Symbolic Learning

Description

This course introduces foundational and advanced methods in Knowledge Representation and Reasoning (KR&R), with a focus on Description Logics (DLs), tableau-based reasoning, and machine-learning approaches to concept learning in ontology engineering. Students learn how to formally model knowledge, reason with ontologies, and apply automated and semi-automated methods to build and refine domain ontologies.

Learning objectives:

- Explain key principles of symbolic knowledge representation and logical formalisms.

- Use Description Logics to model complex domain knowledge.

- Apply tableau algorithms to reason about class subsumption, consistency, and instance checking.

- Design, implement, and evaluate ontologies in OWL.

- Understand and use concept learning techniques (e.g., inductive logic programming, DL-based concept learning) for ontology engineering tasks.

- Integrate symbolic and learning-based methods for ontology refinement.

Topics:

1. Foundations: Logic and Formal Semantics

    Propositional logic refresher

    First-order logic basics

    Description Logics: Syntax and Semantics (Common DLs: ALC, SHOIN, SROIQ)

    Relationship to OWL

2. Reasoning in Description Logics

    Standard reasoning problems: subsumption, satisfiability, consistency, classification.

    Tableau algorithms: Foundations

    Tableau calculus for ALC

    Tableau for expressive DLs (SHIQ, SHOIQ, SROIQ)

    Role of automated reasoners (HermiT, Pellet, FaCT++)

3. Concept Learning for Ontology Engineering

    Algorithms for Concept Learning in DLs

    Search spaces for DL concept hypotheses

    Refinement operators and scoring functions (accuracy, coverage, complexity)

    Inductive Logic Programming basics

    DL-Learner and related frameworks

4. Combining Reasoning and Learning

    Neuro-symbolic perspectives

    Explainable AI via symbolic reasoning

    Practical case studies