more from Robert S. Wolf

Single Idea 13525

[catalogued under 5. Theory of Logic / K. Features of Logics / 10. Monotonicity]

Full Idea

Deductive logic, including first-order logic and other types of logic used in mathematics, is 'monotonic'. This means that we never retract a theorem on the basis of new givens. If T|-φ and T⊆SW, then S|-φ. Ordinary reasoning is nonmonotonic.

Gist of Idea

Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens


Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.7)

Book Reference

Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.54

A Reaction

The classic example of nonmonotonic reasoning is the induction that 'all birds can fly', which is retracted when the bird turns out to be a penguin. He says nonmonotonic logic is a rich field in computer science.