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

• 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. PereiraSpringer LNAI, 1996

– Nonmonotonic ReasoningG. AntoniouMIT 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– 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– Languages– Tools– Methodologies– Applications

• Description Logics– Idem…