bounded latticeとは 意味・読み方・使い方

使用する際の注意点

The greatest element is usually denoted 1 and serves as the identity element of the meet operation, ∧. The least element, usually denoted 0, serves as the identity element of the join operation, ∨. The notations ⊤ and ⊥ are also used, less often, for greatest and least element respectively.

A bounded lattice may be defined formally as a tuple, ${\displaystyle (L,\lor ,\land ,0,1)}$. Regarding ${\displaystyle L}$ as an already defined lattice leads to the join and meet functions being, implicitly, defined in terms of the partial relation, ${\displaystyle \leq }$. Alternatively (regarding ${\displaystyle L}$ as a set), the partial relation can be defined in terms of the join and meet functions.

For any ${\displaystyle x\in L,\ 0\leq x\leq 1}$. That is, the elements 0 and 1 are each comparable with every other element of the lattice.

派生語

• lower bounded lattice
• upper bounded lattice

Further reading

• Lattice (order) on Wikipedia.
• Greatest and least elements on Wikipedia.
• Heyting algebra on Wikipedia.