Mathematical Logic and Its Applications

ISBN-13: 9781461282341 / Angielski / Miękka / 2011 / 386 str.

Dimiter G. Skordev; Dimiter G. Skordev

Opis

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.

Spis treści

Gödel Session (Invited Papers).- Remarks Concerning Kurt Gödel’s Life and Work.- Facets of Incompleteness.- Goder s Life and Work.- Summer School (Invited Papers).- Categorial Grammar Lambda Calculus.- A Constructive Morse Theory of Sets.- Differentiation of Constructive Functions of a Real Variable and Relative Computability.- A Completeness Theorem for Higher-Order Intuitionistic Logic: An Intuitionistic Proof.- Reasoning in Trees.- Non-Deterministic Program Schemata and their Relation to Dynamic Logic.- The Parallel Evaluation of Functional Programs.- Logic Approximating Sequences of Sets.- Intuitionistic Formal Spaces — A First Communication.- On the Logic of Small Changes in Theories, II.- On ‘Logical Relations’ in Program Semantics.- Conference (Contributed Papers).- Search Computabi1ity and Computabi1ity with Numberings Are Equivalent the Case of Finite Set of Objects.- Cut-Elimination Theorem for Higher-Order Classical Logic. An Intuitionistic Proof.- Modal Environment for Boolean Speculations.- Distributive Spaces.- Approximating the Projective Model.- Projection Complete Graph Problems Corresponding to a Branching-Program-Based Characterization of the Complexity Classes HC2, L and NL.- Constructive Theories with Abstract Data Types for Program Synthesis.- A First-Order Logic for Logic Programming.- The Relational Semantics for Branched Quantifiers.- Propositional Dynamic Logic in Two- and More Dimensions.- On a Non-Constructive Type Theory and Program Derivation.- Prime Computabi1ity on Partial Structures.- Complexity Bounded Martin-Löf Tests.- Participants and Contributors.