کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4596038 1336146 2015 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Product representation for default bilattices: An application of natural duality theory
ترجمه فارسی عنوان
بازنمایی محصول برای پیش فرض ها: کاربرد نظریه دوگانگی طبیعی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 219, Issue 7, July 2015, Pages 2962–2988
نویسندگان
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