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A paraconsistent extension of Sylvan's logic
Algebra i logika, Tome 46 (2007) no. 5, pp. 533-547
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We deal with Sylvan's logic $CC_\omega$. It is proved that this logic is a conservative extension of positive intuitionistic logic. Moreover, a paraconsistent extension of Sylvan's logic is constructed, which is also a conservative extension of positive intuitionistic logic and has the property of being decidable. The constructed logic, in which negation is defined via a total accessibility relation, is a natural intuitionistic analog of the modal system S5. For this logic, an axiomatization is given and the completeness theorem is proved.
Keywords: Sylvan's logic, conservative extension, positive intuitionistic logic, completeness theorem. 
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A. B. Gordienko. A paraconsistent extension of Sylvan's logic. Algebra i logika, Tome 46 (2007) no. 5, pp. 533-547. http://geodesic.mathdoc.fr/item/AL_2007_46_5_a0/

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