The second Rehnquist Court has remained unchanged in composition for 8 yr, resulting in a large temporally stable database. This paper reports on a mathematically objective analysis of this ensemble of rulings aimed at extracting key patterns and latent information. Although the rulings of a nine-justice Court require representation in nine dimensions, smaller spaces describe the Court's action...

We present a framework for extending Stone’s representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive latt...

Let £ be a $0$-distributive lattice with the least element $0$, the greatest element $1$, and ${rm Z}(£)$ its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by ${rm T}(G (£))$. It is the graph with all elements of £ as vertices, and for distinct $x, y in £$, the vertices $x$ and $y$ are adjacent if and only if $x vee y in {rm Z}(£)$. The basic properties of the ...

Through an analysis of two different types of floating numeral quantifier (FNQ) constructions in Japanese, the present paper investigates the distributive and non-distributive interpretation in Japanese. Discussion of the interpretative issues related to ambiguity and intonation has indicated that FNQs are potentially ambiguous, offering both distributive and non-distributive readings.