Relational Models for the Lambek Calculus with Intersection and Constants
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arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909103765323776 |
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| author | Kuznetsov, Stepan L. |
| author_facet | Kuznetsov, Stepan L. |
| contents | We consider relational semantics (R-models) for the Lambek calculus extended with intersection and explicit constants for zero and unit. For its variant without constants and a restriction which disallows empty antecedents, Andreka and Mikulas (1994) prove strong completeness. We show that it fails without this restriction, but, on the other hand, prove weak completeness for non-standard interpretation of constants. For the standard interpretation, even weak completeness fails. The weak completeness result extends to an infinitary setting, for so-called iterative divisions (Kleene star under division). We also prove strong completeness results for product-free fragments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_00654 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Relational Models for the Lambek Calculus with Intersection and Constants Kuznetsov, Stepan L. Logic in Computer Science Logic 03G15 F.4.1 We consider relational semantics (R-models) for the Lambek calculus extended with intersection and explicit constants for zero and unit. For its variant without constants and a restriction which disallows empty antecedents, Andreka and Mikulas (1994) prove strong completeness. We show that it fails without this restriction, but, on the other hand, prove weak completeness for non-standard interpretation of constants. For the standard interpretation, even weak completeness fails. The weak completeness result extends to an infinitary setting, for so-called iterative divisions (Kleene star under division). We also prove strong completeness results for product-free fragments. |
| title | Relational Models for the Lambek Calculus with Intersection and Constants |
| topic | Logic in Computer Science Logic 03G15 F.4.1 |
| url | https://arxiv.org/abs/2210.00654 |