Strong completeness of a first-order temporal logic for real time
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909734033948672 |
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| author | Goldblatt, Robert |
| author_facet | Goldblatt, Robert |
| contents | Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms for first-order logic with identity, and develop an alternative ``admissible'' semantics for it, showing that it is strongly complete for admissible models over the reals. By contrast there is no recursive axiomatisation of the first-order temporal logic of admissible models whose time flow is the integers, or any scattered linear ordering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20069 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strong completeness of a first-order temporal logic for real time Goldblatt, Robert Logic 03B44 Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms for first-order logic with identity, and develop an alternative ``admissible'' semantics for it, showing that it is strongly complete for admissible models over the reals. By contrast there is no recursive axiomatisation of the first-order temporal logic of admissible models whose time flow is the integers, or any scattered linear ordering. |
| title | Strong completeness of a first-order temporal logic for real time |
| topic | Logic 03B44 |
| url | https://arxiv.org/abs/2310.20069 |