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Conference Papers Year : 2013

Tractable inference systems: an extension with a deducibility predicate


The main contribution of the paper is a PTIME decision procedure for the satisfiability problem in a class of first-order Horn clauses. Our result is an extension of the tractable classes of Horn clauses of Basin & Ganzinger in several respects. For instance, our clauses may contain atomic formulas S ⊢ t where ⊢ is a predicate symbol and S is a finite set of terms instead of a term. ⊢ is used to represent any possible computation of an attacker, given a set of messages S. The class of clauses that we consider encompasses the clauses designed by Bana & Comon-Lundh for security proofs of protocols in a computational model. Because of the (variadic) ⊢ predicate symbol, we cannot use ordered resolution strategies only, as in Basin & Ganzinger: given S ⊢ t, we must avoid computing S′ ⊢ t for all subsets S′ of S. Instead, we design PTIME entailment procedures for increasingly expressive fragments, such procedures being used as oracles for the next fragment. Finally, we obtain a PTIME procedure for arbitrary ground clauses and saturated Horn clauses (as in Basin & Ganzinger), together with a particular class of (non saturated) Horn clauses with the ⊢ predicate and constraints (which are necessary to cover the application).

Dates and versions

hal-00881068 , version 1 (07-11-2013)



Hubert Comon-Lundh, Véronique Cortier, Guillaume Scerri. Tractable inference systems: an extension with a deducibility predicate. CADE'24 - 24th International Conference on Automated Deduction - 2013, Jun 2013, Lake Placid, United States. pp.91-108, ⟨10.1007/978-3-642-38574-2_6⟩. ⟨hal-00881068⟩
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