Effective Completeness for S4.3.1-Theories with Respect to Discrete Linear Models
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866916693300740096 |
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| author | Nichols, David |
| author_facet | Nichols, David |
| contents | The computable model theory of modal logic was initiated by Suman Ganguli and Anil Nerode in [4]. They use an effective Henkin-type construction to effectivize various completeness theorems from classical modal logic. This construction has the feature of only producing models whose frames can be obtained by adding edges to a tree digraph. Consequently, this construction cannot prove an effective version of a well-known completeness theorem which states that every $\mathsf{S4.3.1}$-theory has a model whose accessibility relation is a linear order of order type $ω$. We prove an effectivization of that theorem by means of a new construction adapted from that of Ganguli and Nerode. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_00317 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Effective Completeness for S4.3.1-Theories with Respect to Discrete Linear Models Nichols, David Logic 03C57, 03B45, 03B44 The computable model theory of modal logic was initiated by Suman Ganguli and Anil Nerode in [4]. They use an effective Henkin-type construction to effectivize various completeness theorems from classical modal logic. This construction has the feature of only producing models whose frames can be obtained by adding edges to a tree digraph. Consequently, this construction cannot prove an effective version of a well-known completeness theorem which states that every $\mathsf{S4.3.1}$-theory has a model whose accessibility relation is a linear order of order type $ω$. We prove an effectivization of that theorem by means of a new construction adapted from that of Ganguli and Nerode. |
| title | Effective Completeness for S4.3.1-Theories with Respect to Discrete Linear Models |
| topic | Logic 03C57, 03B45, 03B44 |
| url | https://arxiv.org/abs/1712.00317 |