Lattice theory

partially ordered set that admits greatest lower and least upper bounds of any two elements

bounded lattice that models intuitionistic propositional logic

a rigorous method of deriving an ontology from a collection of objects and their properties

theorem

In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset. Dually, a meet-semilattice (or lower semilattice) is a partially ordered set which has a meet (or greatest lower bound) for any nonempty finite subset. Every join-semilattice is a meet-semilattice in the inverse order and vice versa.

partially ordered set in which all subsets have both a supremum and infimum

meet-join lattice that satisfies the self-dual modular law

combinatorial sequence of numbers

two related operations on a poset in order theory

reflexive symmetric relation compatible with the operations of an algebraic structure

lattice in which the operations of join and meet distribute over each other

bound lattice in which every element has a complement

graph with a unique median for each three vertices

thumb|right|500px|A modern rendering of the Tonnetz. The A minor Triad (music)|triad is in dark blue, and the C major triad is in dark red. Interpreted as a torus, the Tonnetz has 12 nodes (pitches) and 24 triangles (triads).

distributive lattice of integer partitions