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Bases of Closure Systems

K. Adaricheva and J. B. Nation
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K. Adaricheva: Nazarbayev University, School of Science and Technology
J. B. Nation: University of Hawaii, Department of Mathematics

Chapter Chapter 6 in Lattice Theory: Special Topics and Applications, 2016, pp 181-213 from Springer

Abstract: Abstract In Section 4-2.2 we discussed the fundamental connection between closure systems and sets of implications. In this chapter, we will look into the canonical forms of representations of a closure system by implications. Most of the results are inspired by the structure of the closure lattice and its properties. In particular, we will be concerned with effective representations of closure systems whose closure lattices are join-semidistributive, lower bounded or locally distributive.

Date: 2016
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DOI: 10.1007/978-3-319-44236-5_6

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