Mathematical Logic and Its Applications

Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Remarks Concerning Kurt Gödel’s Life and Work....Pages 3-7
Facets of Incompleteness....Pages 9-21
Godel’s Life and Work....Pages 23-36
Front Matter....Pages 37-37
Categorial Grammar and Lambda Calculus....Pages 39-60
A Constructive Morse Theory of Sets....Pages 61-79
Differentiation of Constructive Functions of a Real Variable and Relative Computability....Pages 81-106
A Completeness Theorem for Higher-Order Intuitionistic Logic: An Intuitionistic Proof....Pages 107-124
Reasoning in Trees....Pages 125-135
Non-Deterministic Program Schemata and Their Relation to Dynamic Logic....Pages 137-147
The Parallel Evaluation of Functional Programs....Pages 149-165
Logic Approximating Sequences of Sets....Pages 167-186
Intuitionistic Formal Spaces — A First Communication....Pages 187-204
On the Logic of Small Changes in Theories II....Pages 205-211
On ‘Logical Relations’ in Program Semantics....Pages 213-229
Front Matter....Pages 231-231
Search Computability and Computability with Numberings Are Equivalent in the Case of Finite Set of Objects....Pages 233-242
Cut-Elimination Theorem for Higher-Order Classical Logic: An Intuitionistic Proof....Pages 243-251
Modal Environment for Boolean Speculations....Pages 253-263
Distributive Spaces....Pages 265-272
Approximating the Projective Model....Pages 273-282
Projection Complete Graph Problems Corresponding to a Branching-Program-Based Characterization of the Complexity Classes NC 1 , L and NL ....Pages 283-292
Front Matter....Pages 231-231
Constructive Theories with Abstract Data Types for Program Synthesis....Pages 293-302
A First Order Logic for Logic Programming....Pages 303-314
The Relational Semantics for Branched Quantifiers....Pages 315-322
Propositional Dynamic Logic in Two- and More Dimensions....Pages 323-329
On a Nonconstructive Type Theory and Program Derivation....Pages 331-340
Prime Computability on Partial Structures....Pages 341-350
Complexity Bounded Martin-Löf Tests....Pages 351-359
Back Matter....Pages 361-371