Canonical formulas for a~paraconsistent analog of the Scott logic
Algebra i logika, Tome 48 (2009) no. 4, pp. 495-519.

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We explore how the technique of canonical formulas can be applied in studying a paraconsistent analog $\mathbf{Ls}$ of the known intermediate Scott logic $\mathbf{SL}$. Canonical formulas are defined which axiomatize $\mathbf{Ls}$ relative to minimal logic and allow us to describe all countermodels of the logic in question.
Keywords: intermediate Scott logic, canonical formulas.
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M. V. Stukachyova. Canonical formulas for a~paraconsistent analog of the Scott logic. Algebra i logika, Tome 48 (2009) no. 4, pp. 495-519. http://geodesic.mathdoc.fr/item/AL_2009_48_4_a3/

[1] A. Chagrov, M. Zakharyaschev, “The undecidability of the disjunction property of propositional logics and other related problems”, J. Symb. Log., 58:3 (1993), 967–1002 | DOI | MR | Zbl

[2] P. Minari, “On the extension of intuitionistic propositional logic with Kreisel–Putnam's and Scott's schemes”, Stud. Log., 45:1 (1986), 55–68 | DOI | MR | Zbl

[3] D. M. Gabbay, D. H. J. de Jongh, “A sequence of decidable finitely axiomatazible intermediate logics with the disjunction property”, J. Symb. Log., 39:1 (1974), 67–78 | DOI | MR | Zbl

[4] H. Rasiowa, An algebraic approach to non-classical logics, Stud. Log. Found. Math., 78, North-Holland Publ. Co., Amsterdam–London, 1974 | MR | Zbl

[5] K. Segerberg, “Propositional logics related to Heyting's and Johansson's”, Theoria, 34 (1968), 26–61 | MR

[6] S. P. Odintsov, “Representations of $j$-algebras and Segerberg's logics”, Log. Anal. Nouv. Sér., 42:165–166 (1999), 81–106 | MR | Zbl

[7] S. P. Odintsov, “On the structure of paraconsistent extensions of Johansson's logic”, J. Appl. Log., 3:1 (2005), 43–65 | DOI | MR | Zbl

[8] M. V. Stukacheva, “O kanonicheskikh formulakh dlya rasshirenii minimalnoi logiki”, Sib. elektron. matem. izv., 3 (2006), 312–334 ; http://semr.math.nsc.ru | MR | Zbl

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