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 subformula property — guarantees that every provable formula admits a proof constructed entirely from its subformulas. Beth tableaux are introduced as a complementary, refutation-based method that establishes validity by decomposing a formula from its main connective into subformulas and deriving contradictions across all branches of a truth-value analysis. The correspondence between the two systems is demonstrated through parallel proofs of classical tautologies.
GenZ is introduced, a generic theorem prover for sequent calculi implemented in Haskell that allows the user to specify a set of sequent rules, over which it performs proof search, and employs the zipper data structure.
Xiaoshuang Yang, Malvin Gattinger, Marianna Girlando et al.· 0 citations
Sequent-style tableaux are a refutation calculus in which each node of the refutation tree carries a finite block of formulae and the structural rules are absorbed into the data structure and the closure criterion. In their original, classical form they rest on an involutive De Morgan negation and on closure upon a com...
In this paper, we show that the two intuitionistic modal logics IS4 and IK4 are decidable. We provide 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 lo...
Marianna Girlando, Roman Kuznets, Sonia Marin et al.· 1 citation
We present an abstract framework for conservation and translation theorems between logical calculi. Unlike previous approaches, our setting does not require the underlying consequence relations to satisfy structural properties such as cut, allowing in particular for cut-free calculi. Moreover, we study translations bet...
We present a domain-theoretical formalization of interaction trees in the Rocq prover. Unlike existing formalizations, ours does not rely on Rocq's built-in coinduction. Hence, we avoid complications occurring in earlier works, such as artificially including silent steps to comply with Rocq's productivity checker, trea...
David Nowak, Vlad Rusu· Electronic Proceedings in Th...· 0 citations
We study infinitary intuitionistic logic by employing both syntactic and semantic methods. First, we introduce a natural deduction system for infinitary predicate logic and study some of its basic properties. We then extend neighbourhood semantics to this setting, providing a soundness and completeness theorem for th...
