[net.ai] Incompleteness in Modal Logic

CLT@SU-AI.ARPA (03/09/84)

From:  Carolyn Talcott <CLT@SU-AI.ARPA>

           [Forwarded from the CSLI bboard by Laws@SRI-AI.]

Subject: SEMINAR IN LOGIC AND FOUNDATIONS OF MATHEMATICS
SPEAKER: Johan van Benthem, University of Groningen

TITLE:  "From Completeness Results to Incompleteness
         Results in Modal Logic"

TIME:   Wednesday, Mar. 14, 4:15-5:30 PM
PLACE:  Stanford Mathematics Dept. Room  383-N


  For a long time the main activity in intensional logic
consisted in proving completeness theorems, matching some
logic with some modal class.  In the early seventies,
however, various incompleteness phenomena were discovered -
e.g. such a match is not always possible.  By now, we know that
the latter phenomenon is the rule rather than the exception,
and the issue of the `semantic power' of the possible worlds
approach has become a rather complex and intriguing one.

  In this talk I will give a survey of the main trends in the
above area, concluding with some open questions and partial
answers.  In particular, a new type of incompleteness theorem
will be presented, showing that a certain tense logic defies
semantic modelling even when both modal class and truth
definition are allowed to vary.