Completeness and Decidability Results for First-order Clauses with Indices

Abdelkader Kersani (1) , Nicolas Peltier (1)

1 LIG - Laboratoire d'Informatique de Grenoble

We define a proof procedure that allows for a limited form of inductive reasoning. The first argument of a function symbol is allowed to belong to an inductive type. We will call such an argument an index. We enhance the standard superposition calculus with a loop detection rule, in order to encode a particular form of mathematical induction. The satisfiability problem is not semi-decidable, but some classes of clause sets are identified for which the proposed procedure is complete and/or terminating.

Domaines: Logique en informatique [cs.LO]

Abdelkader Kersani, Nicolas Peltier. Completeness and Decidability Results for First-order Clauses with Indices. CADE 2013 - 24th International Conference on Automated Deduction, Jun 2013, Lake Placid, NY, United States. pp.58-75, ⟨10.1007/978-3-642-38574-2_4⟩. ⟨hal-00934594⟩