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G.: Approximable concepts, Chu spaces, and information systems. Theory and Applications of Categories (200x
"... ABSTRACT. This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration ..."
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Cited by 12 (8 self)
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ABSTRACT. This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of crossdisciplinary connections. Among other results, we show that the notion of state in Scott’s information system corresponds precisely to that of formal concepts in FCA with respect to all finite Chu spaces, and the entailment relation corresponds to “association rules”. We introduce, moreover, the notion of approximable concept and show that approximable concepts represent algebraic lattices which are identical to Scott domains except the inclusion of a top element. This notion serves as a stepping stone in the recent work [Hitzler and Zhang, 2004] in which a new notion of morphism on formal contexts results in a category equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings. 1.
A cartesian closed category of approximable concept structures
 Proceedings of the International Conference On Conceptual Structures
, 2004
"... Abstract. Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection betwe ..."
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Cited by 6 (4 self)
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Abstract. Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection between formal concept analysis and domain theory as a categorical equivalence, enriching the link between the two areas as outlined in [25]. Building on a new notion of approximable concept introduced by Zhang and Shen [26], this paper provides an appropriate notion of morphisms on formal contexts and shows that the resulting category is equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings. Since the latter categories are cartesian closed, we obtain a cartesian closed category of formal contexts that respects both the context structures as well as the intrinsic notion of approximable concepts at the same time. 1
Structural Operational Semantics and Modal Logic, Revisited
"... A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is reexamined and improved in some aspects. Firstly, a more abstract, conceptual proof of the main compositionality theorem is given, based on an understanding of modal l ..."
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Cited by 3 (1 self)
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A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is reexamined and improved in some aspects. Firstly, a more abstract, conceptual proof of the main compositionality theorem is given, based on an understanding of modal logic as a study of coalgebras in slice categories of adjunctions. Secondly, a more concrete understanding of the assumptions of the theorem is provided, where proving compositionality amounts to finding a syntactic distributive law between two collections of predicate liftings. Keywords: structural operational semantics, modal logic, coalgebra 1
FcAWN: Concept Analysis as a Formal Method for Automated WebMenu Design
 Conceptual Structures at Work, Shaker Verlag
, 2004
"... Abstract. Webmenu is one of the most important and widely used modalities in HumanComputer Interaction (HCI). The design and construction of navigation menus for websites, however, have traditionally been left to the intuition of a web developer. This paper proposes the use of a mathematical theor ..."
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Cited by 1 (1 self)
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Abstract. Webmenu is one of the most important and widely used modalities in HumanComputer Interaction (HCI). The design and construction of navigation menus for websites, however, have traditionally been left to the intuition of a web developer. This paper proposes the use of a mathematical theory called Formal Concept Analysis (FCA) [5, 9, 14, 16, 17] to assist in the design and automatic generation of a navigation hierarchy for a set of web documents. We demonstrate how multilayered menu models can be devised and automatically generated by an adaptation and application of the principle of FCA and its associated algorithms. Our approach, FcAWN (pronounced fawn) – Formal concepts Applied to Web Navigation – reveals a fundamental difference between existing webmenu layouts and the ones generated using FCA: many of today’s webmenu hierarchies are tree structures in which submenus do not overlap, while menuhierarchies obtained using FCA are part of a lattice structure in which submenus are not required to be mutually exclusive. FcAWN is one of the few semiautomated webmenu design methods with which one can construct consistent and logical menu hierarchies for web navigation. 1
Chu Spaces: Towards New Justification for Fuzzy Heuristics
, 2000
"... We show that Chu spaces, a new formalism used to describe parallelism and information flow, provide uniform explanations for different choices of fuzzy methodology, such as choices of fuzzy logical operations, of membership functions, of defuzzification, etc. 1 What Are Chu Spaces? 1.1 World Acc ..."
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We show that Chu spaces, a new formalism used to describe parallelism and information flow, provide uniform explanations for different choices of fuzzy methodology, such as choices of fuzzy logical operations, of membership functions, of defuzzification, etc. 1 What Are Chu Spaces? 1.1 World According to Classical Physics It is well known that measurements can change the measured object: e.g., most methods of chemical analysis destroy a part of the analyzed substance; testing a car often means damaging it, etc. However, in classical (prequantum) physics it was assumed that in principle, we can make this adverse influence as small as possible. Therefore, ideally, each measurement can be described as a function r(x) from the set of all objects X to the set K of all measurement results. These measurements lead to a complete knowledge in the sense that an object x can be uniquely reconstructed from the results r(x) of all such measurements. 1.2 NonDeterminism in Modern Physics: En...
Principal Adviser
, 2006
"... is fully adequate in scope and quality as a dissertation for the degree ..."
Operational Theories and Categorical Quantum Mechanics
, 2013
"... A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative ..."
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A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative theories. Two formalisms which have been used in this context are operational theories, and categorical quantum mechanics. The aim of the present paper is to establish strong connections between these two formalisms. We show how models of categorical quantum mechanics have representations as operational theories. We then show how nonlocality can be formulated at this level of generality, and study a number of examples from this point of view, including Hilbert spaces, sets and relations, and stochastic maps. The local, quantum, and nosignalling models are characterized in these terms. 1