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[Keyword] linear logic(2hit)

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  • A Query System for Texts with Macros

    Keehang KWON  Dae-Seong KANG  Jinsoo KIM  

     
    LETTER-Automata and Formal Language Theory

      Vol:
    E91-D No:1
      Page(s):
    145-147

    We propose a query language based on extended regular expressions. This language extends texts with text-generating macros. These macros make it possible to define languages in a compressed, elegant way. This paper also extends queries with linear implications and additive (classical) conjunctions. To be precise, it allows goals of the form D —ο G and G1&G2 where D is a text or a macro and G is a query. The first goal is solved by adding D to the current text and then solving G. This goal is flexible in controlling the current text dynamically. The second goal is solved by solving both G1 and G2 from the current text. This goal is particularly useful for internet search.

  • Propositional Temporal Linear Logic and Its Application to Concurrent Systems

    Takaharu HIRAI  

     
    PAPER

      Vol:
    E83-A No:11
      Page(s):
    2219-2227

    In computer science, concepts of resource such as data consumption and of time such as execution time are very important. Logical systems which can treat them have been applied in that field. Linear logic has been called a resource conscious logic. The expressive power is enough to describe a dynamic change in process environments. However, linear logic is not enough to treat a dynamic change in environments with the passage of time since it does not include a concept of time directly. A typical example is the relation between linear logic and Petri nets. It is well known that the reachability problem for Petri nets is equivalent to the provability for the corresponding sequent of linear logic. But linear logic cannot naturally represent timed Petri nets which are extensions of ordinary Petri nets with respect to time concept. So we extend linear logic with respect to time concept in order to introduce a resource-conscious and time-dependent logical system, that is, temporal linear logic. This system has some temporal operators "" which means a resource usable only once at the next time, "" which means a resource usable only once at anytime, and a modal storage operator "!" which means a resource usable any times at anytime. We can show that the reachability problem for timed Petri nets is equivalent to the provability for the corresponding sequent of temporal linear logic. In this paper, we also represent the description of synchronous communication model by temporal linear logic. The expressive power of temporal linear logic will be applicable to various fields of computer science.