A construction of an optimal base for conditional attribute and attributional condition implications in triadic contexts

TL;DR

This work extends Triadic Concept Analysis to CAI and ACI by introducing quasi-features and unit pseudo-features, showing that pseudo-features provide a triadic analogue to pseudo-intents for generating minimal bases. It foregrounds context augmentation as a mechanism to derive richer bases and develops algorithms to compute unit pseudo-features and optimal bases, achieving substantial reductions in base size. The approach yields complete, minimal CAI/ACI bases with favorable reduction rates and establishes a complexity bound reflecting the combinatorial nature of feature computation in augmented triadic contexts. This has practical implications for succinctly representing triadic implications in applications leveraging FCA/TCA-structured knowledge.

Abstract

This article studies implications in triadic contexts. Specifically, we focus on those introduced by Ganter and Obiedkov, namely conditional attribute and attributional condition implications. Our aim is to construct an optimal base for these implications.

Figures (5)

• Figure 1: Left: a dyadic formal context ; Right: a simplified representation
• Figure 2: A triadic context
• Figure 3: Representations of the triadic context of Fig. \ref{['tab running context']}; Left context: Object-condition simplified and right context: object-attribute simplified
• Figure 4: Two augmentations: $Z=d{\times}PN$ (left) and $Z=(d{\times}PN) \cup (ac{\times}PRS)$ (right)
• Figure 5: Our running example (left context) and its augmentation by $Z=d{\times}P$ (right context).

Theorems & Definitions (53)

• Example 1
• Example 2
• Example 3
• Definition 1
• Example 4
• Proposition 1
• Definition 2
• Example 5
• Proposition 2
• proof