
Revisiting Countermodel Generation for Minimal Implicational Logic
The LMT^→ sequent calculus was introduced in Santos (2016). This paper p...
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Predicative proof theory of PDL and basic applications
Propositional dynamic logic (PDL) is presented in Schüttestyle mode as ...
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Ruitenburg's Theorem via Duality and Bounded Bisimulations
For a given intuitionistic propositional formula A and a propositional v...
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Trimming Graphs Using Clausal Proof Optimization
We present a method to gradually compute a smaller and smaller unsatisfi...
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Computing a Smaller UnitDistance Graph with Chromatic Number 5 via Proof Trimming
We present a method to gradually compute a smaller and smaller unsatisfi...
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A limitation on the KPT interpolation
We prove a limitation on a variant of the KPT theorem proposed for propo...
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QRAT+: Generalizing QRAT by a More Powerful QBF Redundancy Property
The QRAT (quantified resolution asymmetric tautology) proof system simul...
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Duality between unprovability and provability in forward proofsearch for Intuitionistic Propositional Logic
The inverse method is a saturation based theorem proving technique; it relies on a forward proofsearch strategy and can be applied to cutfree 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 proofsearch 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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