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certain style of inference and certain formal properties. The first sequent calculi systems, LK and LJ, were introduced in 1934/1935 by Gerhard Gentzen...

provability that is frequently used when specifying calculi for deduction. In the sequent calculus, the name sequent is used for the construct, which can be regarded...

the excluded middle. However, the sequent calculus is a fairly expressive framework, and there have been sequent calculi for intuitionistic logic proposed...

statements. There are several types of proof calculi. The most popular are natural deduction, sequent calculi (i.e., Gentzen-type systems), Hilbert systems...

Marta and Pirri, Fiora (1993) "First order abduction via tableau and sequent calculi" Logic Jnl IGPL 1993 1: 99–117; doi:10.1093/jigpal/1.1.99. Oxford Journals...

since many proof calculi are under-determined and can be used for radically different logics. For example, a paradigmatic case is the sequent calculus, which...

argument using modus ponens is said to be deductive. In single-conclusion sequent calculi, modus ponens is the Cut rule. The cut-elimination theorem for a calculus...

negative polarity. Many other sequent calculi has been shown to have the focusing property, notably the nested sequent calculi of both the classical and intuitionistic...

premises relevant to the conclusion of the inference. Gentzen-style sequent calculi can be modified by removing the weakening rules that allow for the...

three-valued Łukasiewicz logic was introduced by Arnon Avron in 1991. Sequent calculi for finite and infinite-valued Łukasiewicz logics as an extension of...

are different types of proof systems including natural deduction and sequent calculi. A semantics is a system for mapping expressions of a formal language...

of proof calculi. The three most well-known styles of proof calculi are: The Hilbert calculi The natural deduction calculi The sequent calculi Each of...

unravelling. As another possibility, completeness proofs based on cut-free sequent calculi usually produce finite models directly. Most of the modal systems used...

of natural deduction. This would include various forms of sequent calculi or tableau calculi. But other theorists use the term in a more narrow sense,...

part because S5 does not describe every kind of modality of interest. Sequent calculi and systems of natural deduction have been developed for several modal...

are as simple as in Getzen's original sequent calculus there is little need to analyse them, but proof calculi of deep inference such as display logic...

framework of sequent calculi used in structural proof theory to provide analytic calculi for logics that are not captured in the sequent framework. A...

in any formal system. Since Gentzen's work, natural deduction and sequent calculi have been widely applied in the fields of proof theory, mathematical...

used here and below is unrelated to the notion of structural rules in sequent calculi.) A structural consequence relation is called a propositional logic...

unravelling. As another possibility, completeness proofs based on cut-free sequent calculi usually produce finite models directly. Most of the modal systems used...