Satisfiability

We say that a logical statement is satisfiable when there exists at least one truth assignment that makes the overall statement true.

In our Logika truth tables, this corresponds to statements that are either contingent or a tautology. (Contradictory statements are NOT satisfiable.)

For example, consider the following truth tables:

          *
-----------------------
p q r | p → q V ¬r ∧ p
-----------------------
T T T |   T   T F  F
T T F |   T   T T  T
T F T |   F   F F  F
T F F |   T   T T  T
F T T |   T   T F  F
F T F |   T   T T  F
F F T |   T   F F  F
F F F |   T   F T  F
------------------------

Contingent

- T: [T T T] [T T F] [T F F] [F T T] [F T F] [F F T] [F F F]
- F: [T F T]

And

      *
------------
p | p V ¬p 
------------
T |   T F
F |   T T
-------------

Tautology

Both of these statements are satisfiable, as they have at least one (or more than one) truth assignment that makes the overall statement true.