Abstract
We review a few of the developments of dynamic logic from the author’s perspective. As implied by the title the review is not intended as a survey of the field as a whole but rather as how the author’s outlook on imperative programs and their logics evolved during the four decades up to the start of this millennium.
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- 1.
- 2.
An R-module is a vector space just when the ring R is a field.
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I had not used the term “multimodal” explicitly in any of my earlier papers. Rennie’s n-multiply modal calculus based on constants \(M_1,M_2,\ldots ,M_n\) [52] is a much earlier related concept.
References
Barr, M.: \(*\)-Autonomous Categories. Lecture Notes in Mathematics, vol. 752. Springer, Berlin (1979)
Beth, E.W.: The Foundations of Mathematics. North Holland, Amsterdam (1959)
Brock, J.D., Ackerman, W.B.: An anomaly in the specifications of nondeterministic packet systems. Technical report Computation Structures Group Note CSG-33, MIT Lab. for Computer Science, November 1977
Cannon, J.J.: A general purpose group theory program. In: Proceedings of the Second International Conference Theory of Groups, Canberra, pp. 204–217 (1973)
Cannon, J.J.: A draft description of the group theory language cayley. In: Proceedings of the Third ACM Symposium on Symbolic and Algebraic Computation, SYMSAC 1976, pp. 66–84. ACM, New York (1976)
de Bakker, J.W., de Roever, W.P.: A calculus for recursive program schemes. In: Nivat, M. (ed.) Automata, Languages and Programming, pp. 167–196. North Holland (1972)
Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall, Englewood Cliffs (1976)
Ehrenfeucht, A., Zeiger, P.: Complexity measures for regular expressions. J. Comput. Syst. Sci. 12(2), 134–146 (1976)
Fischer, M.J., Ladner, R.E.: Propositional modal logic of programs. In: Proceedings of the 9th ACM Symposium on Theory of Computing, pp. 194–211, Boulder, May 1977. Journal version: Propositional dynamic logic of regular programs, JCSS 18:2 (1979)
Floyd, R.W.: Assigning meanings to programs. In: Schwartz, J.T. (ed.) Mathematical Aspects of Computer Science, pp. 19–32 (1967)
Gentzen, G.: Investigations into logical deductions. In: Szabo, M.E. (ed.) The Collected Papers of Gerhard Gentzen, pp. 68–131. North-Holland, Amsterdam (1934)
Gold, E.M.: Language identification in the limit. Inf. Control 10(5), 447–474 (1967)
Grabowski, J.: On partial languages. Fundam. Inform. IV(2), 427–498 (1981)
Harel, D., Meyer, A.R., Pratt, V.R.: Computability and completeness in logics of programs. In: Proceedings of the 9th Annual ACM Symposium on Theory of Computation, pp. 261–268 (1977)
Henkin, L.: The logic of equality. Amer. Math. Mon. 84(8), 597–612 (1977)
Hintikka, K.J.J.: Form and content ni quantification theory. Acta Philos. Fenni. 8, 7–55 (1955)
Hoare, C.A.R.: An axiomatic basis for computer programming. Commun. ACM 12, 576–580 (1969)
Hoare, C.A.R., Lauer, P.E.: Consistent and complementary formal theories of the semantics of programming languages. Acta Inform. 3, 135–153 (1974)
Jónsson, B., Tarski, A.: Boolean algebras with operators. Part I. Amer. J. Math. 73, 891–939 (1951)
Knuth, D.E., Morris, J., Pratt, V.R.: Fast pattern matching in strings. SIAM J. Comput. 6(2), 323–350 (1977)
Kozen, D.: A representation theorem for models of \(*\)-free PDL. Technical report RC7864, IBM, September 1979
Kozen, D.: Results on the propositional mu-calculus. Theor. Comput. Sci. 23 (1983)
Kripke, S.: A completeness theorem in modal logic. J. Symb. Logic 24(1), 1–14 (1959)
Kripke, S.: Semantical considerations on modal logic. Acta Philos. Fenn. 16, 83–94 (1963)
Ladner, R.E.: The computational complexity of provability in systems of modal propositional logic. SIAM J. Comput. 6(3), 467–480 (1977)
Litvintchouk, S.D., Pratt, V.R.: A proof checker for dynamic logic. In: 5th International Joint Conference on A.I., pp. 552–558, August 1977
Mazurkiewicz, A.: Concurrent program schemes and their interpretations. Technical report DAIMI Report PB-78, Aarhus University, Aarhus (1977)
Nelson, G., Oppen, D.C.: Fast decision algorithms based on union and find. In: 18th IEEE Symposium on Foundations of Computer Science, October 1977
Németi, I.: Every free algebra in the variety generated by the representable dynamic algebras is separable and representable. Theoret. Comput. Sci. 17, 343–347 (1982)
Parikh, R.: A completeness result for a propositional dynamic logic. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol. 64, pp. 403–415. Springer, Heidelberg (1978)
