Relational Models for the Lambek Calculus with Intersection and Constants
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...
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| Published in: | Logical methods in computer science Vol. 19, Issue 4 |
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| Language: | English |
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Logical Methods in Computer Science e.V
01-01-2023
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Kuznetsov, Stepan L. |
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| Snippet | We consider relational semantics (R-models) for the Lambek calculus extended
with intersection and explicit constants for zero and unit. For its variant... We consider relational semantics (R-models) for the Lambek calculus extended with intersection and explicit constants for zero and unit. For its variant... |
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| Title | Relational Models for the Lambek Calculus with Intersection and Constants |
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