Sentence examples for sequent from inspiring English sources

Sequent calculus, decidability.

A decision procedure for such judgements is obtained by casting the grammar logic in the format of a Gentzen-style sequent calculus.

Proof nets, considered statically as graphs satisfying certain correctness criteria, remove spurious choices relating to the order of rule applications in sequent calculi: in this respect, they represent a purely 'declarative' view on categorial deductions.

Independently, in Béziau 2004, it was observed that by putting together the sequent rules for classical conjunction and the rules for classical disjunction, the resulting sequent calculus will (unexpectedly) prove the distributivity between conjunction and disjunction.

Returning to the first example (combining a sequent calculus with an axiomatic system), a better solution was proposed in Cruz-Filipe et al.

Thus, for example, although the formula Pt → E t is (quite properly) not valid on a supervaluational semantics, nevertheless since E t is true on every supervaluation on which Pt is true, the sequent (derivability statement) Pt ⊢ E t is improperly semantically valid.

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.

The word "sequent" used as a noun is a suggestion of Kleene's in his Introduction to Metamathematics (1952: 441), taken up in many languages in the form of purely invented words.

With Kleene's book, Gentzen's sequent calculi became generally known and accessible.

In a sequent calculus presentation one would instead add the inverted form, sometimes called Expansion, of the structural rule Contraction.

This corresponds to the idea of the logical sequent calculus, in which one often restricts initial sequents to the atomic case, i.e., to the case, where no meaning-determining right and left introduction rules are available.