Logic definitions

Question 1

Sound argument

Answer 1

An argument is sound iff it is BOTH valid and all the premises are true

Question 1

Define Validity

Answer 1

An argument is valid iff it is impossible for all the premises to be true and the conclusion false

Question 2

Joint consistency

Answer 2

Sentences are jointly consistent iff it is possible for them to be true together
(opposite of a contradiction)

Question 3

Logical truth

Answer 3

A FOL sentence is a logical truth iff it is true on every interpretation

Question 4

Contradiction

Answer 4

A TFL sentence is a contradiction iff it is false on every valuation

Question 5

Tautology

Answer 5

in TFL, If a sentence is true on every line of a complete truth table, then it is a tautology

Question 6

Tautologically equivalent

Answer 6

Iff sentences have the same TRUTH VALUE (whether F or T) on EVERY valuation then they are tautologically equivalent

Question 7

Jointly tautologically consistent

Answer 7

Iff there is SOME valuation that makes all the sentences true

Question 8

Jointly tautologically inconsistent

Answer 8

Iff there is not one valuation that makes ALL the sentences all true

Question 9

Tautological entailment
A1,A2,…,An ⊨ C

Answer 9

A conclusion is tautological entailed by atomic sentences in TFL iff no valuation of the relevant atomic sentences makes all of the premises true and the conclusion false.

(if on some line of the truth table, the rows are T and the conclusion is F, there is NOT tautological entailment)

Question 10

contingency

Answer 10

Something which is capable of being true or false, but which is neither necessarily true nor necessarily false