A resolution theorem prover for intuitionistic logic

Abstract

Abstract. We use the general scheme of building resolution calculi (also called the inverse method) originating from S.Maslov and G.Mints to design and implement a resolution theorem prover for intuitionistic logic. A number of search strategies are introduced and proved complete. The resolution method is shown to be a decision procedure for a new syntactically described decidable class of intuitionistic logic. The performance of our prover is compared with the performance of a tableau prover for intuitionistic logic presented in [12], using both the benchmarks from the latter and the theorems from J. yon Plato-s constructive geometry [9].

Efficient Intuitionistic Theorem Proving with the Polarized Inverse Method

“…Chaudhuri [3] describes a focused inverse method prover for linear logic. Earlier work is by Tammet [18] who describes an implementation of a forward intuitionistic theorem prover. We did not compare Imogen to his system because it is not part of ILTP.…”

“…This work continues a line of research on building efficient theorem provers for nonclassical logics using the inverse method, following Tammet [18] (for intuitionistic and linear logic), Linprover [4,3] (for intuitionistic linear logic), and the early propositional version of Imogen [12].…”

Imogen: Focusing the Polarized Inverse Method for Intuitionistic Propositional Logic

“…We do not explicitly compare our results to Linprover, which incurs additional overhead due to the necessary maintenance of linearity constraints. We are also aware of two provers for first-order intuitionistic logic based on the inverse method, Gandalf [21] and Sandstorm [9], both of which partially exploit focusing. We do not compare Imogen to these either, since they incur substantial overhead due to unification, contraction, and more complex subsumption.…”

Automated Reasoning with Analytic Tableaux and Related Methods

“…However, as other intuitionistic theorem provers are written in different languages, are run on different machines and (in most cases) deal with firstorder formulae, comparison is hard. An (incomplete) list of other intuitionistic theorem provers is: [2], [4], [8], [11], [12], [13], [14]. Of the two calculi given here, the one with the smallest history and the least checking (the Swiss one) can become inefficient (see example 27.)…”