Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T08:12:16.520Z Has data issue: false hasContentIssue false
  • English
  • Français

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: swirydow@amu.edu.pl
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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