From positive PDL to its non-classical extensions

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Logic Journal of the IGPL 27 (4):522-542 (2019)
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Abstract

We provide a complete binary implicational axiomatization of the positive fragment of propositional dynamic logic. 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.

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10.1093/jigpal/jzz017

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Author Profiles

Igor Sedlár
Czech Academy of Sciences
Vit Puncochar

Citations of this work

Semantic conceptions of information.Luciano Floridi - 2008 - Stanford Encyclopedia of Philosophy.
Neighbourhood Semantics for Modal Relevant Logics.Nicholas Ferenz & Andrew Tedder - 2023 - Journal of Philosophical Logic 52 (1):145-181.

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References found in this work

How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle (ed.), Contemporary aspects of philosophy. Boston: Oriel Press.
Dynamic Logic.Lenore D. Zuck & David Harel - 1989 - Journal of Symbolic Logic 54 (4):1480.

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