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330
Many sorted algebras
- Journal of Formalized Mathematics
, 1994
"... Summary. The basic purpose of the paper is to prepare preliminaries of the theory of many sorted algebras. The concept of the signature of a many sorted algebra is introduced as well as the concept of many sorted algebra itself. Some auxiliary related notions are defined. The correspondence between ..."
Abstract
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Cited by 123 (14 self)
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Summary. The basic purpose of the paper is to prepare preliminaries of the theory of many sorted algebras. The concept of the signature of a many sorted algebra is introduced as well as the concept of many sorted algebra itself. Some auxiliary related notions are defined. The correspondence between
Many sorted quotient algebra
- Journal of Formalized Mathematics
, 1994
"... Summary. This article introduces the construction of a many sorted quotient algebra. A few preliminary notions such as a many sorted relation, a many sorted equivalence relation, a many sorted congruence and the set of all classes of a many sorted relation are also formulated. ..."
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Cited by 20 (0 self)
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Summary. This article introduces the construction of a many sorted quotient algebra. A few preliminary notions such as a many sorted relation, a many sorted equivalence relation, a many sorted congruence and the set of all classes of a many sorted relation are also formulated.
Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations
- Theoretical Computer Science
, 1992
"... This paper generalizes many-sorted algebra (hereafter, MSA) to order-sorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of object-oriented programming), several forms of pol ..."
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Cited by 231 (36 self)
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This paper generalizes many-sorted algebra (hereafter, MSA) to order-sorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of object-oriented programming), several forms
Equations in many sorted algebras
- Journal of Formalized Mathematics
, 1997
"... Summary. This paper is preparation to prove Birkhoff’s Theorem. Some properties of many sorted algebras are proved. The last section of this work shows that every equation valid in a many sorted algebra is also valid in each subalgebra, and each image of it. Moreover for a family of many sorted alge ..."
Abstract
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Cited by 4 (1 self)
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Summary. This paper is preparation to prove Birkhoff’s Theorem. Some properties of many sorted algebras are proved. The last section of this work shows that every equation valid in a many sorted algebra is also valid in each subalgebra, and each image of it. Moreover for a family of many sorted
The symplectic nature of fundamental groups of surfaces
- ADV. MATH
, 1984
"... A symplectic structure on a manifold is a closed nondegenerate exterior 2-form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metric which is Klhler. Many moduli spaces associated with Riemann surfaces have such Kahler structures: the ..."
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Cited by 223 (8 self)
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A symplectic structure on a manifold is a closed nondegenerate exterior 2-form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metric which is Klhler. Many moduli spaces associated with Riemann surfaces have such Kahler structures
Equations in Many Sorted Algebras
, 2003
"... This paper is preparation to prove Birkhoff's Theorem. Some properties of many sorted algebras are proved. The last section of this work shows that every equation valid in a many sorted algebra is also valid in each subalgebra, and each image of it. Moreover for a family of many sorted algeb ..."
Abstract
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Cited by 2 (1 self)
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This paper is preparation to prove Birkhoff's Theorem. Some properties of many sorted algebras are proved. The last section of this work shows that every equation valid in a many sorted algebra is also valid in each subalgebra, and each image of it. Moreover for a family of many sorted
On the algebraization of many-sorted logics
- Recent Trends in Algebraic Development Techniques - Selected Papers
, 2007
"... Abstract. The theory of abstract algebraic logic aims at drawing a strong bridge between logic and universal algebra, namely by generalizing the well known connection between classical propositional logic and Boolean algebras. Despite of its successfulness, the current scope of application of the th ..."
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Cited by 2 (2 self)
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of the theory is rather limited. Namely, logics with a many-sorted language simply fall out from its scope. Herein, we propose a way to extend the existing theory in order to deal also with many-sorted logics, by capitalizing on the theory of many-sorted equational logic. Besides showing that a number
On the Trivial Many Sorted Algebras and Many Sorted Congruences
"... This paper contains properties of many sorted functions between two many sorted sets. Other theorems describe trivial many sorted algebras. In the last section there are theorems about many sorted congruences, which are defined on many sorted algebras. I have also proved facts about natural epimo ..."
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This paper contains properties of many sorted functions between two many sorted sets. Other theorems describe trivial many sorted algebras. In the last section there are theorems about many sorted congruences, which are defined on many sorted algebras. I have also proved facts about natural
Results 1 - 10
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330
