Order-theoretic Foundations

Ganter, Bernhard; Wille, Rudolf

doi:10.1007/978-3-642-59830-2_1

Cited by 162 publications

(319 citation statements)

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“…The smallest complete poset (lattice) containingP k is its Dedekind-MacNeille completion. One way to construct it is to take the set of normal ideals ofP k ordered by inclusion [18] or to take the concept lattices of the formal contexts P k ,P k , ≤ or J k ,P k , ≤ [4]. We denote byP k the Dedekind-MacNeille completion ofP k .…”

Section: Properties Of the Homomorphism Order Of K-posetsmentioning

confidence: 99%

On the Homomorphism Order of Labeled Posets

Kwuida

Lehtonen

2010

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Abstract. Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and infima, and the complexity of certain decision problems involving the homomorphism order of k-posets. Sublattices are also examined.

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Section: Properties Of the Homomorphism Order Of K-posetsmentioning

confidence: 99%

On the Homomorphism Order of Labeled Posets

Kwuida

Lehtonen

2010

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“…Technical details of this are not presented here; see, for example [2]. This is based on the use Formal Concept Analysis [4], lattice theory [3] and aspects of Partially Shared Views (PSV) [13].…”

Section: Semantic Interoperability Through Devolved Ontologymentioning

confidence: 99%

“…Automatic reasoning within this context is underpinned by the use of Formal Concept Analysis [4] and Lattice Theory [3]. The resultant model, e.g.…”

Section: Introductionmentioning

confidence: 99%

Agents for Cross-Organisational Business Interoperability

Stalker

Mehandjiev

2009

Lecture Notes in Business Information Processing

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When citing this source, please use the final published version as above.This document was downloaded from http://tees.openrepository.com/tees/handle/10149/95375 Please do not use this version for citation purposes.All items in TeesRep are protected by copyright, with all rights reserved, unless otherwise indicated. Abstract. Increasing complexity of products and services together with shrinking lead times means that demands are often best satisfied through dynamic networks of collaborating enterprises. Businesses seek agile partnerships where companies focus on core business activities and partners provide complementary expertise. Successful collaboration demands a tight yet flexible integration of business processes. In this paper we focus on issues of process interoperability and the use of agents to support cross-organisational process interoperability. We maintain that an informed decision on the place of agents within this context demands a systematic approach: such an approach forms the core contribution of this paper. We apply a modified version of the function-behaviourstructure (FBS) framework of Gero as an organising schema to develop a clarifying structure; and to help determine the role of software agents. Agents for Cross-Organisational Business InteroperabiltiyIn particular, we use the formal elements of the FBS framework to identify those areas where agents may be applied. We highlight the need to combine this with appropriate mechanisms to promote semantic interoperability.

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“…3 By means of a state context (Definition 3, Table 3 left part), temporal data can be translated into the language of FCA. The dynamics is modeled by a binary relation R ⊆ G × G on the set of states, which gives rise to a transition context K (Definition 4, Table 1): the objects are transitions (elements of the relation) and the attributes the values of the entities defining the input and output state of a transition.…”

Section: Constructing the Knowledge Base -Summary Of The Methodsmentioning

confidence: 99%

“…At present, FCA is a richly developed mathematical theory, and there are practical applications in various fields as data and text mining, knowledge management, semantic web, software engineering or economics [3]. FCA has been used for the analysis of gene expression data in [2] and [13], but this is the first approach of applying it to model (gene) regulatory networks.…”

Section: Introductionmentioning

confidence: 99%

Constructing a Knowledge Base for Gene Regulatory Dynamics by Formal Concept Analysis Methods

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Abstract. Our aim is to build a set of rules, such that reasoning over temporal dependencies within gene regulatory networks is possible. The underlying transitions may be obtained by discretizing observed time series, or they are generated based on existing knowledge, e.g. by Boolean networks or their nondeterministic generalization. We use the mathematical discipline of formal concept analysis (FCA), which has been applied successfully in domains as knowledge representation, data mining or software engineering. By the attribute exploration algorithm, an expert or a supporting computer program is enabled to decide about the validity of a minimal set of implications and thus to construct a sound and complete knowledge base. From this all valid implications are derivable that relate to the selected properties of a set of genes. We present results of our method for the initiation of sporulation in Bacillus subtilis. However the formal structures are exhibited in a most general manner. Therefore the approach may be adapted to signal transduction or metabolic networks, as well as to discrete temporal transitions in many biological and nonbiological areas.

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Order-theoretic Foundations

Cited by 162 publications

References 0 publications

On the Homomorphism Order of Labeled Posets

On the Homomorphism Order of Labeled Posets

Agents for Cross-Organisational Business Interoperability

Constructing a Knowledge Base for Gene Regulatory Dynamics by Formal Concept Analysis Methods

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