# 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.