کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
394584 665814 2010 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the role of logical connectives for primality and functional completeness of algebras of logics
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
On the role of logical connectives for primality and functional completeness of algebras of logics
چکیده انگلیسی

We consider certain finite universal algebras arising from algebraic semantics in implicational logics. They contain a binary operation →→ and two constants 0 and 1 satisfying the axioms 0→x=x→1=x→x=10→x=x→1=x→x=1 and 1→x=x1→x=x valid in most implicational logics. We characterize the completeness (also called primality) of such algebras, i.e. the property that every finitary operation on their universe is a term operation of the algebra (in other words, it is a composition of the basic operations of the algebra). Using clone theory and the knowledge of maximal clones we describe completeness (functional completeness) in terms of nonpreservation of three types of specific relations. If →→ has a simple property and the algebra contains a binary operation ⊙⊙ with a neutral element 1 and a unary operation ¬¬ satisfying ¬(1)=0¬(1)=0 and ¬x=1¬x=1 otherwise, the algebra is functionally complete.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Information Sciences - Volume 180, Issue 8, 15 April 2010, Pages 1345–1353
نویسندگان
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