The Duality of Good Diagnostic Tests

2010 ◽  
pp. 211-244
Author(s):  
Xenia Naidenova
Keyword(s):  
Incremental Learning ◽  
Formal Concept Analysis ◽  
Learning Algorithm ◽  
Test Construction ◽  
Formal Concept ◽  
Good Test ◽  
Algebraic Lattices ◽  
Good Classification ◽  
A Chain ◽  
Mental Acts

The concept of good classification test is redefined in this chapter as a dual element of interconnected algebraic lattices. The operations of lattice generation take their interpretations in human mental acts. Inferring the chains of dual lattice elements ordered by the inclusion relation lies in the foundation of generating good classification tests. The concept of an inductive transition from one element of a chain to its nearest element in the lattice is determined. The special reasoning rules for realizing inductive transitions are formed. The concepts of admissible and essential values (objects) are introduced. Searching for admissible or essential values (objects) as a part of reasoning is based on the inductive diagnostic rules. In this chapter, we also propose a non-incremental learning algorithm NIAGaRa based on a reasoning process realizing one of the ways of lattice generation. Next, we discuss the relations between the good test construction and the Formal Concept Analysis (FCA).

Constructing Galois Lattices as a Commonsense Reasoning Process

2013 ◽  
pp. 34-70 ◽  
Author(s):  
Xenia Naidenova
Keyword(s):  
Formal Concept Analysis ◽  
Formal Concept ◽  
Commonsense Reasoning ◽  
Dual Lattice ◽  
Inclusion Relation ◽  
Galois Lattices ◽  
Algebraic Lattices ◽  
Good Classification ◽  
A Chain ◽  
Mental Acts

The concept of good classification test is used in this chapter as a dual element of the interconnected algebraic lattices. The operations of lattice generation take their interpretations in human mental acts. Inferring the chains of dual lattice elements ordered by the inclusion relation lies in the foundation of generating good classification tests. The concept of an inductive transition from one element of a chain to its nearest element in the lattice is determined. The special reasoning rules for realizing inductive transitions are formed. The concepts of admissible and essential values (objects) are introduced. Searching for admissible and essential values (objects) as a part of reasoning is based on the inductive diagnostic rules. Next, the chapter discusses the relations between constructing good tests and the Formal Concept Analysis (FCA). The decomposition of inferring good classification tests is advanced into two kinds of subtasks that are in accordance with human mental acts. This decomposition allows modeling incremental inductive-deductive inferences. The problems of creating an integrative inductive-deductive model of commonsense reasoning are discussed in the last section of this chapter.

m-Algebraic lattices in formal concept analysis

2019 ◽  
Vol 29 (10) ◽  
pp. 1556-1574
Author(s):  
Zhongxi Zhang ◽  
Qingguo Li ◽  
Nan Zhang
Keyword(s):  
Complete Lattice ◽  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Continuous Functions ◽  
Algebraic Lattice ◽  
Formal Concept ◽  
Algebraic Lattices ◽  
Special Cases ◽  
Cartesian Closed

AbstractThe notion of an m-algebraic lattice, where m stands for a cardinal number, includes numerous special cases, such as complete lattice, algebraic lattice, and prime algebraic lattice. In formal concept analysis, one fundamental result states that every concept lattice is complete, and conversely, each complete lattice is isomorphic to a concept lattice. In this paper, we introduce the notion of an m-approximable concept on each context. The m-approximable concept lattice derived from the notion is an m-algebraic lattice, and conversely, every m-algebraic lattice is isomorphic to an m-approximable concept lattice of some context. Morphisms on m-algebraic lattices and those on contexts are provided, called m-continuous functions and m-approximable morphisms, respectively. We establish a categorical equivalence between LATm, the category of m-algebraic lattices and m-continuous functions, and CXTm, the category of contexts and mapproximable morphisms.We prove that LATm is cartesian closed whenevermis regular and m > 2. By the equivalence of LATm and CXTm, we obtain that CXTm is also cartesian closed under same circumstances. The notions of a concept, an approximable concept, and a weak approximable concept are showed to be special cases of that of an m-approximable concept.

scholarly journals Continuous Domains in Formal Concept Analysis*

2021 ◽  
Vol 179 (3) ◽  
pp. 295-319
Author(s):  
Longchun Wang ◽  
Lankun Guo ◽  
Qingguo Li
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Continuous Functions ◽  
Formal Context ◽  
Formal Concept ◽  
Contractive Mappings ◽  
Continuous Domains ◽  
Algebraic Domains ◽  
Scott Continuous ◽  
Continuous Domain

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.

The Research of Semantic Web Service Matching Algorithm Based on the Formal Concept Analysis

2013 ◽  
Vol 760-762 ◽  
pp. 1708-1712
Author(s):  
Ying Fang Li ◽  
Ying Jiang Li ◽  
Yan Li ◽  
Yang Bo
Keyword(s):  
Semantic Web ◽  
Web Service ◽  
Formal Concept Analysis ◽  
Service Discovery ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Concept ◽  
Semantic Web Service ◽  
Matching Algorithm ◽  
Service Matching

At present, as the number of web services resources on the network drastically increased, how to quickly and efficiently find the needed services from publishing services has become a problem to resolve. Aiming at the problems of low efficiency in service discovery of traditional web service, the formal concept analysis ( FCA) is introduced into the semantic Web service matching, and a Matching Algorithm based semantic web service is proposed. With considering the concept of limited inheritance,this method introduces the concept of limited inheritance to the semantic similarity calculation based on the concept lattice. It is significant in enhancing the service function matching in practical applications through adjust the calculation.

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