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 ( –Reasoning on the Web ( 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. 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 –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…