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Some Issues Concerning Fixed Points in Computational Logic: QuasiMetrics, Multivalued Mappings and the KnasterTarski Theorem
, 2000
"... Many questions concerning the semantics of disjunctive databases and of logic programming systems depend on the xed points of various multivalued mappings and operators determined by the database or program. We discuss known versions, for multivalued mappings, of the KnasterTarski theorem and of th ..."
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Many questions concerning the semantics of disjunctive databases and of logic programming systems depend on the xed points of various multivalued mappings and operators determined by the database or program. We discuss known versions, for multivalued mappings, of the KnasterTarski theorem
Some Issues Concerning Fixed Points in Computational Logic: QuasiMetrics, Multivalued Mappings and the KnasterTarski Theorem
, 2000
"... Many questions concerning the semantics of disjunctive databases and of logic programming systems depend on the fixed points of various multivalued mappings and operators determined by the database or program. We discuss known versions, for multivalued mappings, of the KnasterTarski theorem and of ..."
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Cited by 10 (8 self)
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Many questions concerning the semantics of disjunctive databases and of logic programming systems depend on the fixed points of various multivalued mappings and operators determined by the database or program. We discuss known versions, for multivalued mappings, of the KnasterTarski theorem
Distance kSectors and Zone Diagrams
"... We prove the existence and uniqueness of the zone diagram of a given set of sites in Euclidean space. This was known for point sites in the plane, but our proof is simpler even for this specific case. We also show the existence of a distance ksector between two sites. Both proofs rely on the Knaste ..."
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Cited by 1 (1 self)
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on the Knaster–Tarski theorem on fixed points of monotone functions. 1
Lattices and Orders in Isabelle/HOL
, 2008
"... We consider abstract structures of orders and lattices. Many fundamental concepts of lattice theory are developed, including dual structures, properties of bounds versus algebraic laws, lattice operations versus settheoretic ones etc. We also give example instantiations of lattices and orders, such ..."
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, such as direct products and function spaces. Wellknown properties are demonstrated, like the KnasterTarski Theorem for complete lattices. This formal theory development may serve as an example of applying Isabelle/HOL to the domain of mathematical reasoning about “axiomatic” structures. Apart from the simply
Topology and Iterates in Computational Logic
 Proceedings of the 12th Summer Conference on Topology and its Applications: Special Session on Topology in Computer Science
, 1997
"... We consider the problem of finding models for logic programs P via fixed points of immediate consequence operators, T P . Certain extensions of syntax invalidate the classical approach, adopted in the case of definite programs, using iterates of T P and the KnasterTarski theorem. We discuss alterna ..."
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Cited by 22 (17 self)
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We consider the problem of finding models for logic programs P via fixed points of immediate consequence operators, T P . Certain extensions of syntax invalidate the classical approach, adopted in the case of definite programs, using iterates of T P and the KnasterTarski theorem. We discuss
Least and Greatest Fixed Points, Knaster, and Tarski
"... y of sets and classes, however, we can nevertheless construct a greatest fixed point as [ X`\Phi(X) X: What we would like to have, however, is J := [ x`\Phi(x) x2V x (B) to be the greatest fixed point, where V is the class of all sets. By the KnasterTarski proof we still get J ` \Phi(J ) a ..."
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y of sets and classes, however, we can nevertheless construct a greatest fixed point as [ X`\Phi(X) X: What we would like to have, however, is J := [ x`\Phi(x) x2V x (B) to be the greatest fixed point, where V is the class of all sets. By the KnasterTarski proof we still get J ` \Phi
Topology and Iterates in Computational Logic
"... Email pascalhitzlerstudentunituebingende We consider the problem of nding models for logic programs P via xed points of immediate consequence operators T P Certain extensions of syntax invalidate the classical approach adopted in the case of denite programs using iterates of T P and the Knaster ..."
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and the KnasterTarski theorem We discuss alternatives to the use of this theorem based on elementary notions from topological dynamics This leads us to consider simple syntactic conditions on P employing level mappings taking values in a countable ordinal which ensure convergence to models and xed points
Solving for Set Variables in HigherOrder Theorem Proving
 Proceedings of the 18th International Conference on Automated Deduction
, 2002
"... In higherorder logic, we must consider literals with exible (set variable) heads. Set variables may be instantiated with logical formulas of arbitrary complexity. An alternative to guessing the logical structures of instantiations for set variables is to solve for sets satisfying constraints. U ..."
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Cited by 6 (1 self)
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. Using the KnasterTarski Fixed Point Theorem [ 15 ] , constraints whose solutions require recursive de nitions can be solved as xed points of monotone set functions. In this paper, we consider an approach to higherorder theorem proving which intertwines conventional theorem proving in the form
RECONCILIATION OF ELEMENTARY ORDER AND METRIC FIXPOINT THEOREMS
"... Abstract. We prove two new fixed point theorems for generalized metric spaces and show that various fundamental fixed point principles, including: Banach Contraction Principle, Caristi fixed point theorem for metric spaces, KnasterTarski fixed point theorem for complete lattices, and the BourbakiW ..."
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Abstract. We prove two new fixed point theorems for generalized metric spaces and show that various fundamental fixed point principles, including: Banach Contraction Principle, Caristi fixed point theorem for metric spaces, KnasterTarski fixed point theorem for complete lattices, and the Bourbaki
On the Origins of Bisimulation and
"... Bisimulation and bisimilarity are coinductive notions, and as such are intimately related to fixed points, in particular greatest fixed points. Therefore also the appearance of coinduction and fixed points is discussed, though in this case only within Computer Science. The paper ends with some histo ..."
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historical remarks on the main fixedpoint theorems (such as KnasterTarski) that underpin the fixedpoint theory presented.
Results 1  10
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