On FO2 quantifier alternation over words

We show that each level of the quantifier alternation hierarchy within FO^2[<] -- the 2-variable fragment of the first order logic of order on words -- is a variety of languages. We then use the notion of condensed rankers, a refinement of the rankers defined by Weis and Immerman, to produce a decidable hierarchy of varieties which is interwoven with the quantifier alternation hierarchy -- and conjecturally equal to it. It follows that the latter hierarchy is decidable within one unit: given a formula alpha in FO^2[<], one can effectively compute an integer m such that alpha is equivalent to a formula with at most m+1 alternating blocks of quantifiers, but not to a formula with only m-1 blocks. This is a much more precise result than what is known about the quantifier alternation hierarchy within FO[<], where no decidability result is known beyond the very first levels

Can Quantum Lattice Fluctuations Destroy the Peierls Broken Symmetry Ground State?

The study of bond alternation in one-dimensional electronic systems has had a long history. Theoretical work in the 1930s predicted the absence of bond alternation in the limit of infinitely long conjugated polymers; a result later contradicted by experimental investigations. When this issue was re-examined in the 1950s it was shown in the adiabatic limit that bond alternation occurs for any value of electron-phonon coupling. The question of whether this conclusion remains valid for quantized nuclear degrees of freedom was first addressed in the 1980s. Since then a series of numerical calculations on models with gapped, dispersionless phonons have suggested that bond alternation is destroyed by quantum fluctuations below a critical value of electron-phonon coupling. In this work we study a more realistic model with gapless, dispersive phonons. By solving this model with the DMRG method we show that bond alternation remains robust for any value of electron-phonon coupling

The \mu-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity

It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite words over which the alternation-free fragment is already as expressive as the full mu-calculus. Our current understanding of when and why the mu-calculus alternation hierarchy is not strict is limited. This paper makes progress in answering these questions by showing that the alternation hierarchy of the mu-calculus collapses to the alternation-free fragment over some classes of structures, including infinite nested words and finite graphs with feedback vertex sets of a bounded size. Common to these classes is that the connectivity between the components in a structure from such a class is restricted in the sense that the removal of certain vertices from the structure's graph decomposes it into graphs in which all paths are of finite length. Our collapse results are obtained in an automata-theoretic setting. They subsume, generalize, and strengthen several prior results on the expressivity of the mu-calculus over restricted classes of structures.Comment: In Proceedings GandALF 2012, arXiv:1210.202

The properties of anticausatives crosslinguistically

The causative/anticausative alternation has been the topic of much typological and theoretical discussion in the linguistic literature. This alternation is characterized by verbs with transitive and intransitive uses, such that the transitive use of a verb V means roughly "cause to Vintransitive" (see Levin 1993). The discussion revolves around two issues: the first one concerns the similarities and differences between the anticausative and the passive, and the second one concerns the derivational relationship, if any, between the transitive and intransitive variant. With respect to the second issue, a number of approaches have been developed. Judging the approach conceptually unsatisfactory, according to which each variant is assigned an independent lexical entry, it was concluded that the two variants have to be derivationally related. The question then is which one of the two is basic and where this derivation takes place in the grammar. Our contribution to this discussion is to argue against derivational approaches to the causative / anticausative alternation. We focus on the distribution of PPs related to external arguments (agent, causer, instrument, causing event) in passives and anticausatives of English, German and Greek and the set of verbs undergoing the causative/anticausative alternation in these languages. We argue that the crosslinguistic differences in these two domains provide evidence against both causativization and detransitivization analyses of the causative / anticausative alternation. We offer an approach to this alternation which builds on a syntactic decomposition of change of state verbs into a Voice and a CAUS component. Crosslinguistic variation in passives and anticausatives depends on properties of Voice and its combinations with CAUS and various types of roots

Dative alternation in Indian English: a corpus-based study

The dative alternation refers to the alternation between two constructions that denote some type of transfer: the double object construction (I give my sister a book) vs. the to-dative construction (I give a book to my sister). We examined the motivations behind the dative alternation in Indian English. A corpus study was performed based on a sample of N = 943 sentences that were drawn from the Kolhapur corpus. Using a mixed-effects logistic regression analysis, we evaluated the effect of 14 predictors that are known to influence the dative alternation in other macro-regional varieties of English. Three predictors were found to be significant: the verb (modeled as a random intercept), the pronominality of the Recipient and the difference in length between the Recipient and the Theme. Our results further corroborate earlier findings that the to-dative construction is more frequently used in Indian English than in other varieties. We argue that the latter tendency may be associated with a transfer from Hindi