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22A Concrete Categorical Model for the Lambek Syntactic CalculusMathematical Logic Quarterly 43 (1): 49-59. 1997.We present a categorical/denotational semantics for the Lambek Syntactic Calculus , indeed for a λlD-typed version Curry-Howard isomorphic to it. The main novelty of our approach is an abstract noncommutative construction with right and left adjoints, called sequential product. It is defined through a hierarchical structure of categories reflecting the implicit permission to sequence expressions and the inductive construction of compound expressions. We claim that Lambek's noncommutative product…Read more
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8A Concrete Categorical Model For The Lambek Syntactic CalculuMathematical Logic Quarterly 43 (1): 49-59. 1997.We present a categorical/denotational semantics for the Lambek Syntactic Calculus, indeed for a λlD-typed version Curry-Howard isomorphic to it. The main novelty of our approach is an abstract noncommutative construction with right and left adjoints, called sequential product. It is defined through a hierarchical structure of categories reflecting the implicit permission to sequence expressions and the inductive construction of compound expressions. We claim that Lambek's noncommutative product …Read more
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