# Theory of Data and Knowledge Bases: 2010-2011

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| Schedule C1 — Computer Science Schedule C1 — Mathematics and Computer Science |

| Hilary Term 2011 (16 lectures) |

## Overview

The lecture series provides an understanding of the logical foundations of database query languages and knowledge representation formalisms, the expressive power of such languages/formalisms, and the complexity of query answering and reasoning with such languages/formalisms.## Learning outcomes

By the end of this lecture series, you should have a good understanding of the fundamentals of query languages, understand the trade-off between complexity and expressive power of query languages, and understand some basic formalisms of non-monotonic reasoning. You should be in the position of analyzing a query language and expressing knowledge in suitable logical formalisms.## Prerequisites

Basic knowledge of automata theory (e.g., finite state automata), databases (e.g., the relational data model, relational algebra, SQL), and complexity theory (e.g., NP-completeness) will be assumed. This can be gained from the undergraduate courses Models of Computation, Databases and Computational Complexity, or the MSc courses Introduction to Foundations of Computer Science and Databases. Students who have not studied these courses should talk to the lecturer.

## Synopsis

We will try to cover the following topics:

- A brief introduction to databases, finite model theory, and descriptive complexity.
- Conjunctive queries: complexity and optimization.
- SQL and first-order queries: complexity, limits of expressive power.
- Reasoning with propositional Horn theories.
- Datalog and fixpoint queries: complexity and expressive power.
- Querying semi-structured data.
- Elements of non-monotonic reasoning and closed-world reasoning.
- Problems of data integration and data exchange.
- Advanced material (time permitting).

It is roughly planned to spend two hours for each of the topics 1-8, and to insert additional material (9) dynamically where appropriate.

## Reading list

Books:

- S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995.
- L. Libkin. Elements of Finite Model Theory. Springer, 2004. (selected chapters)

A list of papers covering various relevant topics will be supplied in due course.