Two Axiomatizations of Nelson Algebras

نویسنده

  • Adam Grabowski
چکیده

Nelson algebras were first studied by Rasiowa and BiałynickiBirula [1] under the name N-lattices or quasi-pseudo-Boolean algebras. Later, in investigations by Monteiro and Brignole [3, 4], and [2] the name “Nelson algebras” was adopted – which is now commonly used to show the correspondence with Nelson’s paper [14] on constructive logic with strong negation. By a Nelson algebra we mean an abstract algebra

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity

This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, that the variety $mathbf{RDQDStSH_1}$ of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{RDQDStSH_1}$-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--...

متن کامل

Dually quasi-De Morgan Stone semi-Heyting algebras I. Regularity

This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...

متن کامل

Nabla Algebras and Chu Spaces

This paper is a study into some properties and applications of Moss’ coalgebraic or ‘cover’ modality ∇. First we present two axiomatizations of this operator, and we prove these axiomatizations to be sound and complete with respect to basic modal and positive modal logic, respectively. More precisely, we introduce the notions of a modal ∇-algebra and of a positive modal ∇-algebra. We establish ...

متن کامل

A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events

We give a nitary axiomatization of the algebra of regular events involving only equations and equational implications Unlike Salo maa s axiomatizations the axiomatization given here is sound for all interpretations over Kleene algebras

متن کامل

Characterisations of Nelson Algebras

Nelson algebras arise naturally in algebraic logic as the algebraic models of Nelson’s constructive logic with strong negation. This note gives two characterisations of the variety of Nelson algebras up to term equivalence, together with a characterisation of the finite Nelson algebras up to polynomial equivalence. The results answer a question of Blok and Pigozzi and clarify some earlier work ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Formalized Mathematics

دوره 23  شماره 

صفحات  -

تاریخ انتشار 2015