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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 • • • • 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:xN→xR – 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…