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Canonical formulas for a paraconsistent analog of the Scott logic

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Algebra and Logic Aims and scope

We explore how the technique of canonical formulas can be applied in studying a paraconsistent analog Ls of the known intermediate Scott logic SL. Canonical formulas are defined which axiomatize Ls relative to minimal logic and allow us to describe all countermodels of the logic in question.

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References

  1. A. Chagrov and M. Zakharyaschev, “The undecidability of the disjunction property of propositional logics and other related problems,” J. Symb. Log., 58, No. 3, 967-1002 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Minari, “On the extensions of intuitionistic propositional logic with Kreisel–Putnam’s and Scott’s schemes,” Stud. Log., 45, No. 1, 55-68 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  3. D. M. Gabbay and D. H. de Jongh, “A sequence of decidable finitely axiomatizable intermediate logics with the disjunction property,” J. Symb. Log., 39, No. 1, 67-78 (1974).

    Article  MATH  Google Scholar 

  4. H. Rasiowa, An Algebraic Approach to Non-Classical Logics, Stud. Log. Found. Math., 78, North-Holland, Amsterdam (1974).

    Book  MATH  Google Scholar 

  5. K. Segerberg, “Propositional logics related to Heyting’s and Johansson’s,” Theoria, 34, 26-61 (1968).

    Article  MathSciNet  Google Scholar 

  6. S. P. Odintsov, “Representations of j-algebras and Segerberg’s logics,” Log. Anal., Nouv. Sér., 42, Nos. 165/166, 81-106 (1999).

    MATH  MathSciNet  Google Scholar 

  7. S. P. Odintsov, “On the structure of paraconsistent extensions of Johansson’s logic,” J. Appl. Log., 3, No. 1, 43-65 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  8. M. V. Stukachyova, “Canonical formulas for extensions of minimal logic,” Sib. Electr. Math. Rep. (http://semr.math.nsc.ru), 3, 312-334 (2006).

    Google Scholar 

  9. S. P. Odintsov, “Algebraic semantics and Kripke semantics for extensions of minimal logic,” Log. Invest. (http://www.logic.ru/LogStud/02/No2-06.html), 2 (1999).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    M. V. Stukachyova

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  1. M. V. Stukachyova
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Correspondence to M. V. Stukachyova.

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Supported by RFBR (project No. 09-01-00090-a) and by the Council for Grants (under RF President) for State Support of Leading Scientific Schools (grant NSh-335.2008.1).

Translated from Algebra i Logika, Vol. 48, No. 4, pp. 495-519, July-August, 2009.

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Stukachyova, M.V. Canonical formulas for a paraconsistent analog of the Scott logic. Algebra Logic 48, 282–297 (2009). https://doi.org/10.1007/s10469-009-9059-8

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  • DOI: https://doi.org/10.1007/s10469-009-9059-8

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