Logical proof involving antecedents and consequents
For other uses, see Sequent (disambiguation).
In mathematical logic, a sequent is a very general kind of conditional assertion.
A sequent may have any number m of condition formulas Ai (called "antecedents") and any number n of asserted formulas Bj (called "succedents" or "consequents"). A sequent is understood to mean that if all of the antecedent conditions are true, then at least one of the consequent formulas is true. This style of conditional assertion is almost always associated with the conceptual framework of sequent calculus.
In mathematical logic, a sequent is a very general kind of conditional assertion. A 1 , … , A m ⊢ B 1 , … , B n . {\displaystyle A_{1},\,\dots ,A_{m}\...
logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard...
Sequent Computer Systems was a computer company that designed and manufactured multiprocessing computer systems. They were among the pioneers in high-performance...
response to a sound that is generally regarded as benign or unremarkable. Sequent Repatterning therapy for misophonia aims to break the linkage between the...
intuitions. Proof-theoretically, it derives from an analysis of classical sequent calculus in which uses of (the structural rules) contraction and weakening...
In structural proof theory, the nested sequent calculus is a reformulation of the sequent calculus to allow deep inference. Alwen Tiu; Egor Ianovski; Rajeev...
DYNIX (DYNamic UnIX) was a Unix-like operating system developed by Sequent Computer Systems, based on 4.2BSD and modified to run on Intel-based symmetric...
natural deduction. For this reason he introduced his alternative system, the sequent calculus, for which he proved the Hauptsatz both for classical and intuitionistic...
In mathematical logic, the cut rule is an inference rule of sequent calculus. It is a generalisation of the classical modus ponens inference rule. Its...
proof theory comes from a technical notion introduced in the sequent calculus: the sequent calculus represents the judgement made at any stage of an inference...
Patent claim The assertion of a proposition; see Douglas N. Walton A right Sequent, in mathematics Another term for an advertising slogan Health claim A term...
significant substructural logics are relevance logic and linear logic. In a sequent calculus, one writes each line of a proof as Γ ⊢ Σ {\displaystyle \Gamma...
is sequent calculus, which has two sorts, propositions as in ordinary propositional calculus, and pairs of lists of propositions called sequents, such...
formula in the end sequent of a cut-free proof is a subformula of one of the premises. This allows one to show consistency of the sequent calculus easily;...
In sequent calculus, the completeness of atomic initial sequents states that initial sequents A ⊢ A (where A is an arbitrary formula) can be derived from...
noncommutative multiplicative connectives of the Lambek calculus. Its sequent calculus relies on the structure of order varieties (a family of cyclic...
is an inference rule of a sequent calculus that does not refer to any logical connective but instead operates on the sequents directly. Structural rules...
for radically different logics. For example, a paradigmatic case is the sequent calculus, which can be used to express the consequence relations of both...
negative polarity. Many other sequent calculi has been shown to have the focusing property, notably the nested sequent calculi of both the classical and...
recursive formula below and is naturally ordered, whereas a Walsh matrix is sequency-ordered. Confusingly, different sources refer to either matrix as the Walsh...
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