Heyting algebra
A Heyting algebra is a mathematical structure used in logic and theoretical computer science, particularly in intuitionistic logic—a system that rejects the law of excluded middle (that every statement is either true or false).
Where Boolean algebra models classical logic, Heyting algebra models reasoning that requires constructive proof.
The structure formalizes a logic in which proving something false isn't the same as proving its negation true.
Confined within limits
- meetCome into contact
- joinConnect or enlist
- distributiveConcerning fair division
- isomorphismStructure-preserving bijective map
frame · locale · complete · modular · complemented · dual · universal property · filter
Active knowledge-building theory
- logical connectivesSymbols joining logical statements
- implicationIndirect suggestion or consequence
- negationDenial or cancellation
- conjunctionWord joining clauses together
disjunction · sequent calculus · natural deduction · decidability · double negation · soundness · validity
Withdrawal or reduction
- pushoutForced expulsion from group
- adjunctionAttaching one thing another
- sheafBound bundle of stalks
bounded
Confined within limits
- meetCome into contact
- joinConnect or enlist
- distributiveConcerning fair division
isomorphism · frame · locale · complete · modular · complemented · dual · universal property · filter · ideal
constructivism
Active knowledge-building theory
- logical connectivesSymbols joining logical statements
- implicationIndirect suggestion or consequence
- negationDenial or cancellation
conjunction · disjunction · sequent calculus · natural deduction · decidability · double negation · soundness · validity
locale
Specific place or area
- nucleusCentral controlling part
pullback
Withdrawal or reduction
- pushoutForced expulsion from group
- adjunctionAttaching one thing another
- sheafBound bundle of stalks
- Constructive Logicintuitionism, constructivism, double negation, natural deduction, sequent calculus
- Intuitionismconstructivism, intuitive knowledge, self-evidence
- logicpremise, premises, conclusion, conclusions, inference
- abstract algebragroup, isomorphism, commutator, congruence, ideal
- nonclassical logicfuzzy logic
- order theorylattice, upper bound, lower bound, comparable, incomparable