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Knowledge Representation and
Reasoning

Representação do Conhecimento e
Raciocínio Computacional
José Júlio Alferes and Carlos Viegas Damásio
What is it ?
• What data does an intelligent “agent” deal with?
- Not just facts or tuples.
• How does an “agent” knows what surrounds it?
What are the rules of the game?
– One must represent that “knowledge”.
• And what to do afterwards with that knowledge?
How to draw conclusions from it? How to reason?
• Knowledge Representation and Reasoning  AI
Algorithms and Data Structures  Computation
What is it good for ?
• Fundamental topic in Artificial Intelligence
– Planning
– Legal Knowledge
– Model-Based Diagnosis
• Expert Systems
• Semantic Web (http://www.w3.org)
– Reasoning on the Web (http://www.rewerse.com)
• Ontologies and data-modeling
What is this course about?
• Logic approaches to knowledge
representation
• Issues in knowledge representation
– semantics, expressivity, complexity
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Representation formalisms
Forms of reasoning
Methodologies
Applications
Bibliography
• Will be pointed out as we go along (articles,
surveys) in the summaries at the web page
• For the first part of the syllabus:
– Reasoning with Logic Programming
J. J. Alferes and L. M. Pereira
Springer LNAI, 1996
– Nonmonotonic Reasoning
G. Antoniou
MIT Press, 1996.
What prior knowledge?
• Computational Logic
• Introduction to Artificial Intelligence
• Logic Programming
Logic for KRR
• Logic is a language conceived for representing
knowledge
• It was developed for representing mathematical
knowledge
• What is appropriate for mathematical knowledge
might not be so for representing common sense
• What is appropriate for mathematical knowledge
might be too complex for modeling data.
Mathematical knowledge vs
common sense
• Complete vs incomplete knowledge
– "x:xN→xR
– go_Work → use_car
• Solid inferences vs default ones
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In the face incomplete knowledge
In emergency situations
In taxonomies
In legal reasoning
...
Monotonicity of Logic
• Classical Logic is monotonic
T |= F → T U T’ |= F
• This is a basic property which makes sense
for mathematical knowledge
• But is not desirable for knowledge
representation in general!
Non-monotonic logics
• Do not obey that property
• Appropriate for Common Sense Knowledge
• Default Logic
– Introduces default rules
• Autoepistemic Logic
– Introduces (modal) operators which speak about
knowledge and beliefs
• Logic Programming
Logics for Modeling
• Mathematical 1st order logics can be used
for modeling data and concepts. E.g.
– Define ontologies
– Define (ER) models for databases
• Here monotonicity is not a problem
– Knowledge is (assumed) complete
• But undecidability, complexity, and even
notation might be a problem
Description Logics
• Can be seen as subsets of 1st order logics
– Less expressive
– Enough (and tailored for) describing
concepts/ontologies
– Decidable inference procedures
– (arguably) more convenient notation
• Quite useful in data modeling
• New applications to Semantic Web
– Languages for the Semantic Web are in fact Description
Logics!
In this course (revisited)
• Non-Monotonic Logics
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Languages
Tools
Methodologies
Applications
• Description Logics
– Idem…