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On the Unusual Effectiveness of Logic in Computer Science

  • Joseph Y. Halpern (a1), Robert Harper (a2), Neil Immerman (a3), Phokion G. Kolaitis (a4), Moshe Y. Vardi (a5) and Victor Vianu (a6)...


In 1960, E. P. Wigner, a joint winner of the 1963 Nobel Prize for Physics, published a paper titled On the Unreasonable Effectiveness of Mathematics in the Natural Sciences [61]. This paper can be construed as an examination and affirmation of Galileo's tenet that “The book of nature is written in the language of mathematics”. To this effect, Wigner presented a large number of examples that demonstrate the effectiveness of mathematics in accurately describing physical phenomena. Wigner viewed these examples as illustrations of what he called the empirical law of epistemology, which asserts that the mathematical formulation of the laws of nature is both appropriate and accurate, and that mathematics is actually the correct language for formulating the laws of nature. At the same time, Wigner pointed out that the reasons for the success of mathematics in the natural sciences are not completely understood; in fact, he went as far as asserting that “… the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.”



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[1] Abiteboul, S., Hull, R., and Vianu, V., Foundations of databases, Addison-Wesley, Reading, Massachusetts, 1995.
[2] Abiteboul, S. and Vianu, V., Generic computation and its complexity, Proceedings of the 23rd ACM Symposium on Theory of Computing, 1991, pp. 209219.
[3] Büchi, J. R., On a decision method in restricted second order arithmetic, Proceedings of the International Congress on Logic, Methodology and Philosophy of Science 1960, Stanford University Press, Stanford, 1962, pp. 112.
[4] Burch, J. R., Clarke, E. M., McMillan, K. L., Dill, D. L., and Hwang, L. J., Symbolic model checking: 1020 states and beyond, Information and Computation, vol. 98 (1992), no. 2, pp. 142170.
[5] Church, A., A note on the Entscheidungsproblem, The Journal of Symbolic Logic, vol. 1 (1936), pp. 4044.
[6] Clarke, E. M., Emerson, E. A., and Sistla, A. P., Automatic verification of finite-state concurrent systems using temporal logic specifications, ACM Transactions on Programming Languages and Systems, vol. 8 (1986), no. 2, pp. 244263.
[7] Codd, E. F., A relational model of data for large shared data banks, Communications of the ACM, vol. 13 (1970), no. 6, pp. 377387.
[8] Curry, H. B. and Feys, R., Combinatory logic, North-Holland, 1958.
[9] Curry, H. B., Hindley, J. R., and Seldin, J. P., Combinatory logic, Volume 2, North-Holland, 1972.
[10] Davis, M., Influences of mathematical logic on computer science, The universal Turing machine: A half-century survey (Herken, R., editor), Oxford University Press, 1988, pp. 315326.
[11] Davis, M., The universal computer, Norton, 2000.
[12] Ebbinghaus, H. D. and Flum, J., Finite model theory, Perspectives in Mathematical Logic, Springer-Verlag, 1995.
[13] Ehrenfeucht, A., An application of games to the completeness problem for formalized theories, Fundamenta Mathematicae, vol. 49 (1961), pp. 129141.
[14] Fagin, R., Generalized first-order spectra and polynomial-time recognizable sets, Complexity of computation (Karp, R. M., editor), SIAM-AMS Proceedings, vol. 7, 1974, pp. 4373.
[15] Fagin, R., Halpern, J. Y., Moses, Y., and Vardi, M. Y., Reasoning about knowledge, MIT Press, Cambridge, Massachusetts, 1995.
[16] Fraïssé, R., Sur quelques classifications des systèmes de relations, Publ. Sci. Univ. Alger. Sér. A, vol. 1 (1954), pp. 35182.
[17] Garey, M. and Johnson, D. S., Computers and intractability: A guide to the theory of NP-completeness, W. Freeman and Co., San Francisco, 1979.
[18] Girard, J.-Y., Lafont, Y., and Taylor, P., Proofs and types, Cambridge Tracts in Theoretical Computer Science, vol. 7, Cambridge University Press, Cambridge, England, 1989.
[19] Gödel, K., Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik, vol. 38 (1931), pp. 173198.
[20] Goering, R., Model checking expands verification's scope, Electronic Engineering Today, (1997).
[21] Gray, J., Notes on database operating systems, Operating systems: An advanced course (Bayer, R., Graham, R. M., and Seegmuller, G., editors), Lecture Notes in Computer Science, vol. 66, Springer-Verlag, Berlin/New York, 1978, also appears as IBM Research Report RJ 2188, 1978.
[22] Halpern, J. Y. and Moses, Y., Knowledge and common knowledge in a distributed environment, Journal of the ACM, vol. 37 (1990), no. 3, pp. 549587.
[23] Hamming, R. W., The unreasonable effectiveness of mathematics, American Mathematical Monthly, vol. 87 (1980), pp. 8190.
[24] Henkin, L., Monk, J. D., and Tarski, A., Cylindric algebras, Part I, North Holland, 1971, Part II, North Holland, 1985.
[25] Hintikka, J., Knowledge and belief, Cornell University Press, Ithaca, New York, 1962.
[26] Holzmann, G. J., The model checker SPIN, IEEE Transactions on Software Engineering, vol. 23 (1997), no. 5, pp. 279295, special issue on Formal Methods in Software Practice.
