Makoto Kanazawa

Weak vs. strong readings of donkey sentences and monotonicity inference in a dynamic setting

In this paper, I show that the availability of what some authors have called the weak reading and the strong reading of donkey sentences with relative clauses is systematically related to monotonicity properties of the determiner. The correlation is different from what has been observed in the literature in that it concerns not only right monotonicity, but also left monotonicity (persistence/antipersistence). I claim that the reading selected by a donkey sentence with a double monotone determiner is in fact the one that validates inference based on the left monotonicity of the determiner. This accounts for the lack of strong reading in donkey sentences with ↑ MON → determiners, which have been neglected in the literature. I consider the relevance of other natural forms of inference as well, but also suggest how monotonicity inference might play a central role in the actual process of interpretation. The formal theory is couched in dynamic predicate logic with generalized quantifiers.

The Lambek calculus enriched with additional connectives

Some formal properties of enriched systems of Lambek calculus with analogues of conjunction and disjunction are investigated. In particular, it is proved that the class of languages recognizable by the Lambek calculus with added intersective conjunction properly includes the class of finite intersections of context-free languages.

The Pumping Lemma for Well-Nested Multiple Context-Free Languages

Seki et al. (1991) proved a rather weak pumping lemma for multiple context-free languages, which says that any infinite m-multiple context-free language contains a string that is pumpable at some 2m substrings. We prove a pumping lemma of the usual universal form for the subclass consisting of well-nested multiple context-free languages. This is the same class of languages generated by non-duplicating macro grammars and by coupled-context-free grammars.

Angluin's theorem for indexed families of r.e. sets and applications

We extend Angluin s theorem to char acterize identi ability of indexed families of r e languages as opposed to indexed families of recursive languages We also prove some variants characterizing conservativity and two other similar restrictions paralleling Zeug mann Lange and Kapur s results for indexed families of recursive languages

Dynamics, Polarity, and Quantification

The topics of the papers in this collection run the gamut from empirical coverage of polarity item systems in a variety of languages to results in metatheoretical reasoning about quantifier reducibility. A recurrent theme throughout is the improvement (or replacement) of notions of quantificational scope in linguistic analysis by formally sophisticated analyses of the properties of quantifiers and their dynamic interpretations. The authors have written to admirable standards of formalisation and clarity of exposition and their results deserve thoughtful consideration and incorporation into linguistic semantics.

Multidimensional trees and a Chomsky–Schützenberger–Weir representation theorem for simple context-free tree grammars

Weir [34] proved a Chomsky-Schutzenberger-like representation theorem for the string languages of tree-adjoining grammars, where the Dyck language Dn in the Chomsky-Schutzenberger characterization is replaced by the intersection D2n ∩ g(D2n), where g is a certain bijection on the alphabet consisting of 2n pairs of brackets. This paper presents a generalization of this theorem to the string languages that are the yield images of the tree languages generated by simple (i.e., linear and non-deleting) context-free tree grammars. This result is obtained through a natural generalization of the original Chomsky-Schutzenberger theorem to the tree languages of simple context-free tree grammars. We use Rogers’s [24,23] notion of multi-dimensional trees to state this latter theorem in a very general, abstract form.

The complexity and generative capacity of lexicalized abstract categorial grammars

Previous studies have shown that some well-known classes of grammars can be simulated by Abstract Categorial Grammars (de Groote 2001) in straightforward ways. These classes of grammars all generate subclasses of the PTIME languages. While the exact generative capacity of the class of ACGs and the complexity of its universal membership problem are both unknown, we show that the universal membership problem for the class of lexicalized ACGs is NP-complete and the languages generated by lexicalized ACGs form a subclass of NP which includes some NP-complete languages.

On the Lumping Semantics of Counterfactuals

Kratzer (1981) discussed a naive premise semantics of counterfactual conditionals, pointed to an empirical inadequacy of this interpretation, and presented a modification—partition semantics—which Lewis (1981) proved equivalent to Pollocks (1976) version of his ordering semantics. Subsequently, Kratzer (1989) proposed lumping semantics, a different modification of premise semantics, and argued it remedies empirical failings of ordering semantics as well as of nao¨ve premise semantics. We show that lumping semantics yields truth conditions for counter- factuals that are not only different from what she claims they are, but also inferior to those of the earlier versions of premise semantics.

Computing interpolants in implicational logics

Abstract I present a new syntactical method for proving the Interpolation Theorem for the implicational fragment of intuitionistic logic and its substructural subsystems. This method, like Prawitz’s, works on natural deductions rather than sequent derivations, and, unlike existing methods, always finds a ‘strongest’ interpolant under a certain restricted but reasonable notion of what counts as an ‘interpolant’.

The Failure of the Strong Pumping Lemma for Multiple Context-Free Languages

Seki et al. (Theor. Comput. Sci. 88(2):191–229, 1991) showed that every m-multiple context-free language L is weakly 2m-iterative in the sense that either L is finite or L contains a subset of the form