We present a new proof of weak normalization for intuitionistic natural deduction. The distinguishing features of this proof are that it works only with cuts rather than cut segments, provides explicit local rules for determining whether to contract a whole proof or reduce one of its subproofs, and in the latter case, which subproof to reduce. We also discuss a formalization of the entire proof in Lean, and present a deterministic algorithm for weak normalization.
It is proved that $\mathbf{B}_{ti}$ is the multiple-succedent sequent calculus read upside down, that $\mathbf{G}_{ti}$ admits the structural rules, and that $\mathbf{B}_{ti}$ is sound and complete for Kripke semantics, with the finite model property and a block-theoretic proof of the disjunction property.
A survey of propositional modal logic in an intuitionistic setting, including a new logic $\textbf{KI}$ for which it is proved completeness, and a deeper look at the logics lying between the CML and IML traditions.
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 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...
The logic FOT is a team-based logic whose expressive power coincides with first-order logic at the level of both sentences and open formulas. In contrast to dependence and independence logics, which can define stronger second-order team properties, FOT is designed to capture exactly elementary team properties, modulo t...
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...
Giulio Fellin· 0 citations
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