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Generalized quantifiers in formal concept analysis

M. Eugenia Cornejo, Juan Carlos Díaz-Moreno, Jesús Medina
2021 Journal of Computational and Applied Mathematics  
Different properties and characterizations are studied and they have been applied to formal concept analysis, presenting the conjunctive and implicative concept-forming operators in this outstanding theory  ...  An interesting possibility, of decreasing the impact of this possible noise in the final results, is the consideration of generalized quantifiers.  ...  Formal-concept operators with generalized quantifiers This section will use generalized quantifiers to provide formal-concept operators with a weaker existential nature.  ... 
doi:10.1016/j.cam.2021.113772 fatcat:z3schs2zibdgxg3wsu3uoeijqy

Efficient Implementation of Semantic Relations in Lexical Databases

Uta Priss
1999 Computational intelligence  
The formalization of relations is based on a modeling of hierarchical relations in Formal Concept Analysis.  ...  framework of research on natural language analysis and formalization.  ...  More details on Formal Concept Analysis can be found in Ganter & Wille (1997) .  ... 
doi:10.1111/0824-7935.00083 fatcat:nqrmyoat2fdffb6uki4c2rnyge

Reviews

Klaus Wuttich
2003 Logic and Logical Philosophy  
Sher focuses her analysis on the philosophical significance of the generalization of quantifiers for a general characterization of logic and logical constants.  ...  In the last decades the importance of the notion of generalized quantifiers for mathematics, cognitive sciences and natural language analysis was brought out explicitly in a rich body of literature.  ...  The emphasis on the theoretical grounds for the generalization of quantifiers leads to genuine logical results belonging to the main themes of modern logic.  ... 
doi:10.12775/llp.1994.010 fatcat:g2updyzdt5htpey4t7tridfjqe

Generalization effect of quantifiers in a classification based on relational concept analysis

Agnès Braud, Xavier Dolques, Marianne Huchard, Florence Le Ber
2018 Knowledge-Based Systems  
Generalization effect of quantifiers in a classification based on relational concept analysis. Knowledge-Based Systems, Elsevier, 2018, 160, pp.  ...  This is achieved by iterating on Formal Concept Analysis (FCA). It can be used to discover knowledge patterns and implication rules in multi-relational datasets.  ...  Among them, Relational Concept Analysis (RCA) is a descriptive approach based on Formal Concept Analysis (FCA) that both builds a classification (a lattice of formal concepts) for each category of objects  ... 
doi:10.1016/j.knosys.2018.06.011 fatcat:vwimo6slang3vn6hbmhhv4whcy

Quantified Formal-Concept Operators

Maria Eugenia Cornejo, Juan Carlos Díaz-Moreno, Juan López-Rodríguez, Jesús Medina
2020 International Conference on Concept Lattices and their Applications  
Generalized quantifiers allow to decrease the outermost character of the universal and existential quantifiers. Concept-forming operators in Formal Concept Analysis have a universal character.  ...  This paper introduces a first approximation to quantified formal-concept operators with the main goal of decreasing this universal character and be less sensitive to noisy data.  ...  Formal-concept operators with generalized quantifiers This section will generalize the notion of generalized quantifier given in [25] by using adjoint triples.  ... 
dblp:conf/cla/CornejoDLM20 fatcat:4fhu4dpilzcl5nzmfe2lelst7y

A STUDY ON LIMITS TEACHING IN THE COLLEGE ANALYSIS MAJOR

Hye Young Oh
2014 Korean Journal of Mathematics  
In addition, we try to improve the understanding of -δ procedure of the limit taught in analysis.  ...  In this study, we consider the informal and formal definition of limit on the basis of middle and high school curriculum, and then analyze the reason of difficulties experienced when sophomores learn the  ...  Limit concept in analysis is the concept which distinguish analysis from other branch and the basic concept in understanding infinite concept.  ... 
doi:10.11568/kjm.2014.22.1.169 fatcat:udmop6u4qvgbfpqvddnywnc3x4

Mathematics Teacher Candidates' Conceptual Knowledges of the Concept of Limit in Single-Variable Functions

Birgül YILDIZ, Gonca İNCEOĞLU
2020 Turkish Online Journal of Qualitative Inquiry  
in the Analysis I course in their second year.  ...  The results showed that the teacher candidates' concept definitions were generally based on the right-left limit equation theorem and the dynamic form of the limit.  ...  When teacher candidates were asked to define the concept of limit, they generally turned to the formal definition.  ... 
doi:10.17569/tojqi.748187 fatcat:wpmo5vmiprcitew55ptd27obby

Which Mathematical Logic is the Logic of Mathematics?

