By Richard Moot
This publication is meant for college students in computing device technological know-how, formal linguistics, mathematical common sense and to colleagues attracted to categorial grammars and their logical foundations. those lecture notes current categorial grammars as deductive platforms, within the method referred to as parsing-as-deduction, and the ebook contains particular proofs in their major houses. The papers are geared up in topical sections on AB grammars, Lambek’s syntactic calculus, Lambek calculus and montague grammar, non-associative Lambek calculus, multimodal Lambek calculus, Lambek calculus, linear good judgment and facts nets and evidence nets for the multimodal Lambek calculus.
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Additional resources for The Logic of Categorial Grammars: A Deductive Account of Natural Language Syntax and Semantics
Going even further one can learn from unstructured sentences that are simply sequences of words: once again this is done by considering all possible structures on such sentences. This extension was investigated by Kanazawa (Kanazawa, 1998). Each of these extensions increases the complexity of the algorithm considerably, as one can imagine, but nevertheless the existence of learning algorithms for categorial grammars is a good property which is shared by few other formalisms for natural language syntax.
11. The order of a formula A is defined as follows. o(p) = 0 when p is an atomic type o(A \ B) = max(o(A) + 1, o(B)) o(B / A) = max(o(A) + 1, o(B)) Thus, the order of (np \ S) / np is 1, but the order of S / (np \ S) is two. 12. A provable sequent A1 , . . , An p of the product free Lambek calculus with o(Ai ) ≤ 1 and p a primitive type (and therefore of order zero) is provable with \e and /e only — in other words AB derivations and L derivations coincide when types are of order at most one. Proof.
Hint: assign atomic formulas b and e to “both” and “either” respectively. 2. 10? 3. 2. 6. 4. 7. Consider the following context-free grammar, which is already in Greibach normal form. S → aA S → bB S → aSA S → bSB A→a B→b 1. What is the language generated by this grammar? 2. Transform the grammar into an AB grammar. : Die syntaktische Konnexit¨at. : A quasi arithmetical notation for syntactic description. : On categorial and phrase-structure grammars. : Identification of reversible dependency tree languages.
The Logic of Categorial Grammars: A Deductive Account of Natural Language Syntax and Semantics by Richard Moot