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The talk introduces Modal Logic as an extension of classical propositional and First Order Logics. We discuss motivations of Lewis to create modal logic system, axioms and rules of proof. Several examples illustrate deriving theorems from axioms. "Muddy Children" puzzle is used to explain the principles of dealing with uncertainty problems where a temporal lack of response is used as additional information. Other examples include "Narrow Bridge" problem/game which relates to the problem of necessary evil in the world, robot planning and law and robot morality problems, especially related to military robots and use of force by police. Kripke semantics and Model Checking are explained on examples. The goal of the lecture is to present informally the main ideas of modal logic and related logics, such as Temporal or Deontic Logics, and some of their applications.
Marek Perkowski obtained his M.S. degree in Electronics and Ph.D. degree in automatic control from Institute of Automatic Control, Department of Electronics, Technical University of Warsaw, Warsaw, Poland. He studied also pure mathematics at University of Warsaw. In years 1981-1983 he was a Visiting Assistant Professor at University of Minnesota in Minneapolis and since 1983 he works for Department of Electrical and Computer Engineering at Portland State University where he is a full professor and director of Intelligent Robotics Laboratory. He worked for Cypress Semiconductor (co-author of WARP, the first FPGA compiler of VHDL), Intel Supercomputer, Sharp Microelectronics, GTE and other companies in areas of computer architecture, CAD tools for logic synthesis and image processing. Dr. Perkowski invented Kronecker Decision Diagrams and lattices and contributed to logic synthesis software that is used in US industry. In 1994 he worked for Machine Learning group in Wright Laboratories of U.S. Air Force applying logic decomposition as a machine learning approach to pattern recognition and continued this work on several grants. He is an author of more than 300 papers in CAD, logic synthesis, multiple-valued logic, machine learning, robotics and quantum computing. He had visiting professor and visiting scientist positions in the Netherlands, France, Japan and Korea. In years 2002-2004 he was professor in KAIST – Korean Advanced Institute of Science and Technology where he participated in research on humanoid robotics and quantum computing. He chaired the IEEE Technical Committee on Multiple-Valued Logic in years 2003-2005 and is currently chair of IEEE Computational Intelligence Society Task Force on Quantum Computing. His main current interests are in quantum circuits and algorithms, humanoid bipeds, emotional quantum robots, robotics for teenagers and Grover algorithm. He collaborates with many groups worldwide.
Modality (Logic), First-order logic, Axioms, Conditionals (Logic), Proof theory, Verification (Logic)
Logic and Foundations
Perkowski, Marek, "Modal Logic and its Applications, Explained using Puzzles and Examples" (2011). Systems Science Friday Noon Seminar Series. 60.