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.
| Original language | English |
|---|---|
| Title of host publication | Lattice Theory |
| Subtitle of host publication | Special Topics and Applications |
| Publisher | Springer International Publishing |
| Pages | 181-213 |
| Number of pages | 33 |
| Volume | 2 |
| ISBN (Electronic) | 9783319442365 |
| ISBN (Print) | 9783319442358 |
| DOIs | |
| Publication status | Published - Jan 1 2016 |
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ASJC Scopus subject areas
- Mathematics(all)
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Bases of closure systems. / Adaricheva, Kira; Nation, J. B.
Lattice Theory: Special Topics and Applications. Vol. 2 Springer International Publishing, 2016. p. 181-213.Research output: Chapter in Book/Report/Conference proceeding › Chapter
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TY - CHAP
T1 - Bases of closure systems
AU - Adaricheva, Kira
AU - Nation, J. B.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85018076865&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85018076865&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-44236-5_6
DO - 10.1007/978-3-319-44236-5_6
M3 - Chapter
SN - 9783319442358
VL - 2
SP - 181
EP - 213
BT - Lattice Theory
PB - Springer International Publishing
ER -