A Note on Negation in Categorial Grammar

A version of strong negation is introduced into Categorial Grammar.The resulting syntactic calculi turn out to be systems of connexivelogic.     

Infinite Set Unification with Application to Categorial Grammar

In this paper the notion of unifier is extended to the infinite set case. The proof of existence of the most general unifier of any infinite, unifiable set of types (terms) is presented. Learning procedure, based on infinite set unification, is described.     

关于不可化归的多态式量词句的CCG探析

广义量词理论对英语中一些特定的量词句进行分析,把其中两个单态式量词合并成一个多态式量词。Keenan证明了这个多态式量词的意义不能化归为两个单态式量词的意义,即多态式量词的意义不能从两个单态式量词的标准意义推演出来。Keenan的研究是很有价值的,但本文尝试从另外的角度思考,对汉语类似的多态式量化句进行个案处理,采纳组合范畴语法针对自然语言表层结构的词汇主义方法,遵循部分表达式的意义决定整体表达式意义的组合原则,从两个单态式量词的非标准意义推演出整个多态式量词句的量化意义。     

The Generality Constraint and Categorial Restrictions

We should not admit categorial restrictions on the significance of syntactically well formed strings. Syntactically well formed but semantically absurd strings, such as 'Life's but a walking shadow' and 'Caesar is a prime number', can express thoughts; and competent thinkers both are able to grasp these and ought to be able to. Gareth Evans' generality constraint, though Evans himself restricted it, should be viewed as a fully general constraint on concept possession and propositional thought. For (a) even well formed but semantically cross-categorial strings often do possess substantive inferential roles; (b) hearers exploit these inferential roles in interpreting such strings metaphorically; (c) there is no good reason to deny truth-conditions to strings with inferential roles.     

Categorial grammars determined from linguistic data by unification

We provide an algorithm for determining a categorial grammar from linguistic data that essentially uses unification of type-schemes assigned to atoms. The algorithm presented here extends an earlier one restricted to rigid categorial grammars, introduced in [4] and [5], by admitting non-rigid outputs. The key innovation is the notion of an optimal unifier, a natural generalization of that of a most general unifier.     

On Learnability of Restricted Classes of Categorial Grammars

In this paper we present learning algorithms for classes of categorial grammars restricted by negative constraints. We modify learning functions of Kanazawa [10] and apply them to these classes of grammars. We also prove the learnability of intersection of the class of minimal grammars with the class of k-valued grammars. Presented by Wojciech Buszkowski     

Categorial Indeterminacy,Generality and Logical Form in Wittgenstein's Tractatus

Many commentators have attempted to say, more clearly than Wittgenstein did in his Tractatus logico‐philosophicus, what sort of things the ‘simple objects’ spoken of in that book are. A minority approach, but in my view the correct one, is to reject all such attempts as misplaced. The Tractarian notion of an object is categorially indeterminate: in contrast with both Frege's and Russell's practice, it is not the logician's task to give a specific categorial account of the internal structure of elementary propositions or atomic facts, nor, correlatively, to give an account of the forms of simple objects. The few commentators who have hitherto maintained this view have mainly devoted themselves to establishing that this was Wittgenstein's intention, and do not much address the question why Wittgenstein held that it is not the logician's business to say what the objects are. The present paper means to fill this lacuna by placing this view in the context of the Tractatus's treatment of logic generally, and in particular by connecting it with Wittgenstein's treatment of generality and with his reaction to Russell's approach to logical form.     

Arithmetic as Grammar

What is a number? Using material from Wittgenstein’s 1930s lectures, I argue that this question expresses a disorientation best overcome by recollecting rules that govern the number words. Why do we have the rules we do? We may be persuaded to adopt one rule rather than another by experience, when experiment shows it to be the more convenient way; we may also be persuaded by the “experience” of a new aspect. Mathematics is a “motley of techniques” for doing certain things; religion is a certain spirit meant to pervade everything we do. An important likeness is that in both instruction is essentially grammatical.     

Logic and Grammar

Grammar can be formulated as a kind of substructural propositional logic. In support of this claim, we survey bare Gentzen style deductive systems and two kinds of non-commutative linear logic: intuitionistic and compact bilinear logic. We also glance at their categorical refinements.