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Complete lattices
 Journal of Formalized Mathematics
, 1992
"... Summary. In the first section the lattice of subsets of distinct set is introduced. The join and meet operations are, respectively, union and intersection of sets, and the ordering relation is inclusion. It is shown that this lattice is Boolean, i.e. distributive and complementary. The second sectio ..."
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Cited by 119 (33 self)
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section introduces the poset generated in a distinct lattice by its ordering relation. Besides, it is proved that posets which have l.u.b.’s and g.l.b.’s for every two elements generate lattices with the same ordering relations. In the last section the concept of complete lattice is introduced
Some Properties of Complete Lattice
"... In this paper, properties of the subset of complete lattice, complemented lattice, complete complemented lattice had been discussed. ..."
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In this paper, properties of the subset of complete lattice, complemented lattice, complete complemented lattice had been discussed.
Aggregation Functionals on Complete Lattices
"... The aim of this paper is to introduce some classes of aggregation functionals when the evaluation scale is a complete lattice. Two different types of aggregation functionals are introduced and investigated. We consider a targetbased approach that has been studied in Decision Theory and we focus on ..."
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The aim of this paper is to introduce some classes of aggregation functionals when the evaluation scale is a complete lattice. Two different types of aggregation functionals are introduced and investigated. We consider a targetbased approach that has been studied in Decision Theory and we focus
FIXED POINTS AND COMPLETE LATTICES
"... Abstract. Tarski proved in 1955 that every complete lattice has the fixed point property. Later, Davis proved the converse that every lattice with the fixed point property is complete. For a chain complete ordered set, there is the well known AbianBrown fixed point result. As a consequence of the A ..."
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Abstract. Tarski proved in 1955 that every complete lattice has the fixed point property. Later, Davis proved the converse that every lattice with the fixed point property is complete. For a chain complete ordered set, there is the well known AbianBrown fixed point result. As a consequence
Fixpoints in Complete Lattices 1
"... Summary. Theorem (5) states that if an iterate of a function has a unique fixpoint then it is also the fixpoint of the function. It has been included here in response to P. Andrews claim that such a proof in set theory takes thousands of lines when one starts with the axioms. While probably true, su ..."
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to prove as in the Mizar development of cardinals the ≤ relation is synonymous with ⊆. Section 3 introduces the notion of the lattice of a lattice subset provided the subset has lubs and glbs. The main theorem of Section 4 is the Tarski theorem (43) that every monotone function f over a complete lattice L
Division of mappings between complete lattices
"... Keywords: The importance for image processing of a good theory for morphological operators in complete lattices is now well understood. In this paper we introduce inverses and quotients of mappings between complete lattices which are analogous to inverses and quotients of positive numbers. These con ..."
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Keywords: The importance for image processing of a good theory for morphological operators in complete lattices is now well understood. In this paper we introduce inverses and quotients of mappings between complete lattices which are analogous to inverses and quotients of positive numbers
Free Distributive Completions of Partial Complete Lattices
"... The free distributive completion of a partial complete lattice is the complete lattice that it is freely generated by the partial complete lattice `in the most distributive way'. This can be described as being a universal solution in the sense of universal algebra. Free distributive completions ..."
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Cited by 2 (1 self)
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The free distributive completion of a partial complete lattice is the complete lattice that it is freely generated by the partial complete lattice `in the most distributive way'. This can be described as being a universal solution in the sense of universal algebra. Free distributive
Complete Lattices and UpTo Techniques
, 2007
"... We propose a theory of upto techniques for proofs by coinduction, in the setting of complete lattices. This theory improves over existing results by providing a way to compose arbitrarily complex techniques with standard techniques, expressed using a very simple and modular semicommutation propert ..."
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Cited by 11 (6 self)
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We propose a theory of upto techniques for proofs by coinduction, in the setting of complete lattices. This theory improves over existing results by providing a way to compose arbitrarily complex techniques with standard techniques, expressed using a very simple and modular semi
Results 1  10
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235,550