Geodesic
A hybrid calculus for logic~$N^*$: Residual finiteness and decidability
Algebra i logika, Tome 50 (2011) no. 3, pp. 351-367.

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It is proved that logic $N^*$ is residually finite and decidable. A hybrid calculus for the logic is constructed based on a tabular calculus for intuitionistic logic. It is shown that the hybrid calculus is sound and complete.
Keywords: modal logic, intuitionistic logic, tabular calculus
Mots-clés : hybrid calculus. 
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S. A. Drobyshevich. A hybrid calculus for logic~$N^*$: Residual finiteness and decidability. Algebra i logika, Tome 50 (2011) no. 3, pp. 351-367. http://geodesic.mathdoc.fr/item/AL_2011_50_3_a3/

[1] P. Cabalar, S. P. Odintsov, D. Pearce, “Logical foundations of well-founded semantics”, Principles of knowledge representation and reasoning, Proc. 10th Int. Conf. (KR2006), eds. P. Doherty et al., AAAI Press, Menlo Park, California, 2006, 25–36

[2] W. Rautenberg, Klassische und nichtklassische Aussagenlogik, Logik Grundlagen Math., 22, Friedr. Vieweg and Sohn., Braunschweig Wiesbaden, 1979 | MR | Zbl

[3] K. Dosen, “Negation as a modal operator”, Rep. Math. Logic, 20 (1986), 15–28 | MR | Zbl

[4] K. Dosen, “Negation in the light of modal logic”, What is negation?, Appl. Log. Ser., 13, eds. Dov M. Gabbay et al., Kluwer Acad. Publ., Dordrecht, 1999, 77–86 | MR | Zbl

[5] S. P. Odintsov, “Combining intuitionistic connectives and Routley negation”, Sib. Electr. Math. Rep., 7 (2010), 21–41 | MR

[6] R. Routley, V. Routley, “The semantics of first degree entailment”, Nous, 6 (1972), 335–359 | DOI | MR

[7] S. P. Odintsov, H. Wansing, “Inconsistency-tolerant description logic. II. A tableau algorithm for $\mathcal{CALC}^\mathrm C$”, J. Appl. Log., 6:3 (2008), 343–360 | DOI | MR | Zbl

[8] S. A. Drobyshevich, “Filtration for logic $N^*$”, Maltsevskie chteniya, tez. dokl., 2010, 41