4. TAUTOLOGY,
CONTRADICTION,
CONTINGENT
• A TAUTOLOGY – A SENTENCE THAT IS TRUE IN EVERY
MODEL
• A CONTRADICTION – A SENTENCE THAT IS FALSE IN EVERY
MODEL
• CONTIGENT SENTENCE – A SENTENCE THAT IS NEITHER
TAUTOLOGY NOR CONTRADICTION
5. VALIDITY IN QL
• A SET OF SENTENCES IS VALID IFF THERE IS NO
MODEL WHERE THE PREMISES ARE TRUE AND THE
CONCLUSION IS FALSE. OTHERWISE, THE SET OF
SENTENCES IS INVALID
6. LOGICAL EQUIVALENCY
AND CONSISTENCY
• A SET OF SENTENCES IS LOGICALLY EQUIVALENT WHEN A |= B
and B |= A
• A SET OF SENTENCES IS CONSISTENT WHEN THERE IS AT LEAST
ONE MODEL IN WHICH ALL OF THE SENTENCES ARE TRUE
7. PRACTICE: PART E
1. Da & Db
We need to show that it’s contingent.
1) This sentence is false in this model:
UD: {Abby, Billy}
Ext. (D) = {Billy}
ref (a) = Abby
ref (b) = Billy
2) This sentence is true in this model:
UD: {Abby, Billy}
Ext. (D) = {Abby, Billy}
ref (a) = Abby
ref (b) = Billy
