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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 "

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.11 pp.2219-2227

- Publication Date
- 2000/11/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Concurrent Systems Technology)

- Category

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Takaharu HIRAI, "Propositional Temporal Linear Logic and Its Application to Concurrent Systems" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 11, pp. 2219-2227, November 2000, doi: .

Abstract: 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 "

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_11_2219/_p

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@ARTICLE{e83-a_11_2219,

author={Takaharu HIRAI, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Propositional Temporal Linear Logic and Its Application to Concurrent Systems},

year={2000},

volume={E83-A},

number={11},

pages={2219-2227},

abstract={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 "

keywords={},

doi={},

ISSN={},

month={November},}

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TY - JOUR

TI - Propositional Temporal Linear Logic and Its Application to Concurrent Systems

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2219

EP - 2227

AU - Takaharu HIRAI

PY - 2000

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E83-A

IS - 11

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - November 2000

AB - 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 "

ER -