相关论文: Inception Display Calculi

The present paper aims at establishing formal connections between correspondence phenomena, well known from the area of modal logic, and the theory of display calculi, originated by Belnap. These connections have been seminally observed and…

A recent strand of research in structural proof theory aims at exploring the notion of analytic calculi (i.e. those calculi that support general and modular proof-strategies for cut elimination), and at identifying classes of logics that…

By exploiting the algebraic and order theoretic mechanisms behind Sahlqvist correspondence, the theory of unified correspondence provides powerful tools for correspondence and canonicity across different semantics and signatures, covering…

Display calculi are generalized sequent calculi which enjoy a `canonical' cut elimination strategy. That is, their cut elimination is uniformly obtained by verifying the assumptions of a meta-theorem, and is preserved by adding or removing…

We consider two styles of proof calculi for a family of tense logics, presented in a formalism based on nested sequents. A nested sequent can be seen as a tree of traditional single-sided sequents. Our first style of calculi is what we call…

The unified correspondence theory for distributive lattice expansion logics (DLE-logics) is specialized to strict implication logics. As a consequence of a general semantic consevativity result, a wide range of strict implication logics can…

We extend the theory of unified correspondence to a very broad class of logics with algebraic semantics given by varieties of normal lattice expansions (LEs), also known as `lattices with operators'. Specifically, we introduce a very…

We introduce a proper display calculus for first-order logic, of which we prove soundness, completeness, conservativity, subformula property and cut elimination via a Belnap-style metatheorem. All inference rules are closed under uniform…

We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and sub-formula property. Properness (i.e. closure under uniform substitution of all parametric…

Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex…

We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of…

Refutation calculi are formal systems developed to derive the invalid formulas of a given logic. While the notion of refutation calculi has played a key role in the development of tableaux calculi, a refutation approach to display calculi…

We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…

The present paper provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems which…

This paper presents a sound, complete, and decidable analytic tableau system for the logic of evidence and truth \letf, introduced in Rodrigues, Bueno-Soler \& Carnielli (Synthese, DOI: 10.1007/s11229-020-02571-w, 2020). \letf\ is an…

We define and study translations between the maximal class of analytic display calculi for tense logics and labeled sequent calculi, thus solving an open problem about the translatability of proofs between the two formalisms. In particular,…

In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics).…

We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of "signature" for specifying syntactic constructions. In the spirit of Initial…

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path…