Mathematical Logic and Its Applications

Front Cover
Dimiter G. Skordev
Springer Science & Business Media, Dec 6, 2012 - Mathematics - 386 pages
The Summer School and Conference on Mathematical Logic and its Applications, September 24 - October 4, 1986, Druzhba, Bulgaria, was honourably dedicated to the 80-th anniversary of Kurt Godel (1906 - 1978), one of the greatest scientists of this (and not only of this) century. The main topics of the Meeting were: Logic and the Foundation of Mathematics; Logic and Computer Science; Logic, Philosophy, and the Study of Language; Kurt Godel's life and deed. The scientific program comprised 5 kinds of activities, namely: a) a Godel Session with 3 invited lecturers b) a Summer School with 17 invited lecturers c) a Conference with 13 contributed talks d) Seminar talks (one invited and 12 with no preliminary selection) e) three discussions The present volume reflects an essential part of this program, namely 14 of the invited lectures and all of the contributed talks. Not presented in the volltme remai ned si x of the i nvi ted lecturers who di d not submi t texts: Yu. Ershov - The Language of!:-expressions and its Semantics; S. Goncharov - Mathematical Foundations of Semantic Programming; Y. Moschovakis - Foundations of the Theory of Algorithms; N. Nagornyj - Is Realizability of Propositional Formulae a GBdelean Property; N. Shanin - Some Approaches to Finitization of Mathematical Analysis; V. Uspensky - Algorithms and Randomness - joint with A.N.
 

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Contents

Remarks Concerning Kurt Gödels Life and Work
4
Gödels Life and Work
23
Categorial Grammar and Lambda Calculus
39
A Constructive Morse Theory of Sets
61
Differentiation of Constructive Functions of a Real Variable
81
Reasoning in Trees
125
NonDeterministic Program Schemata and their Relation to Dynamic Logic
137
The Parallel Evaluation of Functional Programs
149
Modal Environment for Boolean Speculations
253
Distributive Spaces
265
Approximating the Projective Model
273
Projection Complete Graph Problems Corresponding to a BranchingProgram
283
Constructive Theories with Abstract Data Types for Program Synthesis
293
A FirstOrder Logic for Logic Programming
303
The Relational Semantics for Branched Quantifiers
315
Propositional Dynamic Logic in Two and More Dimensions
323

Logic Approximating Sequences of Sets
167
Intuitionistic Formal Spaces A First Communication
187
On the Logic of Small Changes in Theories II
205
On Logical Relations in Program Semantics
213
Search Computability and Computability with Numberings Are Equivalent
233
CutElimination Theorem for HigherUrder Classical Logic
243
On a NonConstructive Type Theory and Program Derivation
331
Prime Computability on Partial Structures
341
Complexity Bounded MartinLöf Tests
351
Participants and Contributors
361
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