Courses
The summer school features eight courses, each treating a different subject within the area of logic for artificial intelligence, and each being taught by a lecturer with an outstanding international reputation.Description Logics
Lecturer: Ulrike Sattler
Description Logics (DLs) are an
important family of logic-based
formalisms that have been developed for the representation of
conceptual knowledge. Recently, DLs have attracted increased interest
since they form the logical basis of ontology languages such as
OWL. This course is targeted at participants with a basic background
in Knowledge Representation or Logic. It covers the basic principles
of representing knowledge with DLs and also some more advanced
research topics from the field. Starting from basic Description Logics
such as ALC, we gradually increase the expressive power of the
presented Logics. We discuss reasoning procedures such as tableau and
automata-based algorithms and analyze the complexity of the relevant
inference problems. Many examples from knowledge representation are
presented as well as system demonstrations illustrating the practical
relevance of DLs. This course provides the participants with a general
understanding of DLs, the current state- of-the-art of reasoning
techniques for expressive DLs, and their applications.
Logic-based Knowledge Representation and Reasoning for the Semantic Web
Lecturer: Heiner Stuckenschmidt
The course will briefly introduce the
basic ideas of the semantic web
In terms of machine-readable metadata and ontologies as a basis for
exchanging information. After briefly introducing basic concepts of
Description logics, which are a common basis for knowledge
representation on the semantic web, the course will focus on
extensions of standard Description logic languages and reasoning
algorithms that address the specific problems of semantic web
applications such as dealing with distributed, heterogeneous and
incompatible or inconsistent representations. The prospective schedule
of the course is as follows:
Day 1) Introduction
- Semantic Web Technologies
- Description Logics
Day 2) Distributed Representations
- Distributed Description Logics
- C-OWL and Related Formalism
Day 3) Approximate Reasoning
- Approximation for Scalability
- Approximation for Robustness
Day 4) Diagnosis and Repair
- Diagnosing Inconsistencies
- Repairing Ontology Mappings
Logic-based techniques for information integration
Lecturer: Marie-Christine Rousset
Faced with the multiplicity and the
heterogeneity of
the information availale online, the information integration problem
is a key challenge which must be addressed in a principled way.
The goal of this course is to show that logic is particularly
appropriate as a formal background with associated automatic reasoning
techniques for describing and querying heterogeneous pre-existing
autonomous data sources.
Seen from that logical point of view, the informaton integration
problem is twofold. The modeling problem consists in specifying in a
logical language semantic mappings between the pre-existing sources,
possibly through a pivot ontology. The reasoning problem consists in
designing appropriate reasoning algorithms to reformulate and
decompose queries through the relevant data sources and to combine
their answers.
In this course, we will emphasize the impact of the semantics and the
expressive power of the logical languages used to describe the data
sources onto the complexity of query answering.
In the first part of the course, we will present the mediator model
for information integration, which is centered on a pivot ontology for
expressing both the users queries and the views describing the data
sources. In this setting, we will relate the problems of query
answering and rewriting using views to reasoning problems in logic
(reasoning on incomplete data, computing prime imlicants), and we will
present complexity results and algorithms.
In the second part, we will introduce the principles of semantic peer
to peer data management systems based on distributed ontologies and
mappings. In this setting, query rewriting is distributed and can be
equivalently reduced to distributed consequence finding in the
corresponding logic used to express the local ontologies and the
mappings. We will also discuss the different semantics that can be
given to the formulas corresponding to the mappings, and the implact
of the choice of the desired semantics on the query answering problem.
We will emphasize the importance of the scalability of the underlying
reasoning techniques for making them useful for the future Semantic
Web.
Throughout the course, we will connect the presented logical languages
and techniques to existing information integration systems in which
they are implemented.
Logic, Probability and Learning, or An introduction to Statistical
Relational Learning.
Lecturer: Luc De Raedt
Probabilistic inductive logic
programming (PILP), sometimes also
called statistical relational learning, addresses one of the central
questions of artificial intelligence: the integration of probabilistic
reasoning with first order logic representations and machine
learning. A rich variety of different formalisms and learning
techniques have been developed and they are being applied on
applications in network analysis, robotics, bio-informatics,
intelligent agents, etc.
