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23
Ultimate approximation and its application in nonmonotonic knowledge representation systems
, 2004
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Fixpoint 3valued semantics for autoepistemic logic
 IN PROCEEDINGS OF THE 15TH NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE. MIT PRESS / AAAIPRESS
, 1998
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Ultimate Approximations in Nonmonotonic Knowledge Representation Systems
 IN PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING, PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE (KR2002
, 2002
"... We study fixpoints of operators on lattices. To this end ..."
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Cited by 10 (7 self)
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We study fixpoints of operators on lattices. To this end
On the Yoneda completion of a quasimetric space
 Theoretical Computer Science
, 2002
"... Several theories aimed at reconciling the partial order and the metric space approaches to Domain Theory have been presented in the literature (e.g. [FK97], [BvBR9 8], [Smy89] and [Wag94]). We focus in this paper on two of these approaches: the Yoneda completion of generalized metric spaces of [BvBR ..."
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Cited by 8 (4 self)
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Several theories aimed at reconciling the partial order and the metric space approaches to Domain Theory have been presented in the literature (e.g. [FK97], [BvBR9 8], [Smy89] and [Wag94]). We focus in this paper on two of these approaches: the Yoneda completion of generalized metric spaces of [BvBR98], which finds its roots in work by Lawvere ([Law73], cf. also [Wag94]) and which is related to early work by Stoltenberg (e.g. [Sto67], [Sto67a] and [FG84]), and the Smyth completion ([Smy89],[Smy91],[Smy94],[Sun93] and [Sun95]). A netversion of the Yoneda completion, complementing the netversion of the Smyth completion ([Sun95]), is given and a comparison between the two types of completion is presented. The following open question is raised in [BvBR98]: "An interesting question is to characterize the family of generalized metric spaces for which [the Yoneda] completion is idempotent (it contains at least all ordinary metric spaces)." We show that the largest class of quasimetric spaces idempotent under the Yoneda completion is precisely the class of Smythcompletable spaces. A similar result has been obtained independently by B. Flagg and P. Sünderhauf in [FS96]
Extension of Valuations on Locally Compact Sober Spaces.
, 2000
"... We show that every locally finite continuous valuation defined on the lattice of open sets of a regular or locally compact sober space extends uniquely to a Borel measure. ..."
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Cited by 5 (0 self)
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We show that every locally finite continuous valuation defined on the lattice of open sets of a regular or locally compact sober space extends uniquely to a Borel measure.
Relating Multifunctions and Predicate Transformers through Closure Operators
 of Lecture Notes in Computer Science
, 1994
"... . We study relations between predicate transformers and multifunctions in a topological setting based on closure operators. We give topological definitions of safety and liveness predicates and using these predicates we define predicate transformers. State transformers are multifunctions with values ..."
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Cited by 4 (3 self)
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. We study relations between predicate transformers and multifunctions in a topological setting based on closure operators. We give topological definitions of safety and liveness predicates and using these predicates we define predicate transformers. State transformers are multifunctions with values in the collection of fixed points of a closure operator. We derive several isomorphisms between predicate transformers and multifunctions. By choosing different closure operators we obtain multifunctions based on the usual power set construction, on the Hoare, Smyth and Plotkin power domains, and based on the compact and closed metric power constructions. Moreover, they are all related by isomorphisms to the predicate transformers. 1 Introduction There are (at least) two different ways of assigning a denotational semantics to a programming language: forward or backward. A typical forward semantics is a semantics that models a program as a function from initial states to final states. In th...
Interim Bayesian Nash Equilibrium on Universal Type Spaces for Supermodular Games, Working Paper
, 2007
"... We prove the existence of a greatest and a least interim Bayesian Nash equilibrium for supermodular games of incomplete information. There are two main differences from the earlier proofs in Vives (1990) and Milgrom and Roberts (1990): (a) we use the interim formulation of a Bayesian game, in which ..."
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Cited by 4 (0 self)
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We prove the existence of a greatest and a least interim Bayesian Nash equilibrium for supermodular games of incomplete information. There are two main differences from the earlier proofs in Vives (1990) and Milgrom and Roberts (1990): (a) we use the interim formulation of a Bayesian game, in which each player’s beliefs are part of his or her type rather than being derived from a prior; (b) we use the interim formulation of a Bayesian Nash equilibrium, in which each player and every type (rather than almost every type) chooses a best response to the strategy profile of the other players. Given also the mild restrictions on the type spaces, we have a proof of interim Bayesian Nash equilibrium for universal type spaces (for the class of supermodular utilities), as constructed, for example, by Mertens and Zamir (1985). We also weaken restrictions on the set of actions.