LOGIC BASIC TERMS

Question 1

Validity

Answer 1

iff it is impossible to make all of the
premises true and the conclusion false.

Question 2

Jointly Contrary

Answer 2

To show given sentences are jointly contrary, a contradiction must be proved from assuming all the sentences given.

To show that some sentences A1, A2, … An are jointly contrary, construct a proof that takes A1, A2, … An as assumptions and concludes with ⊥

Question 3

Modal logical truth

Answer 3

An ML sentence A is a MODAL LOGICAL TRUTH iff A is true at every world in every interpretation

Question 4

Provably Equivalent

Answer 4

Two sentences are provably equivalent where each can be proved from the other. This requires a pair of proofs where you can derive B from assuming A as the premise, and vice versa.

A –> B :

• provide a pair of proofs: one starts with A and concludes with B, the other starts with B and concludes with A

Question 5

Theorem

Answer 5

A is a THEOREM if and only if there is a proof of A from no assumptions (⊢ A)

Question 6

Logically Equivalent

Answer 6

Two sentences have the same truth value in all possible interpretations.

they are tautological.

Question 7

Modal contradiction

Answer 7

An ML sentence A is a MODAL CONTRADICTION iff A is false at every world in every interpretation

Question 8

Modally consistent

Answer 8

An ML sentence A is MODALLY CONSISTENT iff A is TRUE
at some world in some interpretation

Question 9

Modally valid

Answer 9

A1, A2, … An; ∴C is MODALLY VALID iff there is no world in any interpretation in which all the premises are true and the conclusion is false