Inductive discovery of laws using monotonic rules

We are considering knowledge discovery from data describing a piece of real or abstract world. The patterns being induced put in evidence some laws hidden in the data. The most natural representation of patterns-laws is by ''if..., then...'' decision rules relating some conditions with some decisions. The same representation of patterns is used in multi-attribute classification, thus the data searched for discovery of these patterns can be seen as classification data. We adopt the classification perspective to present an original methodology of inducing general laws from data and representing them by so-called monotonic decision rules. Monotonicity concerns relationships between values of condition and decision attributes, e.g. the greater the mass (condition attribute), the greater the gravity (decision attribute), which is a specific feature of decision rules discovered from data using the Dominance-based Rough Set Approach (DRSA). While in DRSA one has to suppose a priori the presence or absence of positive or negative monotonicity relationships which hold in the whole evaluation space, in this paper, we show that DRSA can be adapted to discover rules from any kind of input classification data, exhibiting monotonicity relationships which are unknown a priori and hold in some parts of the evaluation space only. This requires a proper non-invasive transformation of the classification data, permitting representation of both positive and negative monotonicity relationships that are to be discovered by the proposed methodology. Reported results of a computational experiment confirm that the proposed methodology leads to decision rules whose predictive ability is similar to the best classification predictors. It has, however, a unique advantage over all competitors because the monotonic decision rules can be read as laws characterizing the analyzed phenomena in terms of easily understandable ''if..., then...'' decision rules, while other predictor models have no such straightforward interpretation.