This tutorial starts with an introduction to probabilistic
representations and machine learning, and then continues with an
overview of the state-of-the-art in statistical relational
learning. We start from classical settings for logic learning (or
inductive logic programming) namely learning from entailment, learning
from interpretations, and learning from proofs, and show how they can
be extended with probabilistic methods. While doing so, we review
state-of-the-art statistical relational learning approaches and show
how they fit the discussed learning settings for probabilistic
inductive logic programming.
This tutorial is based on joint work with Dr. Kristian
Kersting.
More information can be found in
De Raedt, L. Logical and Relational Learning, Springer, forthcoming
2007.
Luc De Raedt, Kristian Kersting: Probabilistic logic learning. SIGKDD
Explorations 5(1): 31-48 (2003)
Luc De Raedt, Kristian Kersting:
Probabilistic Inductive Logic Programming. ALT 2004: Lecture Notes in
Computer Science 3244, 19-36, 2004.
Knowledge representation and reasoning in ID-logic.
Lecturer: Marc Denecker
This course presents ID-logic, an
extension of classical logic with
inductive definitions, and its application for knowledge
representation and declarative problem solving. The course starts with
a discussion of the role of knowledge representation in AI, and of
logic for knowledge representation. We then consider certain forms of
inductive definitions found in mathematics, including monotone
definitions (e.g. of transitive closure) and non-monotone definitions
(e.g. of satisfiability $\models$) and discuss their formalization in
ID-logic. The use of (inductive) definitions in knowledge
representation is illustrated, through examples and through their use
for modeling many concepts of non-monotonic and temporal reasoning. We
investigate the logic's use for declarative problem solving through
Model Expansion, a problem solving paradigm that extends SAT-solving
and is related to Answer Set Programming. This course gives a good
picture of the position of ID-logic in the spectrum of mathematical
and computational logics and its relations to logic programming,
description logics and fixpoint logic.
Constraint Programming
Lecturer: Pascal Van Hentenryck
This course presents an overview of constraint programming, its
applications, and recent developments. It highlights the declarative nature of
constraint programming, covers its computational model and
underlying algorithms, describes some real-life applications, and
discusses a variety of topics at the research frontiers.
Logic-based agents.
Lecturer: Fariba Sadri and Bob Kowalski
The tutorial will explore the use of Logic as the thinking component of
an agent’s observation-thought-decision-action cycle. The first part
of this tutorial will be based on a book written by Bob Kowalski and
available on his webpage http://www.doc.ic.ac.uk/~rak/.
The agent Logic that we will explore combines with goals and beliefs.
Beliefs have the form of normal logic programs:
Conclusion if conditions
They can be used to reason backwards to reduce goals that match the
conclusion to sub-goals that correspond to the conditions. They can
also be used to reason forwards to derive conclusions from conditions.
Goals have a more general form than beliefs, but one which includes
implications:
If conditions then conclusions
These are typically used to reason forward, when the conditions hold,
to derive the conclusions as sub-goals. Goals used in this way subsume
condition-action rules in production systems.
Backwards reasoning is a form of proactive thinking. Forwards reasoning
includes reactive thinking, which generates actions in response to
observations of the environment, but also includes a kind of pre-active
thinking, which derives possible outcomes of actions before they are
chosen for execution.
Pre-active thinking provides a link with Decision Theory. To combine
Logic with Decision Theory, an agent needs to evaluate the utilities
and probabilities of the outcomes of different actions. The agent can
then use Decision Theory or some other more tractable alternative, in
the decision-making component of the agent cycle, to choose an action
that aims to maximize expected utility.
