From the positive fragment of PDL to its non-classical extensions

0508255 - ÚI 2020 CH eng A - Abstrakt
Punčochář, Vít - Sedlár, Igor
From the positive fragment of PDL to its non-classical extensions.
AiML 2018: Accepted Short Papers. Bern: Universität Bern, 2018. s. 100-104.
[AiML 2018: Advances in Modal Logic /12./. 27.08.2019-31.08.2019, Bern]
Grant CEP: GA ČR(CZ) GJ18-19162Y
Institucionální podpora: RVO:67985807
Klíčová slova: Lambek calculus * dynamic logic * First Degree Entailment * paraconsistent logic * Propositional Dynamic Logic * substructural logics
http://www.aiml2018.unibe.ch/Booklet%20of%20Short%20Papers.pdf

We provide a complete binary implicational axiomatization of the positive fragment of Propositional Dynamic Logic, extending the work of Dunn [4] on positive modal logic. The intended application of this result are completeness proofs for non-classical extensions of positive PDL. Two examples will be outlined, namely, a paraconsistent extension with modal De Morgan negation and a substructural extension with the residual operators of the Non-associative Lambek calculus.
Trvalý link: http://hdl.handle.net/11104/0299216