Simplifying Implications with Positive and Negative Attributes: A Logic-Based Approach

Abstract

Concepts and implications are two facets of the knowledge contained within a binary relation between objects and attributes. Simplification logic (SL) has proved to be valuable for the study of attribute implications in a concept lattice, a topic of interest in the more general framework of formal concept analysis (FCA). Specifically, SL has become the kernel of automated methods to remove redundancy or obtain different types of bases of implications. Although originally FCA used only the positive information contained in the dataset, negative information (explicitly stating that an attribute does not hold) has been proposed by several authors, but without an adequate set of equivalence-preserving rules for simplification. In this work, we propose a mixed simplification logic and a method to automatically remove redundancy in implications, which will serve as a foundational standpoint for the automated reasoning methods for this extended framework.

Stream Convolution for Attribute Reduction of Concept Lattices

“…Furthermore, the generalization-specialization and partial order relations in the concept lattice implies the inclusion and partial inclusion of concepts, allowing for the extraction and application of rules. Since the introduction of formal concept analysis (FCA) in 1982, the concept lattice has been a research hotspot, including in the domains of construction [3], reduction [4], and rule extraction [5,6]. The main purpose of attribute reduction of a concept lattice is to eliminate redundant information and reduce the complexity of the concept lattice while keeping the relevant information unchanged.…”