Logic prespective on data and knowledge

  • Authors:
  • Lech Polkowski;Andrzej Skowron

  • Affiliations:
  • Institute of Mathematics, Warsaw University of Technology, Poland;Professor of Mathematics, Computer Science and Mechanics, Warsaw University, Poland

  • Venue:
  • Handbook of data mining and knowledge discovery
  • Year:
  • 2002

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Abstract

Logic understood as a study of mechanisms of inference, including inference of knowledge from data, has evolved into many reasoning schemes (languages) differing by understanding of semantics of inference. In this chapter, basic schemes are outlined along with their relation to KDD: classical calculi, many-valued logics, modal logics along with deductive mechanisms: axiomatized schemes, resolution in logic programming. An example of the system DATALOG is discussed. In complex tasks of AI and KDD like pattern recognition or machine learning, inductive reasoning is frequent in applications aimed at defining relevant concepts and dependencies among them. We discuss basic aspects of reasoning with knowledge, that is, making inferences in a chosen logical language from a given knowledge base, as well as basic aspects of reasoning about knowledge, that is, making inferences concerning properties of knowledge such as completeness, certainty.