Abstract
A deductive data base theory is developed in first order predicate logic with identity. This development follows the usual method of setting up a deductive theory. Axioms and definitions are written down and theorems are derived. Some of these theorems can be understood as computer programs. A data base is a model of the theory. A model, supposed to characterize a world, can be interrogated by queries which are theorems of the theory. A main result of the paper is the formalization of good programming methods so that derivations can be used as efficient computations when answering queries.
Keywords
Logic Program Binary Tree Binary Tree Search Proof Procedure Empty List
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Bentley, J. L. [1975] Multidimensional Binary Search Trees Used for Associative Searching, CACM 18, 9 (September 1975), 509–516.MATHGoogle Scholar
- 2.Bibel, W. [1976] A Uniform Approach to Programming, Report 7633, Technische Universität München, 1976.Google Scholar
- 3.Bruynooghe, M. [1976] An Interpreter for Predicate Logic Programs, Part 1. Report CW 10, Applied Maths & Programming Division, Katholieke Univ Leuven, Belgium, Oct 1976.Google Scholar
- 4.Chang, C. L. [1978] DEDUCE 2: Further Investigations of Deduction in Relational Data Bases, In Logic and Data Bases (H. Gallaire and J. Minker, Eds.), Plenum Press, New York, New York, 1978, 201–236.Google Scholar
- 5.Clark, K. [1978] Negation as Failure, In Logic and Data Bases (H. Gallaire and J. Minker, Eds.), Plenum Press, New York, New York, 1978, 293–322.Google Scholar
- 6.Clark, K. and Tärnlund, S-Å. [1977] A First Order Theory of Data and Programs, Proc. IFIP Congress 1977, North-Holland Publishing Company, Amsterdam, 1977, 939–944.Google Scholar
- 7.Codd, E. F. [1970] A Relational Model for Large Shared Data Banks, CACM 13, 6 (June 1970), 377–387.Google Scholar
- 8.Colmerauer, A., Kanoui, H., Pasero, R. and Roussel, P. [1972] Un Systeme de Communication Homme-Machine en Francais, Groupe d’Intelligence Artificielle, U.E.R. de Luminy, Université d’Aix-Marseille, Luminy, 1972.Google Scholar
- 9.Green, C. [1969] “The Application of Theorem Proving to Question-Answering Systems,” Ph.D. Thesis, Computer Science Department, Stanford University, 1969.Google Scholar
- 10.Guttag, J. [1977] Abstract Data Types and the Development of Data Structures, CACM 20, 6 (June 1977), 396–404.MATHGoogle Scholar
- 11.Hayes, P. [1973] Computation and Deduction, Proc. MFCS Conf., Czechoslovakian Academy of Sciences, 1973.Google Scholar
- 12.Hewitt, C. [1972] Description and Theoretical Analysis (Using Schemata) of PLANNER: A Language for Proving Theorems and Manipulating Models in a Robot, A. J. Memo No. 251, MIT Project MAC., 1972.Google Scholar
- 13.Hoare, C.A.R. [1973] Recursive Data Structures, Computer Science Dept., Stanford University, STAN-CS-73–400, Oct. 1973.Google Scholar
- 14.Kellogg, C., Klahr, P. and Travis, L. [1978] Deductive Planning and Pathfinding for Relational Data Bases, In Logic and Data Bases (H. Gallaire and J. Minker, Eds.), Plenum Press, New York, New York, 1978, 179–200.Google Scholar
- 15.Knuth, D. [1968] The Art of Computer Programming, Vol. 1, Fundamental Algorithms, Addison-Wesley, Reading, Massachusetts, 1968.MATHGoogle Scholar
- 16.Knuth, D. [1973] The Art of Computer Programming, Vol. 3, Sorting and Searching, Addison-Wesley, Reading, Massachusetts, 1973.Google Scholar
- 17.Kowalski, R. [1974] Predicate Logic as Programming Language, Proc. IFIP Congress 1974, North-Holland Publishing Company, Amsterdam, 1974, 569–574.Google Scholar
- 18.Kowalski, R. [1978] Logic for Data Description, In Logic and Data Bases (H. Gallaire and J. Minker, Eds.), Plenum Press, New York, New York, 1978, 77–103.Google Scholar
- 19.Liskov, B. H. and Zilles, S. [1974] Programming with Abstract Data Types, ACM SIGPLAN Notices 9, 4 (April 1974), 50–59.Google Scholar
- 20.McCarthy, J., et al. [1962] LISP 1.5 Programmer’s Manual, MIT Press, Cambridge, Massachusetts, 1962, 33–70.Google Scholar
- 21.McCarthy, J. [1963] A Basis for a Mathematical Theory of Computation, In Computer Programming and Formal Systems (P. Braffort and D. Hirschberg, Eds.), North-Holland Publishing Company, Amsterdam, 1963.Google Scholar
- 22.McSkimin, J. R. and Minker, J. [1978] A Predicate Calculus Based Semantic Network for Question-Answering Systems, In Associative Networks ~ The Representation and Use of Knowledge (N. Findler, Ed.), Academic Press, New York, New York, 1978.Google Scholar
- 23.Minker, J. [1978] An Experimental Data Base System Based on Logic, In Logic and Data Bases (H. Gallaire and J. Minker, Eds.), Plenum Press, New York, New York, 1978, 107–147.Google Scholar
- 24.Nicolas, J. M. and Gallaire, H. [1978] Data Bases: Theory vs. Interpretation, In Logic and Data Bases (H. Gallaire and J. Minker, Eds.), Plenum Press, New York, New York, 1978, 33–54.Google Scholar
- 25.Quine, W. V. [1974] Methods of Logic, Third Edition, Rout-ledge & Kegan Paul, London, 1974.Google Scholar
- 26.Reiter, R. [1978] On Closed World Data Bases, In Logic and Data Bases (H. Gallaire and J. Minker, Eds.), Plenum Press, New York, New York, 1978, 55–76.Google Scholar
- 27.Robinson, J. A. [1965] A Machine-Oriented Logic Based on the Resolution Principle, JACM 12, 1 (January 1965), 23–41.MATHCrossRefGoogle Scholar
- 28.Roussel, P. [1975] PROLOG: Manuel de Reference et d’utilisation, Groupe d’Intelligence Artificielle, U.E.R. de Luminy, Marseille, September 1975.Google Scholar
- 29.Tärnlund, S- Å. [1975] Logic Information Processing, Dept. of Inofrmation Processing Computer Science, TRITA-IBADB 1034, The Royal Institute of Technology and The University of Stockholm, Sweden, 1975.Google Scholar
- 30.Tärnlund, S-Å. [1976] A Logical Basis for Data Bases, Department of Information Processing Computer Science, TRITA-IBADB-1029, The Royal Institute of Technology and The University of Stockholm, Sweden, 1976.Google Scholar
- 31.Tärnlund, S- Å. [1977] Horn Clause Computability, BIT 17, 2 (1977), 215–226.MathSciNetMATHCrossRefGoogle Scholar
- 32.van Emden, M. [1978] Computation and Deductive Information Retrieval, In Formal Description of Programming Concepts (E. Neuhold, Ed.), North-Holland Publishing Company, (to appear).Google Scholar
- 33.Warren, D. [1977] Implementing Prolog — Compiling Predicate Logic Programs, Dept. of AI, No. 39, Edinburgh, 1977.Google Scholar
Copyright information
© Plenum Press, New York 1978