Duality between unprovability and provability in forward proof-search for Intuitionistic Propositional Logic
Abstract
The inverse method is a saturation based theorem proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. Here we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability which is prone to constructively ascertain the unprovability of a formula G by providing a concise countermodel for it; in particular we prove that the generated countermodels have minimal height. Moreover, we clarify the role of the saturated database obtained as result of a failed proof-search in FRJ(G) by showing how to extract from such a database a derivation witnessing the Intuitionistic validity of the goal.
Keywords
Cite
@article{arxiv.1804.06689,
title = {Duality between unprovability and provability in forward proof-search for Intuitionistic Propositional Logic},
author = {Camillo Fiorentini and Mauro Ferrari},
journal= {arXiv preprint arXiv:1804.06689},
year = {2020}
}