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This
volume contains the proceedings of the conference Logical Foundations
of Mathematics, Computer Science, and Physics-Kurt Gödels
Legacy, held in Brno, Czech Republic on the 90th anniversary of
his birth. The wide and continuing importance of Gödel s work
in the logical foundations of mathematics, computer science, and
physics is confirmed by the broad range of speakers who participated
in making this gathering a scientific event. Year: 2001 Table of Contents Part I. Invited Papers Gödel's
program for new axioms: Why, where, how and what? Infinite-valued
Gödel Logics with 0-1-Projections and Relativizations. Contributions
of K. Gödel to Relativity and Cosmology. Kurt Gödel
and the constructive Mathematics of A.A. Markov. Hao Wang as
Philosopher. A bottom-up
approach to foundations of mathematics. K-graph Machines:
generalizing Turing's machines and arguments. Forcing on Bounded
Arithmetic. Uniform Interpolation
and Layered Bisimulation. Part II. Contributed Papers Gödel's
Ontological Proof Revisited. A Uniform Theorem
Proving Tableau Method for Modal Logic. Decidability
of the $\exists^*\forall^*$-Class in
the Membership Theory NWL. A Logical Approach
to Comlexity Bounds for Sbutype Inequalities. How to characterize
provably total functions. Completeness
has to be restricted: Gödel's interpretation of the parameter
t. A Bounded Arithmetic
Theory for Constant Depth Threshold Circuits. Information
content and computational complexity of recursive sets. Kurt Gödel
and the Consistency of R##. Best possible
answer is computable for fuzzy SLD-resolution. The finite stages
of inductive definitions. Gödel and
the Theory of Everything. Replacement
$\not\to$ Collection.
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