Jaakko Hintikka
2012 Logica Universalis  
of mathematical concepts, in mathematical theorizing in general.  ...  But the most basic concepts of analysis involve dependent quantifiers. So how did Cauchy and his followers handle dependent quantifiers in defining notions like limit and convergence?  ... 
doi:10.1007/s11787-012-0065-6 fatcat:7egblszkrjg7lmnutjlz2igfqu

Detecting Important Patterns Using Conceptual Relevance Interestingness Measure [article]

Mohamed-Hamza Ibrahim, Rokia Missaoui, Jean Vaillancourt
2021 arXiv   pre-print
While off-the-shelf interestingness indices defined in Formal Concept Analysis may provide an effective relevance evaluation in several situations, they frequently give inadequate results when faced with  ...  massive formal contexts (and concept lattices), and in the presence of irrelevant concepts.  ...  Formal Concept Analysis Formal concept analysis (FCA) is a general mathematical framework for building clusters defined as object sets sharing common attributes.  ... 
arXiv:2110.11262v1 fatcat:ep5v3xzgb5gevjn4rph2oblwta

RCAexplore, a FCA based Tool to Explore Relational Data

Xavier Dolques, Agnès Braud, Marianne Huchard, Florence Le Ber
2019 International Conference on Formal Concept Analysis  
Relational Concept Analysis (RCA) is one variant of Formal Concept Analysis for multi-relational dataset exploration.  ...  quantifier (exist, forall, contains, percentage-quantifiers, etc.), and the considered formal and relational contexts.  ...  Relational Concept Anaysis (RCA) basics Relational Concept Analysis (RCA) is an extension of Formal Concept Analysis [5] which considers relational data, formalized within a relational context family  ... 
dblp:conf/icfca/DolquesBHB19 fatcat:67mtghosl5apjpg6procyqxbmm

Building a shared world: mapping distributional to model-theoretic semantic spaces

Aurélie Herbelot, Eva Maria Vecchi
2015 Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing  
We predict that there is a functional relationship between distributional information and vectorial concept representations in which dimensions are predicates and weights are generalised quantifiers.  ...  We further investigate the generation of natural language quantifiers from such vectors.  ...  Right now, many parsers give the same broad analysis to Mosquitoes are insects and Mosquitoes carry malaria, involving an underspecified/generic quantifier.  ... 
doi:10.18653/v1/d15-1003 dblp:conf/emnlp/HerbelotV15 fatcat:3zuchzfpsff7ldm6lhq3t6at6u

Inferring and quantifying causality in neuronal networks

Daniel Chicharro, Ralph G Andrzejak, Anders Ledberg
2011 BMC Neuroscience  
While Granger provided a measure to study causal interactions for Gaussian linear processes, the underlying concept (Granger causality) can be used to derive a general criterion to test for causality [  ...  We here show that the concept of Granger causality can be used to reliably determine between which nodes in a network causal interactions exist, but in contrast to commonly held beliefs, it is not adequate  ...  While Granger provided a measure to study causal interactions for Gaussian linear processes, the underlying concept (Granger causality) can be used to derive a general criterion to test for causality  ... 
doi:10.1186/1471-2202-12-s1-p192 pmcid:PMC3240292 fatcat:7j6n7pocj5a6veugzfo236jcli

First Notes on Maximum Entropy Entailment for Quantified Implications [chapter]

Francesco Kriegel
2017 Lecture Notes in Computer Science  
In order to pull the technique of maximum entropy entailment to the field of Formal Concept Analysis, we define the notion of entropy of a formal context with respect to the frequency of its object intents  ...  , and then define maximum entropy entailment for quantified implication sets, i.e., for sets of partial implications where each implication has an assigned degree of confidence.  ...  Formal Concept Analysis The field of Formal Concept Analysis was invented for at least two reasons: Firstly, it should formalize the philosophical notion of a concept -which is characterized by its extent  ... 
doi:10.1007/978-3-319-59271-8_10 fatcat:7ws3xf4abbcxpfl4lichvgolxq

J.M. Bocheński's method of philosophical analysis and contemporary applied ontology

Marek Lechniak
2013 Studies in East European thought  
In the second part of the paper I will compare Bocheński's method with the methods of modern applied ontology.  ...  The aim of this article is to reconstruct Bocheński's method of philosophical analysis as well as to clarify the purpose of that method and its basic elements.  ...  9xA x ð Þ or the law of interchanging existential quantifiers with general quantifiers, i.e. 9x8yP x; y ð Þ !  ... 
doi:10.1007/s11212-013-9180-z fatcat:j3m54cfrlzd4lc5gqg65dp76fq

Page 3640 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
The analysis of the suitability of the broader notion of logical quantifier (dwelt upon in the first two chapters) leads to a critical view of the nature of iogicality, which naturally reduces to the analysis  ...  It ba- sically treats a general common form of Henkin’s and Barwise’s branching quantifiers, which in a broad view generalize the con- cept of the scope of quantifiers with respect to variables.  ... 
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