In categorial grammar, a transitive verb 'likes' is typed (NP\S)/NP. When 'likes' combines with its object NP 'cats,' what type does the resulting expression have?
AS — a verb and its object form a complete sentence
BNP\S — a verb phrase that still needs a subject NP to its left
CNP/NP — the verb has consumed one of its two required arguments
D(NP\S)/NP — unchanged, because objects attach to sentences not verbs
Function application: (NP\S)/NP applied to NP yields NP\S. The forward-slash argument (the object, required to the right) is satisfied, leaving a verb phrase that still requires a subject NP to its left (the backslash). NP\S represents 'a function from a left-adjacent NP to a sentence' — exactly what a VP is semantically. The second combination, NP\S applied to a subject NP, yields S. Each step has a precise type-theoretic justification with no additional rules.
Question 2 Multiple Choice
A student argues that 'Cats Mary likes' is grammatical in English because all required elements — subject, verb, object — are present. What does categorial grammar predict?
AIt is grammatical — categorial grammar checks only that all arguments are present, not their order
BIt is ungrammatical — 'likes' is typed (NP\S)/NP, requiring its NP object immediately to the right, but 'Mary' intervenes
CIt is grammatical — the backward slash allows subjects to appear after objects
DCategorial grammar cannot evaluate this string because it requires a phrase-structure tree as input
Directionality is encoded in the slash notation. The forward slash '/' in (NP\S)/NP means 'requires an NP immediately to the right.' In 'Cats Mary likes,' 'likes' cannot combine with 'cats' as its object because 'Mary' intervenes — the type reduction cannot proceed correctly. The slashes enforce word order as a direct consequence of type structure, not as a separate stipulation. This is why the same verb type in an OVS language would carry different slash orientations.
Question 3 True / False
In categorial grammar, a string of words is grammatical if and only if its component types reduce to type S through function application.
TTrue
FFalse
Answer: True
This is the core principle. Every grammatical sentence reduces to type S; any combination that fails to reduce — because wrong types are adjacent or directionality is violated — is ungrammatical. There is only one combinatory rule: function application (A/B + B → A, or B + B\A → A). The entire grammar is this single rule applied to a typed lexicon. Grammaticality is a global property: the whole string must reduce, not merely adjacent pairs.
Question 4 True / False
Categorial grammar requires separate word-order rules — such as 'subjects precede verbs in English' — in addition to type assignments, just as phrase-structure grammars do.
TTrue
FFalse
Answer: False
This is precisely the elegance of the framework. Word order is not stipulated separately — it is encoded in the slash directionality of the type assignments. A forward slash requires the argument to the right; a backward slash requires it to the left. Subject-before-verb order in English emerges because subjects bear the '\' type, requiring the predicate to their right. Languages with different word orders receive the same functional types but with different slash orientations. Word-order variation is a systematic consequence of type directionality, not an additional set of rules.
Question 5 Short Answer
In what sense does categorial grammar 'integrate syntax and semantics,' and why is this considered an advantage?
Think about your answer, then reveal below.
Model answer: In categorial grammar, the syntactic types ARE the semantic types. A transitive verb's syntactic type (NP\S)/NP corresponds exactly to its semantic type as a function from two individual-denoting arguments to a truth value. There is no separate syntactic structure that then gets mapped to a semantic interpretation — the same type-theoretic machinery simultaneously determines what expressions can combine with (syntax) and what they mean (semantics). Every syntactic combination step is also a semantic composition step, eliminating the need for a translation between syntactic and semantic representations. The advantage is parsimony: one type system, one composition rule, two traditionally separate levels of grammar unified.
Frameworks like GB/Minimalism require separate syntactic trees and semantic interpretation rules. Categorial grammar achieves comparable descriptive coverage with a single compositional mechanism, making the relationship between form and meaning transparent at every derivation step.