103 research outputs found

    Towards a generalisation of formal concept analysis for data mining purposes

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    In this paper we justify the need for a generalisation of Formal Concept Analysis for the purpose of data mining and begin the synthesis of such theory. For that purpose, we first review semirings and semimodules over semirings as the appropriate objects to use in abstracting the Boolean algebra and the notion of extents and intents, respectively. We later bring to bear powerful theorems developed in the field of linear algebra over idempotent semimodules to try to build a Fundamental Theorem for K-Formal Concept Analysis, where K is a type of idempotent semiring. Finally, we try to put Formal Concept Analysis in new perspective by considering it as a concrete instance of the theory developed

    Injecting Abstract Interpretations into Linear Cost Models

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    We present a semantics based framework for analysing the quantitative behaviour of programs with regard to resource usage. We start from an operational semantics equipped with costs. The dioid structure of the set of costs allows for defining the quantitative semantics as a linear operator. We then present an abstraction technique inspired from abstract interpretation in order to effectively compute global cost information from the program. Abstraction has to take two distinct notions of order into account: the order on costs and the order on states. We show that our abstraction technique provides a correct approximation of the concrete cost computations

    Order automorphisms on the lattice of residuated maps of some special nondistributive lattices.

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    The residuated maps from a lattice L to itself form their own lattice, which we denote Res(L). In this dissertation, we explore the order automorphisms on the lattice Res(L) where L is a finite nondistributive lattice. It is known that left and right composition of f ∈ Res(L) with automorphisms of L yields an order automorphism of Res(L). It begs the question, then, if all order automorphisms of Res(L) can be classified as such

    Parameterizing the semantics of fuzzy attribute implications by systems of isotone Galois connections

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    We study the semantics of fuzzy if-then rules called fuzzy attribute implications parameterized by systems of isotone Galois connections. The rules express dependencies between fuzzy attributes in object-attribute incidence data. The proposed parameterizations are general and include as special cases the parameterizations by linguistic hedges used in earlier approaches. We formalize the general parameterizations, propose bivalent and graded notions of semantic entailment of fuzzy attribute implications, show their characterization in terms of least models and complete axiomatization, and provide characterization of bases of fuzzy attribute implications derived from data

    A multi-modal logic for Galois connections

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    Advances in Modal Logic 2022 (Rennes, August 22-25
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