On negation in yes/no questions in Serbo-Croatian

The phenomenon discussed in this paper is the so-called expletive negation in negated yes/no questions in Serbo-Croatian. The term expletive negation seems, at this point to be a useful descriptive term for the phenomenon in question. One of the goals of this paper, however, is to show that it is not the correct one. Proposing the existence of semantically vacuous negation is the consequence of the assumption that sentential negation has a fixed position in the clausal hierarchy (Brown and Franks 1995). This approach cannot account for the relevant data in Serbo-Croatian. My claim is that the cases under consideration involve an alternative position of NegP in Serbo-Croatian, above TP. It is confined to the derivation of one semantic type of negated yes/no interrogatives, and it cannot trigger negative concord

When negation is not negation

In this paper I will discuss the formation of different types of yes/no questions in Serbian (examples in (1)), focusing on the syntactically and semantically puzzling example (1d), which involves the negative auxiliary inversion. Although there is a negative marker on the fronted auxiliary, the construction does not involve sentential negation. This coincides with the fact that the negative quantifying NPIs cannot be licensed. The question formation and sentential negation have similar syntactic effects cross-linguistically. This has led to various attempts to formulate a unifying syntactic account of the phenomena (ever since Klima 1964). One striking fact about the two syntactic contexts is that both license weak NPIs (Negative Polarity Items). It has been suggested (cf. Laka 1990, Culicover 1991) that the derivation of both interrogatives and negatives involves the same type of functional projection PolP (polarity phrase). One such account of the formation of negative interrogatives in Serbo- Croatian is offered by Progovac (2005). She proposes that there are two PolPs optionally cooccurring in the same clause, in which both positive and negative polarity items check their positive or negative features (following Haegeman and Zanuttini (1991) feature-checking account of negative structures, and the insights of Brown(1999) on the negation in Russian). On her account, the negative auxiliary question in (1d), is the case when both polarity phrases are present. The higher has [-pos +neg] features, and the lower one (below TP) is [-pos -neg]. Although her account correctly predicts the ungrammaticality of (2a) in contrast with (1c), it wrongly predicts the (2b) to be grammatical. I will argue that Progovac’s theory regarding the nature of the PolP is wrong. It employs both the binary feature valuation on the polarity head and the hierarchical ordering of the two polarity phrases, which eventually leads to overgeneration. On the account presented here the nature of the question marker (li vs zar) is highly relevant. Notice that (1b) and (1d) express presuppositions regarding the truth value of the propositions. In this way they contrast with (1a) and (1c). In addition, the type (1b) (with the question particle zar) can introduce both the positive and negative presupposition as shown in (3), which, semantically, makes this construction compatible with negative auxiliary questions in English (4a). The polarity items licensed in the relevant structures are also of the same type in both languages. The fronted-negative-auxiliary questions (1d) in Serbian are only possible with the particle li. In this case the presupposition is exclusively positive. The peculiar question/focus marking function of li (in Bulgarian and Russian) is well known. However, it is always assumed that its focus marking role is not relevant for the formation of yes/no questions. This I believe is not correct. The syntactic explanation of the interpretational facts points to the following: A) The possibility of the separate lexical encoding (particle zar) of the ‘rhetorical’ yes/no questions in Serbian allows the embedding of both positive and negated sentences, in which case the (weak) NPIs can remain in local relation with the negated verb. B) Recall that Serbian is an NC language, which requires local/c-command relation between the verbal negative marker and the NPI. With the negative inverted auxiliary questions this condition is not met, and the licensing of an n-word is not possible. C) The impossibility of licensing a weak NPI (i-words in the examples below) is due to the nature of the question marker li. (1) a. Da li je Vera videla ikoga / nekoga / *nikoga? DA Q aux Vera see.part.F.Sg anyone someone noone “Did Vera see anyone/someone/noone?” b. Zar je Vera videla ikoga / nekoga / *nikoga? ZAR aux Vera see.part.F.Sg anyone someone noone “Is it really the fact that Vera saw anyone/someone?” c. Je li Vera videla ikoga / nekoga /*nikoga? aux Q Vera see.part.F.Sg anyone someone noone “Did Vera see anyone/someone/noone?” d. Nije li Vera videla *ikoga / nekoga / *nikoga? neg+aux Q Vera see.part.F.Sg anyone someone noone “Didn’t Vera see someone?”/ “Vera saw someone, didn’t she?” (2) a. *Nije li Vera videla nikoga? neg+aux Q Vera see.part.F.Sg noone b. *Nije li Vera videla ikoga? neg+aux Q Vera see.part.F.Sg anyone (3) a. Zar je Vera videla nekoga / ikoga? ZAR aux Vera see.part.F.Sg someone/anyone b. Zar Vera nije videla nekoga/nikoga? ZAR Vera neg+aux see.part.F.Sg someone/anyone (4) a. Didn’t Vera (NOT) see someone/anyone? b. Vera saw someone, didn’t she

Homological Algebra for Persistence Modules

We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module and sheaf tensor product and Hom bifunctors as well as their derived functors, Tor and Ext, and give explicit computations for interval modules. We give a classification of injective, projective, and flat interval modules. We state Kunneth theorems and universal coefficient theorems for the homology and cohomology of chain complexes of persistence modules in both the sheaf and graded modules settings and show how these theorems can be applied to persistence modules arising from filtered cell complexes. We also give a Gabriel-Popescu theorem for persistence modules. Finally, we examine categories enriched over persistence modules. We show that the graded module point of view produces a closed symmetric monoidal category that is enriched over itself.Comment: 41 pages, accepted by Foundations of Computational Mathematic

The syntax of existential sentences in Serbian

Freeze (1992) argued on the basis of data from several different languages that there is a close relationship between existential sentences (stating the existence of an entity) and locative sentences (stating the location of an entity). Freeze (1992) proposes that they are both derived from the same base structure and that the surface differences are rather due to the distinct information structures.This paper argues against this position with the data from Serbian existentials, which show clear syntactic differences from the locatives. Thus, the close relationship between existential and locative sentences that Freeze (1992) observes is conceptual, but not (necessarily) part of the syntax of the language. In order to account for the data, we propose that existential sentences originate from a different syntactic predication structure than the locative ones. The existential meaning arises, as we will show, from the interaction of this predication structure with the structure and meaning of the noun phrase