Definition:Sequent

Definition

A sequent is an expression in the form:

$\phi_1, \phi_2, \ldots, \phi_n \vdash \psi$

where $\phi_1, \phi_2, \ldots, \phi_n$ are premises (any number of them), and $\psi$ the conclusion (only one), of an argument.

Also presented as

Instead of presenting the sequent all on one line, separated by commas, it is often arranged in a vertical form:

\(\ds \phi_1\)

\(\)

\(\ds \)

\(\ds \phi_2\)

\(\)

\(\ds \)

\(\ds \ldots\)

\(\)

\(\ds \)

\(\ds \phi_n\)

\(\)

\(\ds \)

\(\ds \vdash \ \ \)

\(\ds \psi\)

\(\)

\(\ds \)

Which form is preferred depends on personal taste or convenience.

A long sequent with complex premises is often better presented in the vertical form, whereas a simpler sequent which is easily comprehended at a glance may merit the single-line treatment.

Sources

• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): $\S 1.2$: Conditionals and Negation
• 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.2$: Natural Deduction