Logics of time and computation
Logics of time and computation
A Proof System for Finite Trees
CSL '95 Selected Papers from the9th International Workshop on Computer Science Logic
Filtration theorem for dynamic algebras with tests and inverse operator
Logic of Programs and Their Applications, Proceedings
Modal Expressiveness of Graph Properties
Electronic Notes in Theoretical Computer Science (ENTCS)
Polyadic Dynamic Logics for HPSG Parsing
Journal of Logic, Language and Information
A Logical Approach to Hamiltonian Graphs
Electronic Notes in Theoretical Computer Science (ENTCS)
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We present modal logics for four classes of finite graphs: finite directed graphs, finite acyclic directed graphs, finite undirected graphs and finite loopless undirected graphs. For all these modal proof theories we discuss soundness and completeness results with respect to each of these classes of graphs. Moreover, we investigate whether some well-known properties of undirected graphs are modally definable or not: k-colouring, planarity, connectivity and properties that a graph is Eulerian or Hamiltonian. Finally, we present an axiomatization for colouring and prove that it is sound and complete with respect to the class of finite k-colourable graphs. One of most interesting feature of this approach is the use of the axioms of Dynamic Logic together with the Löb axiom to ensure acyclicity.