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On the weak completeness of a fragment of linear temporal logic.

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Title: On the weak completeness of a fragment of linear temporal logic.
Authors: Baratella, Stefano1 (AUTHOR)
Source: Journal of Logic & Computation. Jul2025, Vol. 35 Issue 5, p1-12. 12p.
Subjects: Completeness theorem, Logic, Semantics methodology
Abstract: The main contribution of this work is an expanded and detailed version of a rather sketchy proof, which first appeared in Finger and Gabbay (1992, J. Logic Lang. Inf. , 1 , 203–233), of a weak completeness theorem for the until-free fragment LTL |${\_}$| of linear temporal logic. More precisely we show that LTL |${\_}$| is determined by the linearly ordered frame of the natural numbers. As a minor contribution, we also show that, under an ad hoc semantics and with a significant restriction on the admissible valuation maps, LTL |${\_}$| can be regarded as a logic for the discrete first quadrant. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: On the weak completeness of a fragment of linear temporal logic.
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  Data: The main contribution of this work is an expanded and detailed version of a rather sketchy proof, which first appeared in Finger and Gabbay (1992, J. Logic Lang. Inf. , 1 , 203–233), of a weak completeness theorem for the until-free fragment LTL |${\_}$| of linear temporal logic. More precisely we show that LTL |${\_}$| is determined by the linearly ordered frame of the natural numbers. As a minor contribution, we also show that, under an ad hoc semantics and with a significant restriction on the admissible valuation maps, LTL |${\_}$| can be regarded as a logic for the discrete first quadrant. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1093/logcom/exaf037
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      – Code: eng
        Text: English
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        PageCount: 12
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      – SubjectFull: Completeness theorem
        Type: general
      – SubjectFull: Logic
        Type: general
      – SubjectFull: Semantics methodology
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      – TitleFull: On the weak completeness of a fragment of linear temporal logic.
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              Text: Jul2025
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              Y: 2025
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