Petri, C.A.: Fundamentals of a theory of asynchronous information flow. In: Proceedings of the IFIP Congress 62, Munich, pp. 386–390 (1962). North-Holland, Amsterdam
Pnueli, A.: The temporal logic of programs. In: 18th IEEE Symposium on Foundations of Computer Science, pp. 46–57, October 1977
Pratt, V.R.: Translation of lewis carroll’s syllogisms into logic. Masters Thesis, August 1969
Pratt, V.R.: Semantical considerations on Floyd-Hoare logic. In: Proceedings of the 17th Annual IEEE Symposium on Foundations of Computer Science, pp. 109–121, October 1976
Pratt, V.R.: A practical decision method for propositional dynamic logic. In: Proceedings of the 10th Annual ACM Symposium on Theory of Computing, San Diego, pp. 326–337, May 1978
Pratt, V.R.: Axioms or algorithms. In: Proceedings of the 6th Symposium on Mathematical Foundations of Computer Science, Olomouc, Czech. (1979)
Pratt, V.R.: Dynamic algebras: Examples, constructions, applications. Technical report MIT/LCS/TM-138, M.I.T. Laboratory for Computer Science, July 1979
Pratt, V.R.: Dynamic logic. In: Proceedings of the 6th Conference on Logic, Methodology, and Philosophy of Science, Hanover, West Germany, pp. 251–261 (1979)
Pratt, V.R.: Process logic. In: Proceedings of the 6th Annual ACM Symposium on Principles of Programming Languages, San Antonio, pp. 93–100, January 1979
Pratt, V.R.: Dynamic algebras and the nature of induction. In: 12th ACM Symposium on Theory of Computation, Los Angeles, April 1980
Pratt, V.R.: A near optimal method for reasoning about action. J. Comput. Syst. Sci. 2, 231–254 (1980). Also MIT/LCS/TM-113, M.I.T., Sept. 1978
Pratt, V.R.: A decidable mu-calculus. In: Proceedings of the 22nd IEEE Conference on Foundations of Computer Science, pp. 421–427, October 1981
Pratt, V.R.: Using graphs to understand PDL. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 387–396. Springer, Heidelberg (1982). https://doi.org/10.1007/BFb0025792
Pratt, V.R.: Position statement. Circulated at the Panel on Mathematics of Parallel Processes, chair A.R.G. Milner, IFIP-83, September 1983
Pratt, V.: The pomset model of parallel processes: unifying the temporal and the spatial. In: Brookes, S.D., Roscoe, A.W., Winskel, G. (eds.) CONCURRENCY 1984. LNCS, vol. 197, pp. 180–196. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-15670-4_9
Pratt, V.: Two-way channel with disconnect. In: Denvir, B.T., Harwood, W.T., Jackson, M.I., Wray, M.J. (eds.) The Analysis of Concurrent Systems. LNCS, vol. 207, pp. 110–114. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-16047-7_39
Pratt, V.R.: Modeling concurrency with geometry. In: Proceedings of the 18th Annual ACM Symposium on Principles of Programming Languages, pp. 311–322, January 1991
Pratt, V.R.: The duality of time and information. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 237–253. Springer, Heidelberg (1992). https://doi.org/10.1007/BFb0084795
Pratt, V.R.: Dynamic algebras: examples, constructions, applications. Stud. Logica 50(3/4), 571–605 (1992)
Pratt, V.R.: Transition and cancellation in concurrency and branching time. Math. Struct. Comp. Sci. 13(4), 485–529 (2003). Special issue on the difference between sequentiality and concurrency
Rasiowa, H., Sikorski, R.: The Mathematics of Metamathematics. Polska Akademia Nauk. Monografie matematyczne, vol. 41. Drukarnia Uniwersytetu, Warsaw (1963)
Rennie, M.K.: Models for multiply modal systems. Zeitschr. j. math. Logik und Grundlagen d. Math. 16, 175–186 (1970)
Salwicki, A.: Formalized algorithmic languages. Bull. Acad. Pol. Sci., Ser. Sci. Math. Astr. Phys. 18(5), 227–232 (1970)
Savitch, W.J.: Relationships between nondeterministic and deterministic tape complexities. J. Comput. Syst. Sci. 4, 177–192 (1970)
Smullyan, R.: First Order Logic. Springer, Berlin (1968)
Stone, M.: The theory of representations for Boolean algebras. Trans. Amer. Math. Soc. 40, 37–111 (1936)
Valiev, M.K.: On axiomatization of deterministic propositional dynamic logic. In: Proceedings of the 6th Symposium on Mathematical Foundations of Computer Science, Olomouc, Czech. (1979)
Zhegalkin, I.I.: On the technique of calculating propositions in symbolic logic. Matematicheskii Sbornik 43, 9–28 (1927)
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Pratt, V. (2018). Dynamic Logic: A Personal Perspective. In: Madeira, A., Benevides, M. (eds) Dynamic Logic. New Trends and Applications. DALI 2017. Lecture Notes in Computer Science(), vol 10669. Springer, Cham. https://doi.org/10.1007/978-3-319-73579-5_10
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