On Relational Interpretation of Multimodal Categorial Logics
نویسنده
چکیده
Several recent results show that the Lambek Calculus L and its close relative L1 are sound and complete under (possibly relativized) relational interpretation. This paper transfers these results to L3, the multimodal extension of the Lambek Calculus that was proposed in Moortgat (1996). Two simple relational interpretations of L3 are proposed and shown to be sound and complete. The completeness proofs make heavy use of the method of relational labeling from Kurtonina (1995). Finally, it is demonstrated that relational interpretation provides a semantic justification for the translation from L3 to L from Versmissen (1996).
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