From positive PDL to its non-classical extensions

We provide a complete binary implicational axiomatization of the positive fragment of propositional dynamic logic (PDL). The intended application of this result are completeness proofs for non-classical extensions of positive PDL. Two examples are discussed in this article, namely, a paraconsistent...

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Bibliographic Details
Published in:Logic journal of the IGPL 2019-08, Vol.27 (4), p.522-542
Main Authors: Sedlár, Igor, Punčochář, Vít
Format: Article
Language:English
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Summary:We provide a complete binary implicational axiomatization of the positive fragment of propositional dynamic logic (PDL). The intended application of this result are completeness proofs for non-classical extensions of positive PDL. Two examples are discussed in this article, namely, a paraconsistent extension with modal De Morgan negation and a substructural extension with the residuated operators of the non-associative Lambek calculus. Informal interpretations of these two extensions are outlined.
ISSN:1367-0751
1368-9894
DOI:10.1093/jigpal/jzz017