Assertion

Let W be a set.  An assertion of W is a tuple <A,s> where A is a set of sequents of W and s is a sequent of W.  The sequents in A are the assumptions of the assertion and s is its conclusion.

An assertion is written as
 

A ⊨ s

or as
 

p, q, . . .

s

where A = {p, q, . . .} is the set of assumptions.  If the set of assumptions is empty then the assertion is written
 

⊨ s

or simply as
 

s

There is no difference, other than appearance, due to the manner in which an assertion is presented.