Efficient Intuitionistic Theorem Proving with the Polarized Inverse Method

Imogen: Focusing the Polarized Inverse Method for Intuitionistic Propositional Logic

In this paper we describe Imogen, a theorem prover for intuitionistic propositional logic using the focused inverse method. We represent fine-grained control of the search behavior by polarizing the input formula. In manipulating the polarity of atoms and subformulas, we can often improve the search time by several orders of magnitude. We tested our method against seven other systems on the pro...

Thesis Proposal: Practical Automated Theorem Proving with the Polarized Inverse Method

Formal, mechanically checked reasoning as envisioned by Leibniz has in the past few decades become a reality. Proof assistants are programs that can rigorously and mechanically check the details of logical arguments. Formal reasoning supported by proof assistants has applications to nearly all areas of computer science, from formal including specifying and verifying critical properties of hardw...

A Resolution Theorem Prover for Intuitonistic Logic

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 is introduced and proved complete. The resolution method is shown to be a decision procedure for a new syntactically described decidable class of intuitionistic ...

Structural sharing for efficient proof-search in propositional intuitionistic logic

A Focusing Inverse Method Theorem Prover for First-Order Linear Logic

We present the theory and implementation of a theorem prover for first-order intuitionistic linear logic based on the inverse method. The central proof-theoretic insights underlying the prover concern resource management and focused derivations, both of which are traditionally understood in the domain of backward reasoning systems such as logic programming. We illustrate how resource management...