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首页> 外文期刊>Journal of pure and applied algebra >Product representation for default bilattices: An application of natural duality theory
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Product representation for default bilattices: An application of natural duality theory

机译：默认功能的产品表示：自然对偶理论的应用

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Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model situations in which information is prioritised and so can be viewed hierarchically. These default bilattices are not interlaced: the lattice operations of one lattice structure do not preserve the order of the other one. The well-known product representation theorem for interlaced bilattices does not extend to bilattices which fail to be interlaced and the lack of a product representation has been a handicap to understanding the structure of default bilattices. In this paper we study, from an algebraic perspective, a hierarchy of varieties of default bilattices, allowing for different levels of default. We develop natural dualities for these varieties and thereby obtain a concrete representation for the algebras in each variety. This leads on to a form of product representation that generalises the product representation as this applies to distributive bilattices. (C) 2014 Elsevier B.V. All rights reserved.
机译：双点阵（即具有两个点阵结构的集合）提供了一种代数工具，可以同时对适当语言中句子的有效性和知识进行建模。尤其是，某些功能已被用来对信息被优先排序的情况进行建模，因此可以分层查看。这些默认的能力不是交错的：一个晶格结构的晶格操作不会保留另一个晶格结构的顺序。隔行扫描功能的众所周知的产品表示定理不会扩展到不能隔行扫描的功能，并且缺少产品表示形式已经成为理解默认功能的结构的障碍。在本文中，我们从代数的角度研究了违约能力种类的层次结构，允许不同级别的违约。我们为这些品种开发了自然对偶，从而获得了每个品种中代数的具体表示。这导致了一种产品表示形式，当适用于分布式功能时，该产品表示形式可以概括该产品表示形式。 （C）2014 Elsevier B.V.保留所有权利。

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