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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1804.06689
- arXiv:
- arXiv:1804.06689
- Bibcode:
- 2018arXiv180406689F
- Keywords:
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- Mathematics - Logic;
- Computer Science - Logic in Computer Science
- E-Print:
- doi:10.1145/3372299