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

Authors: Vít Punčochář, Igor Sedlár
Publication year: 2018
Publication type: Abstrakt
Periodical: AiML 2018: Accepted Short Papers
Projects: Non-classical logical models of information dynamics
Bibliographic citation: PUNČOCHÁŘ, Vít, SEDLÁR, Igor. From the positive fragment of PDL to its non-classical extensions. In: AiML 2018: Accepted Short Papers. Bern: Universität Bern, 2018, S. 100-104. Dostupné z: http://www.aiml2018.unibe.ch/Booklet%20of%20Short%20Papers.pdf
ID: 508255

Abstract

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.