heyting algebra
Word Rarity
Very rare
Frequency: Zipf frequency 0.00 in modern English
24
Scrabble Score
14
Letters
4
Syllables
11
Unique Chars
Meaning
noun
A bounded lattice, L, modified to serve as a model for a logical calculus by being equipped with a binary operation called "implies", denoted → (sometimes ⊃ or ⇒), defined such that (a→b)∧a ≤ b and, moreover, that x = a→b is the greatest element such that x∧a ≤ b (in the sense that if c∧a ≤ b then c ≤ a→b).
Example Sentences
- "The laws of Heyting algebra embody a rich and profound mathematical structure that is manifest in a variety of contexts. It arises from the epistemological deliberations of Brouwer, the topologisation (localisation) of set-theoretic notions, and the categorial formulation of set theory, all of which, although interrelated, are independently motivated. The ubiquity lends weight, not to the suggestion that the correct logic is in fact intuitionistic instead of classical, but rather to the recognition that thinking in such terms is simply inappropriate — in the same way that it is inappropriate to speak without qualification about the correct geometry."
- "which is just obvious."
- "1997, J. G. Stell, M. W. Worboys, The Algebraic Structure of Sets and Regions, Stephen C. Hirtle, Andrew U. Frank (editors), Spatial Information Theory A Theoretical Basis for GIS: International Conference, Proceedings, Springer, LNCS 1329, page 163, The main contention of this paper is that Heyting algebras, and related structures, provide elegant and natural theories of parthood and boundary which have close connections to the above three ontologies."
Etymology
After Dutch mathematician Arend Heyting, who developed the theory as a way of modelling his intuitionistic logic.
Inflected Forms
Phrases
bi-Heyting algebra
biHeyting algebra
co-Heyting algebra
coHeyting algebra
complete Heyting algebra
Heyting prealgebra
pseudo-complement
relative pseudo-complement
Frequently Paired Words
Synonyms
pseudo-Boolean algebra