The Inverse Method for Many-Valued Logics

Kovács, Laura; Mantsivoda, Andrei; Voronkov, Andrei

doi:10.1007/978-3-642-45114-0_2

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2020

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Cited by 3 publications

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“…The method has been popularized by Degtyarev and Voronkov [6], who provide the general recipe to design forward calculi, with applications to Classical Predicate Logic and some non-classical logics. Further extensions can be found in [2,7,15]. A significant investigation is presented in [4,5], where focused calculi and polarization of formulas are exploited to reduce the search space in forward proof-search for Intuitionistic Logic.…”

Section: Introductionmentioning

confidence: 99%

Duality between Unprovability and Provability in Forward Refutation-search for Intuitionistic Propositional Logic

Fiorentini

Ferrari

2020

ACM Trans. Comput. Logic

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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.

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