The Common Order-Theoretic Structure of Version Spaces and ATMS's (1991)
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| Venue: | In Proceedings of the National Conference on Artificial Intelligence |
| Citations: | 6 - 0 self |
BibTeX
@INPROCEEDINGS{Gunter91thecommon,
author = {Carl A. Gunter and Teow-hin Ngair and Devika Subramanian},
title = {The Common Order-Theoretic Structure of Version Spaces and ATMS's},
booktitle = {In Proceedings of the National Conference on Artificial Intelligence},
year = {1991},
pages = {500--505},
publisher = {AAAI Press}
}
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Abstract
We demonstrate how order-theoretic abstractions can be useful in identifying, formalizing, and exploiting relationships between seemingly dissimilar AI algorithms that perform computations on partially-ordered sets. In particular, we show how the order-theoretic concept of an anti-chain can be used to provide an efficient representation for such sets when they satisfy certain special properties. We use anti-chains to identify and analyze the basic operations and representation optimizations in the version space learning algorithm [10] and the assumption-based truth maintenance system (ATMS) [2, 3]. Our analysis allows us to (1) extend the known theory [7, 10, 8] of admissibility of concept spaces for incremental version space merging, and (2) develop new, simpler label-update algorithms for ATMS's with DNF assumption formulas. Contents 1 Introduction 2 2 Representing Sets as Anti-Chains 4 3 Version Spaces 17 4 Assumption-Based Truth Maintenance Systems 32 5 Extended ATMS's 46 6 Ackno...
