Sequent

Word SEQUENT
Character 7
Hyphenation se quent
Pronunciations /ˈsiːkwənt/

Definitions and meanings of "Sequent"

What do we mean by sequent?

Following in order or time; subsequent. adjective

Following as a result; consequent. adjective

A result; a consequence. noun

Continuing in the same course or order; following; succeeding.

Following by natural or logical consequence.

A follower. noun

A sequence or sequel; that which follows as a result. noun

That which follows by an observed order of succession: used, in opposition to antecedent, where one wishes to avoid the implication of the relation of effect to cause that would be conveyed by the use of consequent. noun

A follower. noun

That which follows as a result; a sequence. noun

Following; succeeding; in continuance. adjective

Following as an effect; consequent. adjective

That comes after in time or order; subsequent. adjective

That follows on as a result, conclusion etc.; consequent to, on, upon. adjective

Recurring in succession or as a series; successive, consecutive. adjective

Something that follows in a given sequence. noun

An element of a sequence, usually a sequence in which every entry is an axiom or can be inferred from previous elements. noun

A follower. noun

In regular succession without gaps adjective

Following or accompanying as a consequence adjective

Something that follows in a given sequence.

A disjunctive set of logical formulae which is partitioned into two subsets; the first subset, called the antecedent, consists of formulae which are valuated as false, and the second subset, called the succedent, consists of formulae which are valuated as true. (The set is written without set brackets and the separation between the two subsets is denoted by a turnstile symbol, which may be read "give(s)".)

A follower.

A sequential calculus

Synonyms and Antonyms for Sequent

The word "sequent" in example sentences

He therefore invented another logical calculus that he called sequent calculus (Sequenzenkalkul, literally “calculus of sequences”) and made it the central topic of his thesis. ❋ Unknown (2009)

The ten thralls answered him with one mouth and in sequent words, saying, Whatso thou biddest us, ❋ Unknown (2006)

If at any stage of this “reduction process” the conclusion of a sequent is a compound formula, you have to consider any conjunct or any instance of universal quantification as a possible conclusion. ❋ Unknown (2009)

Gentzen seems not to have noticed the latter, but seems to have thought rather the contrary, by the failure of this property for the elimination of cuts in sequent calculus. ❋ Unknown (2009)

The earliest application of sequent calculus in mathematics was in the proof theory of arithmetic, in Gentzen's thesis and in a decisive way in the 1938 proof of the consistency of arithmetic. ❋ Unknown (2009)

Ketonen wanted to formulate Skolem's formal rules of proof within sequent calculus. ❋ Unknown (2009)

Natural deduction has led to the Curry-Howard correspondence and to connections with functional programming, and sequent calculus is often used in systems of automatic proof search, as in logic programming. ❋ Unknown (2009)

Inside the magazine, she is shown wearing a range of outfits, including a sequent top and leather pants. ❋ Unknown (2009)

Ketonen's best-known discovery is a sequent calculus for classical propositional logic the logical rules of which are all invertible, meaning that whenever a sequent is of a form that matches the conclusion of a logical rule, the corresponding premisses, defined uniquely from the given sequent and the rule, are also derivable. ❋ Unknown (2009)

A remarkable step ahead in the development of systems of sequent calculus was taken by Oiva Ketonen in his doctoral thesis of 1944. ❋ Unknown (2009)

Ketonen's idea was to define a system of proof search: one starts from a given sequent to be derived, chooses a formula in it, and writes the premisses of a rule that can conclude the given sequent. ❋ Unknown (2009)

The former created in 1951 an infinitary sequent calculus to present consistency proofs in a perspicuous way, the latter instead used a more traditional Gentzen-style calculus. ❋ Unknown (2009)

However, Ketonen's work was mostly known only through its review by Bernays and only the logical part on sequent calculus was explained in detail there. ❋ Unknown (2009)

Failure of the aims of Hilbert through Gödel's incompleteness theorems; Gentzen's creation of the two main types of logical systems of contemporary proof theory, natural deduction and sequent calculus ❋ Unknown (2009)

Kleene's work of the early 1950's also pioneered a remarkable development in sequent calculus, namely the ❋ Unknown (2009)

Every body know their truth by sequent 12 on Thursday, Sep 3, 2009 at 2: 00: 12 AM ❋ Unknown (2009)

With Kleene's book, Gentzen's sequent calculi became generally known and accessible. ❋ Unknown (2009)

Gentzen shows that by proceeding in this way under the assumption that the sequent in question is derivable, either a true equation is found as a conclusion, or a false equation as an assumption. ❋ Unknown (2009)

A cut with such a sequent as one premiss has the other premiss equal to the conclusion and can therefore be deleted. ❋ Unknown (2009)

Ketonen's proof of invertibility of the logical rules of his sequent calculus used the structural rule of cut. ❋ Unknown (2009)

Cross Reference for Sequent

  • Sequent cross reference not found!

What does sequent mean?

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