[27] Howard, William A., The formulas-as-types notion of construction, To H. B. Curry: Essays in combinatory logic, lambda calculus and formalism (Seldin, J. P. and Hindley, J. R., editors), Academic Press, 1980, pp. 479490.
[28] Immerman, N., Number of quantifiers is better than number of tape cells, Journal of Computer and System Sciences, vol. 22 (1981), no. 3, pp. 384406.
[29] Immerman, N., Upper and lower bounds for first-order expressibility, Journal of Computer and System Sciences, vol. 25 (1982), pp. 7698.
[30] Immerman, N., Relational queries computable in polynomial time, Information and Control, vol. 68 (1986), pp. 86104.
[31] Immerman, N., Languages which capture complexity classes, SIAM Journal on Computing, vol. 16 (1987), no. 4, pp. 760778.
[32] Immerman, N., Nondeterministic space is closed under complement, SIAM Journal on Computing, vol. 17 (1988), pp. 935938.
[33] Immerman, N., Dspace[nk] = var[k + 1], Proceedings of the 6th IEEE Symposium on Structure in Complexity Theory, 1991, pp. 334340.
[34] Immerman, N., Descriptive complexity: a logician's approach to computation, Notices of the American Mathematical Society, vol. 42 (1995), no. 10, pp. 11271133.
[35] Immerman, N., Descriptive complexity, Springer-Verlag, 1999.
[36] Jacobs, B., Categorical logic and type theory, Studies in Logic and the Foundations of Mathematics, vol. 141, Elsevier, Amsterdam, 1999.
[37] Kanellakis, P. C., Elements of relational database theory, Handbook of theoretical computer science (Van Leeuwen, J., editor), Elsevier, 1991, pp. 10741156.
[38] Kripke, S., A semantical analysis of modal logic I: normal modal propositional calculi, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 9 (1963), pp. 6796, announced in Journal of Symbolic Logic , vol. 24 (1959), p. 323.
[39] Kurshan, R. P., Computer aided verification of coordinating processes, Princeton University Press, 1994.
[40] Kurshan, R. P., Formal verification in a commercial setting, The Verification Times, (1997).
[41] Lichtenstein, O. and Pnueli, A., Checking that finite-state concurrent programs satisfy their linear specifications, Proceedings of the 13th ACM Symposium on Principles of Programming Languages, 1985, pp. 97107.
[42] Maier, D., The theory of relational databases, Computer Science Press, 1983.
[43] Manna, Z. and Waldinger, R., The logical basis for computer programming, Addison-Wesley, 1985.
[44] Martin-Löf, P., Intuitionistic type theory, Studies in Proof Theory, Bibliopolis, Naples, Italy, 1984.
[45] Mitchell, J. C., Foundations for programming languages, Foundations of Computing, MIT Press, 1996.
[46] Plotkin, G., A structural approach to operational semantics, Technical Report DAIMI–FN–19, Computer Science Department, Aarhus University, 1981.
[47] Pnueli, A., The temporal logic of programs, Proceedings of the 18th IEEE Symposium on Foundation of Computer Science, 1977, pp. 4657.
[48] Queille, J. P. and Sifakis, J., Specification and verification of concurrent systems in Cesar, Proceedings of the 5th International Symposium on Programming, Lecture Notes in Computer Science, vol. 137, Springer-Verlag, 1981, pp. 337351.
[49] Reynolds, John C., Three approaches to type structure, Tapsoft, Springer-Verlag, 1985.
[50] Reynolds, John C., Theories of programming languages, Cambridge University Press, 1998.
[51] Silberschatz, A., Korth, H., and Sudarshan, S., Database system concepts, McGraw-Hill, 1997.
[52] Tarditi, David, Morrisett, Greg, Cheng, Perry, Stone, Chris, Harper, Robert, and Lee, Peter, TIL: A type-directed optimizing compiler for ML, ACM SIGPLAN Conference on Programming Language Design and Implementation, Philadelphia, Pennsylvania, 05 1996, pp. 181192.
[53] Tarski, A., Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica, vol. 1 (1935), pp. 261405.
[54] Turing, A., On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, Series 3, vol. 42 (1936/37), pp. 230265.
[55] Ullman, J. D., Principles of database and knowledge base systems, Computer Science Press, 1988.
[56] Vardi, M. Y., The complexity of relational query languages, Proceedings of the 14th ACM Symposium on Theory of Computing, San Francisco, 1982, pp. 137146.
[57] Vardi, M. Y., An automata-theoretic approach to linear temporal logic, Logics for concurrency: Structure versus automata (Moller, F. and Birtwistle, G., editors), Lecture Notes in Computer Science, vol. 1043, Springer-Verlag, Berlin, 1996, pp. 238266.
[58] Vardi, M. Y. and Wolper, P., An automata-theoretic approach to automatic program verification, Proceedings of the 1st symposium on logic in computer science, Cambridge, 06 1986, pp. 332344.
[59] Vardi, M. Y. and Wolper, P., Reasoning about infinite computations, Information and Computation, vol. 115 (1994), no. 1, pp. 137.
[60] Vianu, V., Databases and finite-model theory, Descriptive complexity and finite models (Immerman, Neil and Kolaitis, Phokion, editors), Dimacs Series in Discrete Mathematics and Theoreticcal Computer Science, American Mathematical Society, 1997, Proceedings of a Dimacs Workshop 01 14-17, 1996, Princeton University.
[61] Wigner, E. P., The unreasonable effectiveness of mathematics in the natural sciences, Communications on Pure and Applied Mathematics, vol. 13 (1960), pp. 114.


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