We introduce a logic called C2PDLS, motivated by some reasoning about graph rewriting systems. C2PDLS is an extension of both combinatory propositional dynamic logic, usually written CPDL, and converse propositional dynamic logic, usually written CPDL too. In addition to the existing features of both CPDLs, the introduced logic offers the possibility to use the notion of substitutionsà la Hoare within its formulae. Such substitutions reflect the effect of some actions on graph structures such as addition or deletion of edges or nodes. These last features led us to introduce restricted universal roles over subsets of the universe. We propose a sound and complete deductive system for C2PDLS and show that its validity problem is decidable.
J. H. Brenas et al. REF investigate such logics for graph transformations and define C2PDLS, a combination of both combinatory and converse propositional dynamic logics, augmented by substitutions.
C2PDLS: A Combination of Combinatory and Converse PDL with Substitutions
SCSS
Computer Science