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Combining of Circuits
, 2002
"... this paper. 1. COMBINING OF MANY SORTED SIGNATURES Let S be a many sorted signature. A gate of S is an element of the operation symbols of S ..."
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Cited by 93 (25 self)
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this paper. 1. COMBINING OF MANY SORTED SIGNATURES Let S be a many sorted signature. A gate of S is an element of the operation symbols of S
Homomorphisms of many sorted algebras
 Journal of Formalized Mathematics
, 1994
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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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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.
Definitions and basic properties of boolean and union of many sorted sets
 Journal of Formalized Mathematics
, 1995
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Certain Facts about Families of Subsets of Many Sorted Sets
, 2002
"... this paper. 1. Preliminaries For simplicity, we follow the rules: I, G, H, i are sets, A, B, M are many sorted sets indexed by I, s 1 , s 2 , s 3 are families of subsets of I, v, w are subsets of I, and F is a many sorted function indexed by I ..."
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Cited by 9 (4 self)
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this paper. 1. Preliminaries For simplicity, we follow the rules: I, G, H, i are sets, A, B, M are many sorted sets indexed by I, s 1 , s 2 , s 3 are families of subsets of I, v, w are subsets of I, and F is a many sorted function indexed by I
On the composition of macro instructions of standard computers
 Formalized Mathematics
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The Equational Characterization of Continuous Lattices
, 2003
"... The class of continuous lattices can be characterized by infinitary equations. Therefore, it is closed under the formation of subalgebras and homomorphic images. Following the terminology of [18] we introduce a continuous lattice subframe to be a sublattice closed under the formation of arbitrary i ..."
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Cited by 7 (0 self)
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The class of continuous lattices can be characterized by infinitary equations. Therefore, it is closed under the formation of subalgebras and homomorphic images. Following the terminology of [18] we introduce a continuous lattice subframe to be a sublattice closed under the formation of arbitrary infs and directed sups. This notion corresponds with a subalgebra of a continuous lattice in [16]. The class of completely distributive lattices is also introduced in the paper. Such lattices are complete and satisfy the most restrictive type of the general distributivity law. Obviously each completely distributive lattice is a Heyting algebra. It was hard to find the best Mizar implementation of the complete distributivity equational condition (denoted by CD in [16]). The powerful and well developed Many Sorted Theory gives the most convenient way of this formalization. A set double indexed by K, introduced in the paper, corresponds with a family {x j,k: j ∈ J,k ∈ K ( j)}. It is defined to be a suitable many sorted function. Two special functors: Sups and Infs as counterparts of Sup and Inf respectively, introduced in [33], are also defined. Originally the equation in Definition 2.4 of [16, p. 58] looks as follows: j∈J k∈K ( j)x j,k = � � f ∈M j∈Jx j, f ( j), where M is the set of functions defined on J with values f(j) ∈ K ( j).
Institution of many sorted algebras. Part I: Signature reduct of an algebra
 Journal of Formalized Mathematics
, 1996
"... Summary. In the paper the notation necessary to construct the institution of many ..."
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Cited by 7 (7 self)
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Summary. In the paper the notation necessary to construct the institution of many