Logic of execution: An outline

  • Takayasu Ito
Part I: Theoretical Aspects Of Concurrency
Part of the Lecture Notes in Computer Science book series (LNCS, volume 491)


Logic of Execution is a logical framework of executing sentences, and it is aimed to provide a logical basis of concurrency and parallelism. We use
to express that the success of execution of A produces the success of execution of B. We assume that an execution of a statement will fall into one of success,failure and pending. We consider a set of executional operators: [;] (sequential execution), [+] (disjunctive execution), [V] (execution by non-deterministic choice), [&] (conjunctive execution), [|] (concurrent execution), [#] (parallel execution), [¬] (negation) and [C] (completion). A deductive system of Logic of Success of Execution is given in a propositional level. On the basis of this Logic of Execution how to execute propositional sentences is discussed,giving a set of executional rules for a sentence composed from the logical connectives. From the standpoint of the traditional logics the logic of execution has the 2-level structures:
  1. (1)

    the logical framework of execution for the executional operators, and

  2. (2)

    the framework to execute logical sentences ; that is, a set of rules to transform a logical sentence into a formula of the logic of execution.


The logic of execution is more expressible than Girard's Linear Logic, since it treats various modes of execution, including [V],[|] and [#]. Some remarks are given in connection with the traditional logics, and some topics for future study are also mentioned.


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  1. [1]
    J.Y. Girard: Linear Logic, Theoretical Computer Science, vol.50,pp.1–102 (1987)CrossRefGoogle Scholar
  2. [2]
    T.Ito: On Behaviors of Parallel Processes with Duration,Proceedings of Conference on Information Sciences and Systems,pp.455–467(1985)Google Scholar
  3. [3]
    T.Ito: Recovery from Deadlock and Starvation by the Forcing Method, Proceedings of Conference on Information Sciences and Systems,pp.521–527(1988){This was also presented at the first UK/Japan Workshop in Computer Science held at Sendai,July 6–7,1987.}Google Scholar
  4. [4]
    T.Ito and R.H.Halstead: Parallel Lisp, Springer LNCS, vol.441(1990)Google Scholar
  5. [5]
    H.Ono: Structural Rules and a Logical Hierarchy, Mathematical Logic,(ed. P.P.Petkov), pp.95–105,Plenum(1990)Google Scholar
  6. [6]
    D. Prawitz: Natural Deduction, Almquist & Wiksell, Stockholm(1965)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Takayasu Ito
    • 1
  1. 1.Department of Information Engineering Faculty of EngineeringTohoku UniversitySendaiJapan

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