Computation, Logic, Philosophy: A Collection of Essays

ISBN-13: 9780792302186 / Angielski / Twarda / 1991 / 373 str.

Hao Wang; Hao Wang Hao;Wang Hao

Opis

Et moi, .... si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non. The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series."

Spis treści

One. Broad Issues.- 1. On Formalization.- 1.1 Systematization [1955(53)].- 1.2 Communication.- 1.3 Clarity and consolidation.- 1.4 Rigour.- 1.5 Approximation to intuition.- 1.6 Application to philosophy.- 1.7 Too many digits.- 1.8 Ideal language.- 1.9 How artificial language?.- 1.10 The paradoxes.- 2. The Concept of Computability [(1953)].- 2.1 Formalizing intuitive concepts.- 2.2 The intuitive concept of computability.- 2.3 Computation by theoretical machines.- 2.4 General recursive functions.- 2.5 Constructive proofs.- 2.6 Effective methods.- 2.7 Speed functions.- 2.8 Transfinite recursions.- 2.9 The indeterminate domain of computable functions.- 3. Process and Existence in Mathematics [1961(60)].- 4. Logic, Computation and Philosophy [1971(66)].- 4.1 Logic and logical positivism.- 4.2 What is mathematics?.- 4.3 Logic and computation.- 4.4 Relatively undecidable propositions and absolutely unsolvable problems.- 4.5 Foundations of set theory.- 4.6 What is mathematics? (continued).- Two. Automated Theorem Proving(ATP).- 5. Computer Theorem Proving and Artificial Intelligence [1984(82)].- Appendix: Citation for Haowang as Winner of “Milestone” Award in Automatic Theorem-Proving.- 6. Proving Theorems by Pattern Recognition, I [1960(59)].- 6.1 Introduction.- 6.2 A program that does 9 chapters of Principia in 9 minutes.- 6.3 The E1A case solved with sequential tables.- 6.4 General remarks.- 7. Observations on ATP.- 7.1 Mechanical mathematics and inferential analysis [1963(61)].- 7.2 The mechanization of mechanical arguments [1963(62)a].- 7.3 Formalization and automatic theorem—proving [1965(64)].- 8. Some Data for ATP.- 8.1 On axioms of conditional set existence [1967(66)].- 8.2 Natural hulls and set existence [1967(66)a].- 8.3 A theorem on definitions of the Zermelo-Neumann ordinals [1967(66)b].- 9. Proving Theorems by Pattern Recognition, II [1961(60)a].- 9.1 A survey of the decision problem.- 9.2 The Skolem, case.- 9.3 The A2E satisfiability case.- 9.4 The A1E1A1 satisfiability case.- 9.5 A proof procedure for the predicate calculus.- 9.6 Remarks on mathematical disciplines.- Three. Decidability and Complexity.- 10. Games, Logic and Computers [1965a].- Appendix: Notes on a Class of Tiling Problems [1975(60)].- 11. Dominoes and the AEA Case of the Decision Problem [1963(62)].- 12. Towards Feasible Solutions of the Tautology Problem (with B.Dunhan) [1976(74)].- 12.1 Computational complexity and Boolean validity.- 12.2 A brief overview with some general observations.- 12.3 Some basic properties of Boolean validity.- 12.4 Some calculations and classifications.- 12.5 Hard examples and negative results.- 12.6 A feasible decision procedure for biconditional expressions.- 12.7 Two partial methods and an indication of two generic methods.- 13. Ranked Matching and Hospital Interns (with D.A.Martin) [(1977)].- 13.1 Preliminary.- 13.2 Deletion of useless names: Operations I and II.- 13.3 The canonical form T1 of T.- 13.4 The student and hospital optimal assignments.- 13.5 Mixed assignments and a characterization of all stable assignments.- 13.6 The marriage problem.- Four. Topics from Theory to Practice.- 14. Logical Fragments Relevant to Computer Science.- 14.1 Logic of many-sorted theories [1952(50)].- 14.2 Ackermann’s consistency proof [1962(53)].- 14.3 Partial systems of number theory [1962(55)].- 14.4 The calculus of partial predicates and its extension to set theory [1961(61)].- 14.5 Model theory [1974(71)].- 15. Computers and Mathematical Activity.- 15.1 Remarks on machines, sets and the decision problem [1964(63)].- 15.2 Logic and computers [1965].- 15.3 Remarks on mathematics and computers [1970(67)].- 15.4 On the long-range prospects of automatic theorem-proving [1970(68)a].- 16. On Information Processing of the Chinese Language [1979].- The List of the Publications of the Author.