A restriction-centered theory of Reasoning and Computation

Mon., Dec 3, 2012

4:00 - 5:00 PM

400 Cory Hall (Hughes Room)

4:00 - 5:00 PM

400 Cory Hall (Hughes Room)

The theory which is outlined in this lecture, call it RCC for short, is a system of reasoning and computation which is not in the traditional spirit. In large measure, RCC is oriented toward reasoning and computation in an environment of uncertainty, imprecision and partiality of truth. The centerpiece of RCC is the concept of a restriction\a basic concept which is deceptively simple. Informally, a restriction is an answer to a question of the form: What is the value of a variable, X? More concretely, a restriction, R(X), is a limitation on the values which X can take. A restriction is precisiated if R(X) is mathematically well defined; otherwise it is unprecisiated. Generally, restrictions which are described in a natural language are unprecisiated. A restriction is precisiable if it lends itself to precisiation. A restriction is singular if R(X) is a singleton; otherwise it is nonsingular. Nonsingularity implies uncertainty. Examples. Robert is staying at a hotel in Berkeley. He asks the concierge, gHow long will it take me to drive to SF Airport?h Possible answers: one hour; one hour plus minus fifteen minutes; about one hour; usually about one hour, etc. Each of these answers is a restriction on the variable, Driving time. The first two answers are precisiated restrictions. The last two answers are unprecisiated. Another example. Consider the proposition, p: Most Swedes are tall. What is the truth-value of p? Possible answers: True; 0.8; about 0.8; high; likely high, etc. In this case, the first two answers are precisiated restrictions; the rest are unprecisiated. The concept of a restriction is closely related to the concept of information granule\a concept which was introduced in my 1979 paper on information granularity.

The concept of a restriction is considerably more general than the concept of an interval, set, fuzzy set and probability distribution. In one form or another, much of human cognition involves restrictions, particularly in the realms of everyday reasoning and decision-making. Humans have a remarkable capability to reason and, to some degree, compute with restrictions. What is needed is a theory which formalizes this capability. RCC may be viewed as a step in this direction. What should be noted is that existing approaches to reasoning and computation, other than RCC, do not have the capability of reasoning and computation with restrictions which are described in a natural language. The canonical form of a restriction is an expression of the form X isr R, where X is the restricted variable, R is the restricting relation and r is an indexical variable which defines the way in which R restricts X.

There are two principal issues which are addressed in RCC. First, how can a semantic entity, e.g. a proposition, be represented as a restriction? Second, how can restrictions be reasoned and computed with? In RCC, for computation with restrictions what is employed is the extension principle. The extension principle is a collection of computational rules which address the following problem. Assume that Y=f(X). Given a restriction on X and/or a restriction on f, what is the restriction on Y, R(Y), which is induced by R(X) and R(f)? Basically, the extension principle involves propagation of restrictions. In essence, in RCC the objects of reasoning and computation are not values of variables, but restrictions on values of variables. A key to understanding of RCC is that in RCC the focus of attention is shifted from reasoning and computation with values of variables to reasoning and computation with restrictions on values of variables. This shift has wide-ranging ramifications. Representation and computation with restrictions are illustrated with examples.

Bio: LOTFI A. ZADEH is Professor Emeritus in the Computer Science Division, Department of EECS, University of California, Berkeley. In addition, he is serving as the Director of BISC (Berkeley Initiative in Soft Computing).

Lotfi Zadeh is an alumnus of the University of Tehran, MIT and Columbia University. From 1950 to 1959, Lotfi Zadeh was a member of the Department of Electrical Engineering, Columbia University. He joined the Department of Electrical Engineering at UC Berkeley in 1959 and served as its Chair from 1963 to 1968. During his tenure as Chair, he played a key role in changing the name of the Department from EE to EECS.

Lotfi Zadeh held visiting appointments at the Institute for Advanced Study, Princeton, NJ; MIT, Cambridge, MA; IBM Research Laboratory, San Jose, CA; AI Center, SRI International, Menlo Park, CA; and the Center for the Study of Language and Information, Stanford University.

Lotfi Zadeh is a Fellow of the IEEE, AAAS, ACM, AAAI, and IFSA. He is a member of the National Academy of Engineering and a Foreign Member of the Finnish Academy of Sciences, the Polish Academy of Sciences, Korean Academy of Science & Technology, Bulgarian Academy of Sciences, the International Academy of Systems Studies and the Azerbaijan National Academy of Sciences. He is a recipient of the IEEE Education Medal, the IEEE Richard W. Hamming Medal, the IEEE Medal of Honor, the ASME Rufus Oldenburger Medal, the B. Bolzano Medal of the Czech Academy of Sciences, the Kampe de Feriet Medal, the AACC Richard E. Bellman Control Heritage Award, the Grigore Moisil Prize, the Honda Prize, the Okawa Prize, the AIM Information Science Award, the IEEE-SMC J. P. Wohl Career Achievement Award, the SOFT Scientific Contribution Memorial Award of the Japan Society for Fuzzy Theory, the IEEE Millennium Medal, the ACM 2001 Allen Newell Award, the Norbert Wiener Award of the IEEE Systems, Man and Cybernetics Society, Civitate Honoris Causa by Budapest Tech (BT) Polytechnical Institution, Budapest, Hungary, the V. Kaufmann Prize, International Association for Fuzzy-Set Management and Economy (SIGEF), the Nicolaus Copernicus Medal of the Polish Academy of Sciences, the J. Keith Brimacombe IPMM Award, the Silicon Valley Engineering Hall of Fame, the Heinz Nixdorf MuseumsForum Wall of Fame, the Egleston Medal, the Franklin Institute Medal, the Medal of the Foundation by the Trust of the Foundation for the Advancement of Soft Computing, the High State Award eFriendship Orderf, from the President of the Republic of Azerbaijan, the Transdisciplinary Award and Medal of the Society for Design and Process Sciences, other awards and twenty-five honorary doctorates. In 2011, Lotfi Zadeh was inducted into the AI Hall of Fame. He has published extensively (over 200 single-authored papers) on a wide variety of subjects relating to the conception, design and analysis of information/intelligent systems, and is serving on the editorial boards of over seventy journals.

