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SPICE: A New Framework for Data Mining based on Probability Logic and Formal Concept Analysis

Jiang L., Deogun J.

Fundamenta Informaticae

2007

Vol. 78, nr 4

467-485

Formal concept analysis and probability logic are two useful tools for data analysis. Data is usually represented as a two-dimensional context of objects and features. FCA discovers dependencies within the data based on the relation among objects and features. On the other hand, the probability logic represents and reasons with both statistical and propositional probability among data. We propose SPICE - Symbolic integration of Probability Inference and Concept Extraction, which provides a more flexible and robust framework for data mining tasks. Within SPICE, we formalize the important notions of data mining, such as concepts and patterns, and develop new notions such as maximal potentially useful patterns. In this paper, we formalize the association rule mining in SPICE and propose an enhanced rule mining approach, called SPICE association rule mining, to solve the problem of time inefficiency and rule redundancy in general association rule mining. We show an application of the SPICE approach in the Geo-spatial Decision Support System (GDSS). The experimental results show that SPICE can efficiently and effectively discover a succinct set of interesting association rules.

A Fuzzy Modal Logic for Belief Functions

Godo L., Hájek P., Esteva F.

Fundamenta Informaticae

2003

Vol. 57, nr 2-4

127--146

In this paper we introduce a new logical approach to reason explicitly about Dempster-Shafer belief functions. We adopt the following view: one just starts with Boolean formulas j and a belief function on them; the belief of j is taken to be the truth degree of the (fuzzy) proposition Bj standing for ``j is believed''. For our complete axiomatization (Hylbert-style) we use one of the possible definitions of belief, namely as probability of (modal) necessity. This enables us to define a logical system combining the modal logic S5 with an already proposed fuzzy logic approach to reason about probabilities. In particular, our fuzzy logic is the logic P[ 1/2] which puts Lukasiewicz and Product fuzzy logics together.