semilattice

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noun

A partially ordered set that either has a join (a least upper bound) for any nonempty finite subset (a join-semilattice or upper semilattice) or has a meet (or greatest lower bound) for any nonempty finite subset (a meet-semilattice or lower semilattice). Equivalently, an underlying set which has a binary operation which is associative, commutative, and idempotent.

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Meanings

nounsemilattice (plural semilattices)

plural semilattices

  1. mathematicsA partially ordered set that either has a join (a least upper bound) for any nonempty finite subset (a join-semilattice or upper semilattice) or has a meet (or greatest lower bound) for any nonempty finite subset (a meet-semilattice or lower semilattice). Equivalently, an underlying set which has a binary operation which is associative, commutative, and idempotent.

Origin

From semi- + lattice.

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Cite this entry
APA

semilattice. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/semilattice

MLA

“semilattice.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/semilattice. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “semilattice,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/semilattice.

Source: semilattice on Wiktionary, CC BY-SA 4.0.