Prior to the publication of his first paper on fuzzy sets in 1965, Lotfi Zadehfs work was concerned in the main with systems analysis, decision analysis and information systems. His current research is focused on fuzzy logic, semantics of natural languages, computational theory of perceptions, computing with words, extended fuzzy logic and Z-numbers.

The concept of a restriction is considerably more general than the concept of an interval, set, fuzzy set and probability distribution. In one form or another, much of human cognition involves restrictions, particularly in the realms of everyday reasoning and decision-making. Humans have a remarkable capability to reason and, to some degree, compute with restrictions. What is needed is a theory which formalizes this capability. RCC may be viewed as a step in this direction. What should be noted is that existing approaches to reasoning and computation, other than RCC, do not have the capability of reasoning and computation with restrictions which are described in a natural language. The canonical form of a restriction is an expression of the form X isr R, where X is the restricted variable, R is the restricting relation and r is an indexical variable which defines the way in which R restricts X.

There are two principal issues which are addressed in RCC. First, how can a semantic entity, e.g. a proposition, be represented as a restriction? Second, how can restrictions be reasoned and computed with? In RCC, for computation with restrictions what is employed is the extension principle. The extension principle is a collection of computational rules which address the following problem. Assume that Y=f(X). Given a restriction on X and/or a restriction on f, what is the restriction on Y, R(Y), which is induced by R(X) and R(f)? Basically, the extension principle involves propagation of restrictions. In essence, in RCC the objects of reasoning and computation are not values of variables, but restrictions on values of variables. A key to understanding of RCC is that in RCC the focus of attention is shifted from reasoning and computation with values of variables to reasoning and computation with restrictions on values of variables. This shift has wide-ranging ramifications. Representation and computation with restrictions are illustrated with examples.

Bio: LOTFI A. ZADEH is Professor Emeritus in the Computer Science Division, Department of EECS, University of California, Berkeley. In addition, he is serving as the Director of BISC (Berkeley Initiative in Soft Computing).

Lotfi Zadeh is an alumnus of the University of Tehran, MIT and Columbia University. From 1950 to 1959, Lotfi Zadeh was a member of the Department of Electrical Engineering, Columbia University. He joined the Department of Electrical Engineering at UC Berkeley in 1959 and served as its Chair from 1963 to 1968. During his tenure as Chair, he played a key role in changing the name of the Department from EE to EECS.

Lotfi Zadeh held visiting appointments at the Institute for Advanced Study, Princeton, NJ; MIT, Cambridge, MA; IBM Research Laboratory, San Jose, CA; AI Center, SRI International, Menlo Park, CA; and the Center for the Study of Language and Information, Stanford University.

Lotfi Zadeh is a Fellow of the IEEE, AAAS, ACM, AAAI, and IFSA. He is a member of the National Academy of Engineering and a Foreign Member of the Finnish Academy of Sciences, the Polish Academy of Sciences, Korean Academy of Science & Technology, Bulgarian Academy of Sciences, the International Academy of Systems Studies and the Azerbaijan National Academy of Sciences. He is a recipient of the IEEE Education Medal, the IEEE Richard W. Hamming Medal, the IEEE Medal of Honor, the ASME Rufus Oldenburger Medal, the B. Bolzano Medal of the Czech Academy of Sciences, the Kampe de Feriet Medal, the AACC Richard E. Bellman Control Heritage Award, the Grigore Moisil Prize, the Honda Prize, the Okawa Prize, the AIM Information Science Award, the IEEE-SMC J. P. Wohl Career Achievement Award, the SOFT Scientific Contribution Memorial Award of the Japan Society for Fuzzy Theory, the IEEE Millennium Medal, the ACM 2001 Allen Newell Award, the Norbert Wiener Award of the IEEE Systems, Man and Cybernetics Society, Civitate Honoris Causa by Budapest Tech (BT) Polytechnical Institution, Budapest, Hungary, the V. Kaufmann Prize, International Association for Fuzzy-Set Management and Economy (SIGEF), the Nicolaus Copernicus Medal of the Polish Academy of Sciences, the J. Keith Brimacombe IPMM Award, the Silicon Valley Engineering Hall of Fame, the Heinz Nixdorf MuseumsForum Wall of Fame, the Egleston Medal, the Franklin Institute Medal, the Medal of the Foundation by the Trust of the Foundation for the Advancement of Soft Computing, the High State Award eFriendship Orderf, from the President of the Republic of Azerbaijan, the Transdisciplinary Award and Medal of the Society for Design and Process Sciences, other awards and twenty-five honorary doctorates. In 2011, Lotfi Zadeh was inducted into the AI Hall of Fame. He has published extensively (over 200 single-authored papers) on a wide variety of subjects relating to the conception, design and analysis of information/intelligent systems, and is serving on the editorial boards of over seventy journals.

Prior to the publication of his first paper on fuzzy sets in 1965, Lotfi Zadehfs work was concerned in the main with systems analysis, decision analysis and information systems. His current research is focused on fuzzy logic, semantics of natural languages, computational theory of perceptions, computing with words, extended fuzzy logic and Z-numbers.

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Last Modification Date: Wednesday, February 10, 2016