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The Transition to Formal Thinking in Mathematics
"... This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulati ..."
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Cited by 25 (5 self)
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and manipulations. Pure mathematics in university shifts towards a formal framework of axiomatic systems and mathematical proof. In this paper, the transition in thinking is formulated within a framework of ‘three worlds of mathematics’ – the ‘conceptualembodied ’ world based on perception, action and thought
Classification Methods Based on Formal Concept Analysis
"... Abstract. Formal Concept Analysis (FCA) provides mathematical models for many domains of computer science, such as classification, categorization, text mining, knowledge management, software development, bioinformatics, etc. These models are based on the mathematical properties of concept lattices. ..."
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Abstract. Formal Concept Analysis (FCA) provides mathematical models for many domains of computer science, such as classification, categorization, text mining, knowledge management, software development, bioinformatics, etc. These models are based on the mathematical properties of concept lattices
A Formal Foundation for OntologyAlignment Interaction Models
"... Abstract. Ontology alignment foundations are hard to find in the literature. The abstract nature of the topic and the diverse means of practice make it difficult to capture it in a universal formal foundation. We argue that such a lack of formality hinders further development and convergence of prac ..."
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Cited by 12 (9 self)
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of practices, and in particular, prevents us from achieving greater levels of automation. In this article we present a formal foundation for ontology alignment that is based on interaction models between heterogeneous agents on the Semantic Web. We use the mathematical notion of information flow in a
Mathematics Subject Classification
"... Abstract Spatial point processes are stochastic models for point patterns, systems of points scattered in R d . A point process can be used as a generating stochastic mechanism for additional spatial random systems such as random tessellations, random fields and random graphs, which are collectivel ..."
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Abstract Spatial point processes are stochastic models for point patterns, systems of points scattered in R d . A point process can be used as a generating stochastic mechanism for additional spatial random systems such as random tessellations, random fields and random graphs, which
Whom You Know Matters: Venture Capital Networks and Investment Performance,
 Journal of Finance
, 2007
"... Abstract Many financial markets are characterized by strong relationships and networks, rather than arm'slength, spotmarket transactions. We examine the performance consequences of this organizational choice in the context of relationships established when VCs syndicate portfolio company inv ..."
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Cited by 138 (8 self)
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adjacency matrices over trailing fiveyear windows. Using these matrices, we construct five centrality measures based on three popular concepts of centrality: Degree, closeness, and betweenness. Using a numerical example, the Appendix shows in detail how these centrality measures are constructed. Here, we
Morphisms in Logic, Topology, and Formal Concept Analysis
, 2005
"... The general topic of this thesis is the investigation of various notions of morphisms between logical deductive systems, motivated by the intuition that additional (categorical) structure is needed to model the interrelations of formal specifications. This general task necessarily involves considera ..."
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Cited by 3 (2 self)
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The general topic of this thesis is the investigation of various notions of morphisms between logical deductive systems, motivated by the intuition that additional (categorical) structure is needed to model the interrelations of formal specifications. This general task necessarily involves
Category Theory as a Mathematics for Formalizing Ontologies

, 2007
"... Category theory is discussed as an appropriate mathematical basis for the formalization and study of ontologies. It is based upon the notion of the structure manifest in systems of compositional relations and through mappings between systems that preserve composition. With one or two important excep ..."
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Cited by 1 (0 self)
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Category theory is discussed as an appropriate mathematical basis for the formalization and study of ontologies. It is based upon the notion of the structure manifest in systems of compositional relations and through mappings between systems that preserve composition. With one or two important
Expressiveness and complexity of formal systems
, 1998
"... Formalization has a central role in computer science. Communication between man and computers as well as information processing within computer systems require that concepts and objects of the application domain are formally represented through some artificial language. In the last fifty years, the ..."
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Formalization has a central role in computer science. Communication between man and computers as well as information processing within computer systems require that concepts and objects of the application domain are formally represented through some artificial language. In the last fifty years
Fuzzy Concepts and Formal Methods: An Extended Notation for Z
, 1999
"... It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the IS problem domain, ..."
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Cited by 1 (1 self)
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It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the IS problem domain
Mining Patterns in Numerical Data with Formal Concept Analysis
, 2010
"... The thesis of Mehdi Kaytoue addressed the important problem of mining patterns in numerical data, also known as quantitative itemset problem. Usually, numerical data are turned into binary data from which well known itemsets and association rules are extracted. Extracting those patterns is a first ..."
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step for knowledge discovery processes. Nevertheless, transforming the data faces a tradeoff: it comes either with loss of information, or hard computational properties of the resulting binary data. The proposed approach is defined within a well known and mathematically defined framework: formal
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