Semantic Unification A sheaf theoretic approach to natural language

Language is contextual and sheaf theory provides a high level mathematical framework to model contextuality. We show how sheaf theory can model the contextual nature of natural language and how gluing can be used to provide a global semantics for a discourse by putting together the local logical semantics of each sentence within the discourse. We introduce a presheaf structure corresponding to a basic form of Discourse Representation Structures. Within this setting, we formulate a notion of semantic unification --- gluing meanings of parts of a discourse into a coherent whole --- as a form of sheaf-theoretic gluing. We illustrate this idea with a number of examples where it can used to represent resolutions of anaphoric references. We also discuss multivalued gluing, described using a distributions functor, which can be used to represent situations where multiple gluings are possible, and where we may need to rank them using quantitative measures. Dedicated to Jim Lambek on the occasion of his 90th birthday.Comment: 12 page

'Now' with Subordinate Clauses

We investigate a novel use of the English temporal modifier ‘now’, in which it combines with a subordinate clause. We argue for a univocal treatment of the expression, on which the subordinating use is taken as basic and the non-subordinating uses are derived. We start by surveying central features of the latter uses which have been discussed in previous work, before introducing key observations regarding the subordinating use of ‘now’ and its relation to deictic and anaphoric uses. All of these data, it is argued, can be accounted for on our proposed analysis. We conclude by comparing ‘now’ to a range of other expressions which exhibit similar behavior

Events and Countability

There is an emerging view according to which countability is not an integral part of the lexical meaning of singular count nouns, but is ‘added on’ or ‘made available’, whether syntactically, semantically or both. This view has been pursued by Borer and Rothstein among others in order to deal with classifier languages such as Chinese as well as challenges to standard views of the mass-count distinction such as object mass nouns such as furniture. I will discuss a range of data, partly from German, that such a grammar-based view of countability receives support when applied to verbs with respect to the event argument position. Verbs themselves fail to specify events as countable in English and related languages; instead countability is made available only by the use of the event classifier time or else particular lexical items, such as frequency expressions, German beides ‘both’, or the nominalizing light noun -thing. The paper will not adopt or elaborate a particular version of the grammar-based view of countability, but rather critically discuss existing versions and present two semantic options of elaborating the view

Anaphor resolution and the scope of syntactic constraints

An anaphor resolution algorithm is presented which relies on a combination of strategies for narrowing down and selecting from antecedent sets for re exive pronouns, nonre exive pronouns, and common nouns. The work focuses on syntactic restrictions which are derived from Chomsky's Binding Theory. It is discussed how these constraints can be incorporated adequately in an anaphor resolution algorithm. Moreover, by showing that pragmatic inferences may be necessary, the limits of syntactic restrictions are elucidated

Resolving anaphoric references on deficient syntactic descriptions

Syntactic coindexing restrictions are by now known to be of central importance to practical anaphor resolution approaches. Since, in particular due to structural ambiguity, the assumption of the availability of a unique syntactic reading proves to be unrealistic, robust anaphor resolution relies on techniques to overcome this deficiency. In this paper, two approaches are presented which generalize the verification of coindexing constraints to de cient descriptions. At first, a partly heuristic method is described, which has been implemented. Secondly, a provable complete method is specified. It provides the means to exploit the results of anaphor resolution for a further structural disambiguation. By rendering possible a parallel processing model, this method exhibits, in a general sense, a higher degree of robustness. As a practically optimal solution, a combination of the two approaches is suggested

Sloppy Identity

Although sloppy interpretation is usually accounted for by theories of ellipsis, it often arises in non-elliptical contexts. In this paper, a theory of sloppy interpretation is provided which captures this fact. The underlying idea is that sloppy interpretation results from a semantic constraint on parallel structures and the theory is shown to predict sloppy readings for deaccented and paycheck sentences as well as relational-, event-, and one-anaphora. It is further shown to capture the interaction of sloppy/strict ambiguity with quantification and binding.Comment: 20 page