A Brief Roadmap into Uncertain Knowledge Representation via Probabilistic Description Logics

Rafael Peñaloza

doi:10.3390/a14100280

Abstract

Logic-based knowledge representation is one of the main building blocks of (logic-based) artificial intelligence. While most successful knowledge representation languages are based on classical logic, realistic intelligent applications need to handle uncertainty in an adequate manner. Over the years, many different languages for representing uncertain knowledge—often extensions of classical knowledge representation languages—have been proposed. We briefly present some of the defining properties of these languages as they pertain to the family of probabilistic description logics. This limited view is intended to help pave the way for the interested researcher to find the most adequate language for their needs, and potentially identify the remaining gaps.

Highlights

IntroductionLogic-based knowledge representation [1] is one of the fundamental building blocks for (logic-based) artificial intelligence
Logic-based knowledge representation [1] is one of the fundamental building blocks for artificial intelligence
Afterwards, we introduce a class of uncertain knowledge representation formalisms built as extensions of the well-known family of description logics

Summary

Introduction

Logic-based knowledge representation [1] is one of the fundamental building blocks for (logic-based) artificial intelligence. Uncertainty adds a new dimension over which further variants can be constructed—starting from the chosen uncertainty representation up until the source of uncertainty, passing through several additional considerations which impact the semantics and their applicability, underlying assumptions, and reasoning efficiency Given this large landscape of uncertain knowledge representation formalisms, it is easy for a newcomer to become lost in an attempt to understand the area or grasp the most adequate language for their needs. The pattern for extending logical formalisms with probabilities repeats itself almost identically throughout languages What this roadmap does not provide are the tools to deal with other kinds of uncertainty representations [3,4] such as possibility theory [5,6] or evidence theory [7,8]; nor any other kinds of imperfect knowledge such as vagueness [9,10,11] or inconsistency [12,13,14]. This choice limits the class of languages studied, it gives a general overview of the issues encountered, and the kinds of uncertain representation and reasoning available

The Many Faces of Uncertainty

Representing Uncertain Knowledge

Subjective Probabilities

Statistical Logic

Other Approaches

Conclusions