AL seminar (1998)


(45) March 6, 1998
Title:
Amended intuitionistic logic and relativised Kuroda's principle
Speaker:
Leo Esakia ( Georgian Academy of Science )
Abstract:
  We present a short selection of a motivations and results concerning the present state of the theory of the Amended Intuitionistic Predicate Logic and the related Modal System. The theory has opened more questions than it has answered. The Amended Intuitionistic Logic Q*HC is interpreted (via Godel's translation and Solovay's completeness theorem) in terms of a formal provability. Q*HC is obtained from the usual Quantified extension QHC of Heyting propositional calculus HC by postulation the following modified version of the rule of Universal generalization
    /-- (P(a) --> AxP(x))--> P(a)
   --------------------------------
        /-- AxP(x)
  An alternative definition is expressed by the Statement:
The Calculus Q*HC is equivalent to the calculus obtained from the Standard QHC by accepting as an additional axiom the following relativised variant of Kuroda's principle:
   (Ax)[(P(x)-->(Ax)P(x))-->(Ax)P(x)]-->(Ax)P(x).

Last modified: February 26, 1998 by Tasuku Kondou (tasuku@jaist.ac.jp).