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...

The RNA exosome is a multisubunit 3' to 5' exoribonuclease complex that participates in degradation and processing of cellular RNA. To determine the activities and structure of the eukaryotic exosome, we report the reconstitution of 9-subunit exosomes from yeast and human and reconstitution of 10- and 11-subunit exosomes from yeast. Comparative biochemical analysis between purified subunits and...

The goal of this paper is to show how ideas from lattice theory can be used in the implementation of a knowledge representation language. First, the semantics of a simple knowledge representation language is presented. Then we show how to use Birkhoo's Representation Theorem for Finite Distributive Lattices to build incremen-tally what we call a Birkhoo implementation of a knowledge base by pro...

the starting point of this paper is given by priestley’s papers, where a theory of representation of distributive lattices is presented. the purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. in this way, some results of priestley’s papers are extended. in the main theorem, we show that the category of finite fuzzy priestley space...

The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...

Programs and data in distributive categories must be coded in some way in order to be executed on standard architectures. In the original mathematical description of an IMP(G) interpreter [KW93] distributive data were coded as words on a suitable set. We present a new ef cient coding for such data. This coding allows to exploit the known techniques used in run-time environments for object-orien...

We characterize the distributive lattices of Jacobson rings and prove that if a semiring is a distributive lattice of Jacobson rings, then, up to isomorphism, it is equal to the subdirect product of a distributive lattice and a Jacobson ring. Also, we give a general method to construct distributive lattices of Jacobson rings.

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.

The free distributive completion of a partial complete lattice is the complete lattice that it is freely generated by the partial complete latticèin the most distributive way'. This can be described as being a universal solution in the sense of universal algebra. Free distributive completions generalize the constructions of tensor products and of free completely distributive complete lattices o...