Read-Once Resolutions in Horn Formulas
In this paper, we discuss the computational complexity of Read-once resolution (ROR) with respect to Horn formulas. Recall that a Horn formula is a boolean formula in conjunctive normal form (CNF), such that each clause has at most one positive literal. Horn formulas find applications in a number of domains such as program verification and logic programming. It is well-known that deduction in ProLog is based on unification, which in turn is based on resolution and instantiation. Resolution is a sound and complete procedure to check whether a boolean formula in CNF is satisfiable. Although inefficient in general, resolution has been used widely in theorem provers, on account of its simplicity and ease of implementation. This paper focuses on two variants of resolution, viz., Read-once resolution and Unit Read-once resolution (UROR). Both these variants are sound, but incomplete. In this paper, the goal is to check for the existence of proofs (refutations) of Horn formulas under these variants. We also discuss the computational complexity of determining optimal length proofs where appropriate.
- 3.Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238–252 (1977)Google Scholar
- 5.Gallier, J.H.: Logic for Computer Science: Foundations for Automatic Theorem Proving. Dover Books on Computer Science, 1st edn. Dover Publications (2015)Google Scholar
- 6.Iwama, K., Miyano, E.: Intractability of read-once resolution. In: Proceedings of the 10th Annual Conference on Structure in Complexity Theory (SCTC 1995), Los Alamitos, CA, USA, June 1995, pp. 29–36. IEEE Computer Society Press (1995)Google Scholar
- 8.Owre, S., Shankar, N.: The formal semantics of PVS, March 1999Google Scholar