A Canonical Model Construction for Iteration-Free PDL with Intersection

We study the axiomatisability of the iteration-free fragment of Propositional Dynamic Logic with Intersection and Tests. The combination of program composition, intersection and tests makes its proof-theory rather difficult. We develop a normal form for formulae which minimises the interaction between these operators, as well as a refined canonical model construction. From these we derive an axiom system and a proof of its strong completeness.Comment: In Proceedings GandALF 2016, arXiv:1609.0364

Complete axiomatization of a relative modal logic with composition and intersection

International audienceWe consider the question of the complete axiomatization of a relative modal logic with composition and intersection

A new proof of completeness for a relative modal logic with composition and intersection

International audienceThis paper is devoted to the completeness issue of RMLCI, the relative modal logic with composition and intersection - a restriction of the propositional dynamic logic with intersection. The trouble with RMLCI is that the operation of intersection is not modally definable. Using the notion of mosaics, we give a new proof of a theorem considered in a previous paper "Complete axiomatization of a relative modal logic with composition and intersection". The theorem asserts that the proof theory of RMLCI is complete for the standard Kripke semantics of RMLCI

A New Proof of Completeness for a Relative Modal Logic With Composition and Intersection

This paper is devoted to the completeness issue of RMLCI --- the relative modal logic with composition and intersection --- a restriction of the propositional dynamic logic with intersection. The trouble with RMLCI is that the operation of intersection is not modally definable. Using the notion of mosaics, we give a new proof of a theorem considered in a previous paper "Complete axiomatization of a relative modal logic with composition and intersection". The theorem asserts that the proof theory of RMLCI is complete for the standard Kripke semantics of RMLCI. 1 Introduction A relative modal logic is a modal logic the modal operators of which depend on parameters. Among the well-known relative modal logics devised in artificial intelligence and computer science, there are PDL --- the propositional dynamic logic --- introduced by Fischer and Ladner [6], PAL --- the propositional algorithmic logic --- set out by Mirkowska [12], DAL --- the logic for data analysis --- expounded by Fari~n..