Abstract
Rule-based knowledge bases are constantly increasing in volume, thus the knowledge stored as a set of rules is getting progressively more complex and when rules are not organized into any structure, the system is inefficient. In the author’s opinion, modification of both the knowledge base structure and inference algorithms lead to improve the efficiency of the inference process. Rules partition enables reducing significantly the percentage of the knowledge base analysed during the inference process. The form of the group’s representative plays an important role in the efficiency of the inference process. The good performance of this approach is shown through an extensive experimental study carried out on a collection of real knoswledge bases.
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Notes
- 1.
Rules have been extensively used in knowledge representation and reasoning. It is very space efficient: only a relatively small number of facts needs to be stored in the KB and the rest can be derived by the inference rules.
- 2.
- 3.
- 4.
The user has the possibility of creating KBs using a special creator or by importing a KB from a given data source. The format of the KBs enables working with a rule set generated automatically based on the rough set theory as well as with rules given apriori by the domain expert. The KB can have one of the following file formats: XML, RSES, TXT. It is possible to define attributes of any type: nominal, discrete or continuous. There are no limits for the number of rules, attributes, facts or the length of the rule.
- 5.
It allows for partitioning the rules using the algorithm with time complexity not higher than O(nk), where \(n=|R|\) and \(k=|PR|\). Simple strategies create final partition PR by a single search of rules set R according to the value of \(mc(r_i,R_j)\) function described above. For complex strategies, time complexity is rather higher than any simple partition strategy.
- 6.
Let us assume that threshold value \( 0 \le T \le 1\) exists.
- 7.
Thus, conjunction of pairs \((a_i,v_{1i}) (a_2,v_{2i})\ldots (a_s,v_{si})\)) may be both a conditional part of one rule and a representative of some group of rules.
- 8.
When more than one rule matches the working memory (it is called conflict set) and only one has to be selected, it is possible to use the following strategies: random, textual order, recency, specificity and refractoriness [1]. In the research, the author uses the textual order, the recency and the modified specificity strategies. The textual order fires the first matching rule, while the recency fires the rule which uses the data added most recently to the working memory and the specificity (complexity) fires the rule with the most conditions attached, which means that rules with a greater number of conditions or fewer variables are more specific and should be applied earlier because they use more data and can be used for special cases or exceptions to general rules.
- 9.
\(sim(F,R_j) = \frac{|F \cap Profile(R_j)|}{|F \cup Profile(R_j)|}\). The value of \(sim(F,Profile(R_j))\) is equal to 0 if there is no such fact \(f_i\) (or the hypothesis to prove) which is included in the representative of any group \(R_j\). It is equal to 1 if all facts (and/or hypothesis) are included in \(Profile(R_j)\) of group \(R_j\).
- 10.
The inputs are: PR - groups of rules with the representatives and F - the set of facts. The output is F the set of facts, including possible new facts obtained through the inference. The algorithm uses temporary variable R, which is the set of rules that is the result of the previous selection.
- 11.
In this paper, the following strategies are used: FR (first rule) — which fires the first rule in the conflict set (so it is relevant to the textual order strategy), LR (last rule) — which selects the rules recently added to the conflict set (so it works similarly to the recently strategy), SR (shortest rule) — which selects the rule with the smallest number of conditions, LOR (longest rule) — which chooses rules with the greatest number of conditions (so it is relevant to the specificity strategy).
- 12.
The mAHC approach for rules partitioning with using four different thresholds of similarity: \(k=0, k=0.25, k=0.5, k=1.0\).
- 13.
In Fig. 2 they are noticed as \(AHC\_general\), \(mAHC\_general\), \(AHC\_specialized\), \(mAHC\_specialized\), \(AHC\_weighted\) or \(mAHC\_weighted\).
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Acknowledgement
This work is a part of the project “Exploration of rule knowledge bases” founded by the Polish National Science Centre (NCN: 2011/03/D/ST6/03027).
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Nowak-Brzezińska, A. (2016). Mining Rule-Based Knowledge Bases. In: Kozielski, S., Mrozek, D., Kasprowski, P., Małysiak-Mrozek, B., Kostrzewa, D. (eds) Beyond Databases, Architectures and Structures. Advanced Technologies for Data Mining and Knowledge Discovery. BDAS BDAS 2015 2016. Communications in Computer and Information Science, vol 613. Springer, Cham. https://doi.org/10.1007/978-3-319-34099-9_6
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