Gödel logic

In mathematical logic, Gödel logics, sometimes referred to as Dummett logics or Gödel–Dummett logics, is a family of finite- or infinite-valued logics in which the sets of truth values V are closed subsets of the unit interval [0,1] containing both 0 and 1. Different such sets V in general determine different Gödel logics.

Gödel logics have several alternative definitions. Specifically, Gödel logics are:

  • logics of linearly-ordered Heyting algebras
  • logics of (classes of) linearly ordered and countable intuitionistic Kripke structures with constant domains
  • logics of relative comparison, in contrast to Łukasiewicz logic, which is a logic of absolute comparison or metric comparison

The concept is named after Kurt Gödel and Michael Dummett.

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