Sentence examples for intuitionistic from high-quality English sources.

• is fundamental to intuitionistic type theory.

• These laws are not valid in intuitionistic type theory.

• For further discussion, see the entry on intuitionistic logic.

• The system C is a conservative extension of positive intuitionistic logic.

• This dampened the enthusiasm of the mathematical community for the intuitionistic project.

• Later on, Gödel (1932) tried to understand intuitionistic logic in terms of many truth degrees.

• The British philosopher Michael Dummett (1973) developed a philosophical basis for Intuitionism, in particular for intuitionistic logic.

• Meyer Viol (1995a, 1995b) contain further proof- and model-theoretic studies of the epsilon calculus; specifically intuitionistic epsilon calculi.

Use intuitionistic in a sentence.

• Williamson (1982) argues that Fitch’s proof is not a refutation of anti-realism, but rather a reason for the anti-realist to accept intuitionistic logic.

• Intuitionistic dependence logic retains the downwards closure property: if a team satisfies an intuitionistic dependence logic formula then so do all of its subsets.

• In fact, as is common in intuitionistic settings, a plethora of semantic and proof-theoretic methods are available for the study of constructive and intuitionistic set theories.

• Constructive and intuitionistic Zermelo-Fraenkel set theories are axiomatic theories of sets in the style of Zermelo-Fraenkel set theory (ZF) which are based on intuitionistic logic.

• A variety of interpretations for intuitionistic logic have been extended to intuitionistic and constructive set theories, such as realisability, Kripke models and Heyting-valued semantics.

• Both the intuitionistic view of logic as essentially sterile, and the existence of results in intuitionistic logic that are incompatible with classical logic, depend essentially on that conception.

• In intuitionistic reverse mathematics one has a similar aim, but then with respect to intuitionistic theorems: working over a weak intuitionistic theory, axioms and theorems are compared to each other.

• Constructive and intuitionistic Zermelo-Fraenkel set theories are based on intuitionistic rather than classical logic, and represent a natural environment within which to codify and study mathematics based on intuitionistic logic.

intuitionistic sentence examples

• Hence, if intuitionistic mathematics contains objects and principles that do not figure in classical mathematics, it may come about that intuitionistic logic, which then depends also on these non-classical elements, is no proper part of classical logic.

• Double negation elimination and classical contraposition fail to be valid in intuitionistic logic (see the entry on intuitionistic logic); if one of them is added to an axiom system of intuitionistic logic, one obtains a proof system for classical logic.

• logic, history of: intuitionistic logic | logic: intuitionistic | mathematics, philosophy of: intuitionism | mathematics: constructive | proof theory: development of | semantics: Montague | semantics: proof-theoretic | set theory | set theory: constructive and intuitionistic ZF | set theory: Zermelo’s axiomatization of | type theory | type theory: Church’s type theory

• Brouwer, Luitzen Egbertus Jan | category theory | choice, axiom of | logic, history of: intuitionistic logic | logic: intuitionistic | mathematics, philosophy of | mathematics, philosophy of: intuitionism | mathematics: constructive | paradoxes: and contemporary logic | proof theory | semantics: proof-theoretic | set theory | set theory: alternative axiomatic theories | set theory: early development | set theory: non-wellfounded | type theory | type theory: intuitionistic