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### Logical Consequence (Entailment)

Given a set of formulae
**
Φ
**
**
**
and a formula
**
**
**
α
**
**
.
**

**
α
**
**
**
is a
**
logical consequence
**
of
**
Φ
**
**
**
iff
**
**

**
α
**
**
**
is true in every model in which
**
Φ
**
**
**
is true.

Notation:

**
Φ
**
**
**
**
⊧
**
**
**
**
α
**

That means that for every model (interpretation into a domain) in which
**
Φ
**
is true,
**
α
**
must also be true.

**Speaker notes:**