Combining Superposition and Induction: A Practical Realization

Abdelkader Kersani (1) , Nicolas Peltier (1)

1 LIG - Laboratoire d'Informatique de Grenoble

We consider a proof procedure aiming at refuting clause sets containing arithmetic constants (or parameters), interpreted as natural numbers. The superposition calculus is enriched with a loop detection rule encoding a form of mathematical induction on the natural numbers (by "descente infinie"). This calculus and its theoretical properties are described in [2,16]. In the present paper, we focus on more practical aspects. We provide algorithms to apply the loop detection rule in an automatic and efficient way. We describe a research prototype implementing our technique and provide some preliminary experimental results.

Domaines: Logique en informatique [cs.LO]

Abdelkader Kersani, Nicolas Peltier. Combining Superposition and Induction: A Practical Realization. FroCoS 2013 - 9th International Symposium on s of Combining Systems (co-located with TABLEAUX 2013), Sep 2013, Nancy, France. pp.7-22, ⟨10.1007/978-3-642-40885-4_2⟩. ⟨hal-00934610⟩