingle and its extensions, this Journal, vol. 35, pp. 1–13.Google Scholar
Dunn, J. M. [1986], Relevance logic and entailment, Handbook of philosophical logic (Gabbay, D. and Guenthner, F., editors), vol. 3, Reidel, pp. 117–224.Google Scholar
Dunn, J. M. and Restall, G. [2002], Relevance logic, Handbook of philosophical logic (Gabbay, D. and Guenthner, F., editors), vol. 6, Reidel, , pp. 1–128.Google Scholar
Dziobiak, W. [1982], Quasivariety generated by a finite sugihara structure has finitely many subquasi-varieties, submitted to Studia Logica in 1982, not published.Google Scholar
Dziobiak, W. [1983], There are 2ℵ0 with the relevance principle between R and RM, Studia Logica, vol. XLII, no. 1, pp. 49–61.CrossRefGoogle Scholar
Esakia, L. and Meskhi, V. [1978], Five critical systems, Theoria, vol. 40, pp. 52–60.Google Scholar
Font, J. and Rodriguez, G. [1990], Note on algebraic models for relevance logic, Zeitschrift für Mathematische Logic and Grundlagen der Mathematik, vol. 36, pp. 535–540.CrossRefGoogle Scholar
Maksimowa, L. [1972], Predtablicznyje superintuitionistskije logiki, Algebra i Logika, vol. 11, no. 5, pp. 558–570.Google Scholar
Maksimowa, L. [1973], Struktury z implikacjej, Algebra i logika, vol. 12, no. 4, pp. 445–467.Google Scholar
Maksimowa, L. [1974], Pretablicznyje rasshirenija logiki S4 Lewisa, Algebra i Logika, vol. 14, no. 1, pp. 28–55.Google Scholar
Routley, R. and Meyer, R. [1973], The semantics of entailment – I, Truth, semantics and modality (Leblanc, H., editor), North Holland, Amsterdam, pp. 194–243.Google Scholar
Swirydowicz, K. [1995], A remark on the maximal extensions of the relevant logic R, Reports on Mathematical Logic, vol. 29, pp. 19–33.Google Scholar
Swirydowicz, K. [1999], There exist exactly two maximal strictly relevant extensions of the relevant logic R, this Journal, vol. 64, no. 3, pp. 1125–1154.Google Scholar
Urquhart, A. [1993], Failure of interpolation in relevant logics, Journal of Philosophical Logic, vol. 22, pp. 449–479.CrossRefGoogle Scholar
Urquhart, A. [1996], Duality for algebras of relevant logics, Studia Logica, vol. 56, pp. 277–290.CrossRefGoogle Scholar