By Chris Fox
This booklet offers a scientific examine of 3 foundational matters within the semantics of typical language which were rather missed long ago few a long time.
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Extra info for Foundations of intensional semantics
53) A closed Cartesian category (CCC) is a category with suﬃcient structure to provide a model of a higher-order typed λ-calculus. (54) A CCC contains (a) terminal objects (the categorical counterparts of singleton sets); (b) Cartesian products (corresponding to product types); and (c) exponentials (the counterpart of functional types). (55) For any category with the terminal object 1, we can think of an arrow f : 1 → A as the categorical generalization of the set theoretic notion of a member of A.
This approach permits him to characterize intensions independently of modality. He constructs a proof theory which speciﬁes the relation between intensional identity and provable equivalence in a way that allows for ﬁne-grained intensionality. However, it suﬀers from a number of serious formal diﬃculties. First, Bealer’s insistence on using a ﬁrst-order logic without functional types restricts the expressive power of his system in a way that prevents it from representing central features of natural language semantics.
Alternatives to Fine-Grained Intensionality 15 (2) a is the least upper bound of B iﬀ for every upper bound c of B, a ≤ c. The least upper bound of B is also known as the supremum of B (sup B). (3) For a poset A, a is a lower bound of B ⊆ A iﬀ for every b ∈ B, a ≤ b. (4) a is the greatest lower bound of B iﬀ for every lower bound c of B, c ≤ a. The greatest lower bound of B is also known as the inﬁmum of B (inf B). If a poset has a least upper bound and a greatest lower bound, they are unique by virtue of the antisymmetry of the partial order relation ≤.
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