Composing decision procedures: the approach and a case study

Abstract

In this paper we address the problem of strengthening the inferential capabilities of an interactive theorem prover with complex and reusable proof procedures. We focus on the construction of proof procedures built out of decision procedures for (decidable) quantifierfree theories. The idea is to build proof procedures in a structured way. A set of deciders provides the low-level reasoning capabilities, while the high-level (i.e. strategical) reasoning procedures are to be synthesized on top of it. The main goal of the paper is to show that this approach has many advantages and is of wide applicability. As a case study we consider the synthesis of a proof procedure for the existential fragment of first order logic built on top of a prepositional decider. This procedure is particularly well suited for describing our approach, since in it there is a neat separation between the prepositional and the first order reasoning components.

The authors want to thank Alessandro Armando, Enrico Giunchiglia, and Fausto Giunchiglia for the many invaluable suggestions and comments. This work has been supported by the Italian National Research Council (CNR), Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo (Special Project on Information Systems and Parallel Computing).