Common knowledge logic in a higher order proof assistant

Pierre Lescanne (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme

This paper presents experiments on common knowledge logic, conducted with the help of the proof assistant Coq. The main feature of common knowledge logic is the eponymous modality that says that a group of agents shares a knowledge about a certain proposition in a inductive way. This modality is specified by using a fixpoint approach. Furthermore, from these experiments, we discuss and compare the structure of theorems that can be proved in specific theories that use common knowledge logic. Those structures manifests the interplay between the theory (as implemented in the proof assistant Coq) and the metatheory.

Keywords: Common knowledge proof assistant; Higher order logic

Domains: Computer Science [cs]; Artificial Intelligence [cs.AI]; Computer Science [cs]; Logic in Computer Science [cs.LO]

Pierre Lescanne. Common knowledge logic in a higher order proof assistant. Andreï Voronkov & Christoph Weidenbach. Memory of Harald Ganzinger 2013, 7797, Springer, pp.271-284, 2013, Lecture Notes in Computer Science, ⟨10.1007/978-3-642-40206-7_15⟩. ⟨ensl-00199368v3⟩