Single Idea 13541

[catalogued under 5. Theory of Logic / K. Features of Logics / 2. Consistency]

Full Idea

Any system of proof S is said to be 'negation-consistent' iff there is no formula such that |-(S)φ and |-(S)¬φ.

Clarification

The '(S)' should actually be a subscript

Gist of Idea

For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ

Source

David Bostock (Intermediate Logic [1997], 4.5)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.167


A Reaction

Compare Idea 13542. This version seems to be a 'strong' version, as it demands a higher standard than 'absolute consistency'. Both halves of the condition would have to be established.

Related Idea

Idea 13542 A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock]