Logic Definitions

Validity

an argument is valid if an only if it is impossible for all premises to be true and the conclusion false

Tautologically Equivalent

A + B are tautologically equivalent if and only if they have the same truth values on every valuation

Sound

An argument is sound if an only if it is valid and all of its premises are true

Jointly Consistent

Sentences are JOINTLY CONSISTENT if and only if it is possible for them all to be true together

Jointly Inconsistent

Sentences are JOINTLY INCONSISTENT if and only if it is not possible for them all to be true together

Necessary Truth

A sentence is a NECESSARY TRUTH if and only if it is true and it is not possible for it to be false

Necessary Falsehood

A sentence is a NECESSARY FALSEHOOD if and only if it is false and not possible for it to be true

Contingent

A sentence is CONTINGENT if and only if it is possible for it to be true and possible for it to be false

Tautology

A is a TAUTOLOGY iff it is true on every valuation

Contradiction

A is a CONTRADICTION iff it is false on every valuation

Tautologically Equivalent

A and B are TAUTOLOGICALLY EQUIVALENT iff they have the same truth value on every valuation

Jointly Tautologically Consistent

A1, A2, … An are JOINTLY TAUTOLOGOCALLY CONSISTENT iff there is some valuation that makes them all true

Jointly Tautologically Inconsistent

A1, A2, … An are JOINTLY TAUTOLOGOCALLY INCONSISTENT iff there is no valuation that makes them all true

Tautologically Entail

The sentences A1, A2, … An TAUTOLOGOCALLY ENTAIL the sentence C if there is no valuation of the atomic sentences

which makes all of A1, A2, … An true and C false