Abstract
As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we prove that extensions of the logic involved form a four-element chain, the only proper consistent extensions being the least non-paraconsistent extension of it and the classical logic. RID=""ID="" <E5>Mathematics Subject Classification (2000):</E5> 03B50, 03B53, 03G10 RID=""ID="" <E5>Key words or phrases:</E5> Many-valued logic – Paraconsistent logic – Extension – Prevariety – Distributive lattice
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Received 12 August 2000 / Published online: 25 February 2002
RID=""
ID="" <E5>Mathematics Subject Classification (2000):</E5> 03B50, 03B53, 03G10
RID=""
ID="" <E5>Key words or phrases:</E5> Many-valued logic – Paraconsistent logic – Extension – Prevariety – Distributive lattice
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Pynko, A. Extensions of Hałkowska–Zajac's three-valued paraconsistent logic . Arch. Math. Logic 41 , 299 –307 (2002). https://doi.org/10.1007/s001530100115
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DOI: https://doi.org/10.1007/s001530100115