Representing L-Domains as Information Systems

Spreen, Dieter

doi:10.1515/9783110324921.501

Cited by 3 publications

(3 citation statements)

References 19 publications

(35 reference statements)

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“…Theorem 4. 15 The category ISW of information systems with witnesses and approximable mappings is equivalent to the category L of L-domains and Scott continuous functions. Corollary 4.…”

Section: Note That For Approximable Mappings Hmentioning

confidence: 99%

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Generalised Information Systems Capture L-Domains

Spreen

2016

Preprint

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A generalisation of Scott's information systems [14] is presented that captures exactly all L-domains. The global consistency predicate in Scott's definition is relativised in such a way that there is a consistency predicate for each atomic proposition (token) saying which finite sets of such statements express information that is consistent with the given statement.It is shown that the states of such generalised information systems form an L-domain, and that each L-domain can be generated in this way, up to isomorphism. Moreover, the equivalence of the category of generalised information systems with the category of L-domains is derived. In addition, it will be seen that from every generalised information system capturing an algebraic bounded-complete domain a corresponding Scott information system can be obtained in an easy and natural way; similarly for Hoofman's continuous information systems [9] and the continuous bounded-complete domains captured by them.

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“…Theorem 4. 15 The category ISW of information systems with witnesses and approximable mappings is equivalent to the category L of L-domains and Scott continuous functions. Corollary 4.…”

Section: Note That For Approximable Mappings Hmentioning

confidence: 99%

“…A Scott-style logic-oriented approach capturing general L-domains was introduced by the present author in [15]. However, as in the other approaches, consistency witnesses were hidden.…”

Section: Introductionmentioning

confidence: 99%

Generalised Information Systems Capture L-Domains

Spreen

2016

Preprint

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“…To name a few examples, we have Scott's representations of Scott domains as information systems [23], Abramsky's flexible work domain theory in logical form for SFP-domains [1] and its extensions [2,13], some topological investigations by Vickers [26]. More articles about this issue can be found in [14,16,24,25].…”

Section: Introductionmentioning

confidence: 99%

Continuous Domains in Formal Concept Analysis*

Wang

Guo

2021

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Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion of contractive mappings over formal contexts is proposed, which can be viewed as a generalization of interior operators on sets into the framework of FCA. Then, by considering subset-selections consistent with contractive mappings, the notions of attribute continuous formal contexts and continuous concepts are introduced. It is shown that the set of continuous concepts of an attribute continuous formal context forms a continuous domain, and every continuous domain can be restructured in this way. Moreover, the notion of F-morphisms is identified to produce a category equivalent to that of continuous domains with Scott continuous functions. The paper also investigates the representations of various subclasses of continuous domains including algebraic domains and stably continuous semilattices.

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Information systems for continuous semi-lattices

Wang

Zhou

2022

Theoretical Computer Science

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Representing L-Domains as Information Systems

Cited by 3 publications

References 19 publications

Generalised Information Systems Capture L-Domains

Generalised Information Systems Capture L-Domains

Continuous Domains in Formal Concept Analysis*

Information systems for continuous semi-lattices

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