TL;DR
A reduction relation on proof terms with permutative conversions and the property of subject reduction is proved and it is proved that d is a proof term of formula φ under hypotheses Γ.
This paper provides an expository comparison of two foundational proof systems in classical propositional logic: Gentzen's sequent calculus and Beth's semantic tableaux. Gentzen's sequent calculus is presented as a rule-based system built upon the single axiom $\alpha \Rightarrow \alpha$, whose key feature — the subfor...
A translation from a fragment of DTT to polymorphic DHOL is introduced, preserving constructs such as polymorphism and dependent types and suggesting that the translation could be used in a hammer system.
This paper provides a constructive decision procedure, that, given a formula, produces either a proof showing the formula to be valid or a finite countermodel falsifying the formula, thus also proving the finite model property for both logics.
A bilateral labeled sequent calculus incorporating specific verification and falsification rules incorporating specific verification and falsification rules is introduced on Heinrich Wansing’s constructive connexive logic C, shown to exhibit key structural properties.
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