Quantificational Definitions for PL

Question 1

Quantificational Truth

Answer 1

A sentence P of Pl is quantificationally true if and only if P is true on every interpretation.

Question 2

Quantificational Falsity

Answer 2

A sentence P of PL is quantificationally false if and only if P is false on every interpretation

Question 3

Quantificational Indeterminacy

Answer 3

A sentence P of PL is quantificationally indeterminate if and only if P is neither quantificationally true nor quantificationally false

Question 4

Quantificational Equivalence

Answer 4

Sentences P and Qu fo PL are quantificationally equivalent if and only if there is no interpretation on which P and Q have different truth-values.

Question 5

Quantificational Consistency

Answer 5

A set of sentences of Pl is quantificationally consistent if and only if there is at least one interpretation on which all the members of the set are true. A set of sentences of PL is quantificationally inconsistent if and only if the set is not quantificational consistent.

Question 6

Quantificational Entailment

Answer 6

A set (GAMMA) of sentences of PL quantificationally entails a sentence P of PL if and only if there is no interpretation on which ever member of GAMMA is true and P is false.

Question 7

Quantificational Validity

Answer 7

An argument of PL is quantificationally valid if and only if there is no interpretation on which all the premises are true and the conclusion is false. An argument of PL is quantificationally invade if and only if the argument is not quantificationally valid.