Abstract
This chapter focuses on the study of association rules for ordered data by using the system of closed sets of sequences, defined by operator \(\triangle\). Our contribution is a notion of deterministic association rules with order where a set of sequences always implies another sequence in the data. The central advantage of dealing with deterministic rules is that they do not require to select, with little or no formal guidance, one single measure of strength of implication because they always hold. Moreover, since they are pure standard implications, they can be studied in purely logical terms. Indeed, in the second chapter we already mentioned that the set of deterministic association rules derived from classical lattice-theoretic methods axiomatize the minimal Horn upper bound of a binary relation [14]. On the basis of this formalization, the main result of this chapter is a similar characterization of the implications with order as the empirical Horn approximation of the input set of sequences. To allow for this characterization, we will require the definition of certain background Horn conditions to ensure the consistency of the theory. As a consequence of this main result, we can also prove the isomorphy of the lattice of closed sets of sequences and the classical binary lattice when the background Horn conditions hold. Finally, we discuss the computation of all these rules in practice.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springe -Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Garriga, G.C. (2013). Horn Axiomatizations for Sequences. In: Formal Methods for Mining Structured Objects. Studies in Computational Intelligence, vol 475. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36681-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-36681-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36680-2
Online ISBN: 978-3-642-36681-9
eBook Packages: EngineeringEngineering (R0)