We will review a recent agent model called the KGP (Knowledge-Goal-
Plan) model which has been developed during the EU SOCS (Societies of
Computational Entities) project. This agent model provides a
hierarchical and modular architecture of capabilities, transitions and
control, and is based almost entirely on computational logic. It allows
planning, reactivity, goal decision and temporal reasoning. It has
dynamic context dependent control theories that allow formalization of
different agent profiles, and has been developed to deal with dynamic
environments where agents have to adapt and react to changes as well as
pursue goals.
Action Planning: Recent Theoretical and Practical Advances
Lecturer: Bernhard Nebel
In the previous decade, the field of action planning has seen a number
of significant advances. Planning formalisms have been extended to be
raise the expressive power, a number of new algorithmic approaches to
planning have been developed and some of the theoretical problems have
been solved.
After a brief introduction to action planning, I will first sketch the
range of planning frameworks and formalisms, which are currently in
use, and will then go on and introduce new planning techniques that
have enabled us to solve much larger problem instances than
before. One of the interesting questions is then, whether and how
these technique can be extended to more powerful planning
formalisms. In order to answer this question, I will introduce a
formal framework for translating between different planning formalisms
and report on results that have been achieved in this framework. In
particular, I will talk about some recent results concerning domain
axioms in planning languages. Finally, I will briefly sketch how to
extend the classical planning framework in order to cover more complex
settings such us non-deterministic actions and partial observability.
This tutorial is based on joint work with Dr. Kristian Kersting.
More information can be found in
De Raedt, L. Logical and Relational Learning, Springer, forthcoming 2007.
Luc De Raedt, Kristian Kersting: Probabilistic logic learning. SIGKDD Explorations 5(1): 31-48 (2003)
Luc De Raedt, Kristian Kersting: Probabilistic Inductive Logic Programming. ALT 2004: Lecture Notes in Computer Science 3244, 19-36, 2004.
The tutorial will explore the use of Logic as the thinking component of an agent’s observation-thought-decision-action cycle. The first part of this tutorial will be based on a book written by Bob Kowalski and available on his webpage http://www.doc.ic.ac.uk/~rak/.
The agent Logic that we will explore combines with goals and beliefs.
Beliefs have the form of normal logic programs:
Conclusion if conditions
They can be used to reason backwards to reduce goals that match the
conclusion to sub-goals that correspond to the conditions. They can
also be used to reason forwards to derive conclusions from conditions.
Goals have a more general form than beliefs, but one which includes
implications:
If conditions then conclusions
These are typically used to reason forward, when the conditions hold,
to derive the conclusions as sub-goals. Goals used in this way subsume
condition-action rules in production systems.
Backwards reasoning is a form of proactive thinking. Forwards reasoning includes reactive thinking, which generates actions in response to observations of the environment, but also includes a kind of pre-active thinking, which derives possible outcomes of actions before they are chosen for execution.
Pre-active thinking provides a link with Decision Theory. To combine Logic with Decision Theory, an agent needs to evaluate the utilities and probabilities of the outcomes of different actions. The agent can then use Decision Theory or some other more tractable alternative, in the decision-making component of the agent cycle, to choose an action that aims to maximize expected utility.
We will review a recent agent model called the KGP (Knowledge-Goal- Plan) model which has been developed during the EU SOCS (Societies of Computational Entities) project. This agent model provides a hierarchical and modular architecture of capabilities, transitions and control, and is based almost entirely on computational logic. It allows planning, reactivity, goal decision and temporal reasoning. It has dynamic context dependent control theories that allow formalization of different agent profiles, and has been developed to deal with dynamic environments where agents have to adapt and react to changes as well as pursue goals.
After a brief introduction to action planning, I will first sketch the range of planning frameworks and formalisms, which are currently in use, and will then go on and introduce new planning techniques that have enabled us to solve much larger problem instances than before. One of the interesting questions is then, whether and how these technique can be extended to more powerful planning formalisms. In order to answer this question, I will introduce a formal framework for translating between different planning formalisms and report on results that have been achieved in this framework. In particular, I will talk about some recent results concerning domain axioms in planning languages. Finally, I will briefly sketch how to extend the classical planning framework in order to cover more complex settings such us non-deterministic actions and partial observability.
