Although the foundations of Mathematics seemed well established (first-order logic + set theory, for instance), recently these foundations have been seriously challenged by J. Hintikka and - in a lesser degree by M. Fitting. Hintikka argues for an information-Independence Friendly (IF) first-order logic extending traditional first-order logic, but with quite different properties and Fitting argues for a quite different treatment of modalities. Although Hintikka's papers are full of innovative and challenging ideas, many of his ideas are not fully worked out and most of his `proofs' are only sketched. Hintikka's writings can be characterized as being philosophical rather than mathematical. Most, if not all reviews of his book point out several mistakes in, and problems with, his definitions and statements. The main aim of this researchproject is to work out (part of) Hintikka's ideas more precisely, from a mathematical point of view, to give precise definitions and mathematically correct proofs of (some of) his statements.
Fitting has worked out a solution of the inadequate expressive power of modal predicate logic, solving most - if not all - `paradoxes' of modal logic. We also want to investigate the logic that results by extending Hintikka's IF logic with the modalities and predicate abstraction as treated by Fitting.