Knowledge Representation & Reasoning:  2024-2025

Overview

The course provides an introduction to the field. The main focus will be on decidable fragments of first order logic that are well suited for knowledge representation. We explore how such logics can be used to represent knowledge, identify relevant reasoning problems and show how these can be used to support the task of constructing suitable representations. We will also consider the computational properties of these logics, and study algorithms for solving the relevant reasoning problems. We will also discuss logics that depart from first order logic, in particular, temporal and non-monotonic logics.

Learning outcomes

• Students satisfying the prerequisites are expected to understand the fundamental principles of logic-based Knowledge Representation;
• be able to model simple application domains in a logic-based language;
• understand the notion of a reasoning service;
• master the fundamentals of the reasoning algorithms underlying current systems;
• understand the fundamental trade-off between representation power and computational properties of a logic-based representation language;
• be conversant with several widely used knowledge representation languages; and
• understand how the theoretical material covered in the course is currently being applied in practice.

Prerequisites

Students taking this course should have completed the first year Introduction to Formal Proof course (or an equivalent course in a different institution). Students would benefit from taking the third year Computational Complexity course as well as the second year Databases course; however, this is not a requirement.

Synopsis

PART 1: Basic logics for KRR

• Introduction to knowledge-based technologies and knowledge representation
• Propositional Logic as a simple knowledge representation language
• Representing Knowledge in First Order Predicate Logic
• Limitations of Propositional and First Order Predicate Logic

PART 2: Datalog

• Expressive power and computational complexity of Datalog
• Reasoning algorithms for Datalog
• Temporal reasoning in extensions of Datalog
• Existential rules as an extension of Datalog
• Non-monotonic negation and stable model semantics
• Correspondence between Datalog and Graph Neural Networks

PART 3:  Description logics

• Description Logics as Knowledge Representation Languages
• Reasoning in Description Logics
• Lightweight description logics
• Ontologies and Ontology Languages.
• Other Decidable Fragments of First Order Logic for Knowledge Representation

Syllabus

Representing knowledge using logic. Fundamental trade-off between representation power and computational properties.  Fragments of first order logic suited for Knowledge Representation. Reasoning algorithms and implementations, and how reasoning is used to support knowledge representation. Ontology languages for the Semantic Web. Non-monotonic logics.

Reading list

Primary Texts:

• Evgeny Dantsin, Thomas Eiter, Georg Gottlob, Andrei Voronkov, Complexity and Expressive Power of Logic Programming, 2001
• Dingmin Wang, Przemysław Wałęga, Pan Hu, Bernardo Cuenca Grau, Practical Reasoning in DatalogMTL, 2024
• Franz Baader, Ian Horrocks, Carsten Lutz, Uli Sattler, An Introduction to Description Logic, 2017

Classics:

• Stephen A. Cook, The Complexity of Theorem-Proving Procedures, 1971

• Alan M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem, 1937

• Michael Gelfond and Vladimir Lifschitz, The Stable Model Semantics for Logic Programming, 1988

Supplementary List:

• Serge Abiteboul, Richard Hull, and Victor Vianu, Foundations of Databases, 1995

• Frank van Harmelen, Vladimir Lifschitz and Bruce Porter (Eds), Handbook of Knowledge
  Representation, 2008

• Christos H. Papadimitriou, Complexity Theory, 1994

• Ewe Shöning, Logic for Computer Scientists, 2008

Taking our courses

This form is not to be used by students studying for a degree in the Department of Computer Science, or for Visiting Students who are registered for Computer Science courses

Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.