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                                     COLLOQUIUM

                University at Albany - State University of New York

                            Computer Science Department

            Self Verifying Formal Systems and the Incompleteness Theorem

                                   Dan E. Willard

                            Computer Science Department

                                       SUNYA

                  Thursday, December 8, 1994 at 4:00 PM, in LI-98

                                      ABSTRACT

                 Godel's Incompleteness Theorem states essentially  that
            no  logical  system  that is capable of solving the standard
            problems of arithmetic is capable of verifying its own  con-
            sistency.  This talk will review the nature of Godel's clas-
            sic theorem, and outline certain types of  systems  that  we
            have  devised  that  can verify their own consistency.  Next
            semester,  we will be teaching  an  introductory  course  on
            logic   (CSI  530),   and one of the purposes of this collo-
            quium talk is to provide the students with a glimpse of some
            of  the  important  issues in logic discussed next semester.
            In particular, the talk will focus on the fact  that  humans
            seem  to  instinctively  sense  their  own  consistency, but
            Godel's Incompleteness Theorem tells us  that  most  classic
            computing systems are unable to prove their consistency in a
            very strong sense.  So in what sense are humans and  comput-
            ers  theoretically  able  to potentially recognize their own
            consistency?