Lattice-Valued Logic: An Alternative Approach to Treat Fuzziness and Incomparability (Studies in Fuzziness and Soft Computing, 132)

lattice-valued Logic Aims At Establishing The Logical Foundation For Uncertain Information Processing Routinely Performed By Humans And Artificial Intelligence Systems. In This Textbook For The First Time A General Introduction On Lattice-valued Logic Is Given. It Systematically Summarizes Research From The Basic Notions Up To Recent Results On Lattice Implication Algebras, Lattice-valued Logic Systems Based On Lattice Implication Algebras, As Well As The Corresponding Reasoning Theories And Methods. The Book Provides The Suitable Theoretical Logical Background Of Lattice-valued Logic Systems And Supports Newly Designed Intelligent Uncertain-information-processing Systems And A Wide Spectrum Of Intelligent Learning Tasks. Front Matter....Pages N1-xvi Front Matter....Pages 1-1 Introduction....Pages 3-24 Front Matter....Pages 25-25 Concepts and Properties....Pages 27-57 Filters....Pages 59-83 LI -Ideals....Pages 85-99 Homomorphisms and Representations....Pages 101-134 Topological Structure of Filter Spaces....Pages 135-151 Connections with Related Algebras....Pages 153-169 Related Issues....Pages 171-204 Front Matter....Pages 205-205 Lattice-Valued Propositional Logics....Pages 207-257 Lattice-Valued First-Order Logics....Pages 259-304 Uncertainty and Automated Reasoning....Pages 305-359 Back Matter....Pages 361-390 Lattice-valued logic aims at establishing the logical foundation for uncertain information processing routinely performed by humans and artificial intelligence systems. This textbook provides a general introduction to lattice-valued logic