Modulo Counting on Words and Trees

We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a technique for deciding the satisfiability problem. In the case of words this gives a new proof of EXPSPACE upper bound, and in the case of trees it gives a 2EXPTIME algorithm. This algorithm is optimal: we prove a matching lower bound by a generic reduction from alternating Turing machines working in exponential space; the reduction involves a development of a new version of tiling games

Logic and Automata

Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field

The flexible nature of verb movement

This study offers a new theory of verb movement parametrization. The author proposes to look upon verb movement as an operation that the verb undertakes in order to protect one or more of its features. It is no longer a movement to a prefabricated position but a structure-creating operation. Output conditions require that properties such as rich agreement and tense must be visible in a particular structural position. In this light, two conditions are formulated in order to capture the operations commonly known as V to I movement and V to C movement. Independently motivated properties of a particular language, however, can cause a condition to be satisfied without verb movement taking place. This explains the well-known observation that the position of the finite verb in a declarative clause is subject to significant cross-linguistic differences. In some languages, such as Dutch and German, the position of the finite verb is not the same as in main and imbedded clauses. An important consequence of the analysis is that languages differ in the amount of structure that they generate in over syntax. The cross-linguistic distribution of expletives offers strong support for this claim. The flexible nature of verb movement is of interest to any scholar studying word order variation and parameter theory. Since the theory is developed against the background of central issues and problems in modern theoretical linguistics, it should appeal to syntacticians in general

Aspects of morphosyntactic constraints on quantification in English and Polish

The topic of dissertation “Aspects of morphosyntactic constraints on quantification in English and Polish” is numerals and lexemes expressing quantity such as many, much, a few/little, several/a few functioning as modifiers in nominal phrases in English and Polish. The subject matter analyzed in the present work is syntax of nominal phrases containing quantifiers within a generative grammar, more specifically in the recent permutations of generative model as discussed by Chomsky (1995, 2001), and according to a novel approach to grammar, i.e. nanosyntax, as introduced by Starke (2009); Caha (2009, 2010 ) or Taraldsen (2009). The major aspect of this work is the structure of nominal phrases containing quantifiers as well as the mechanism of case distribution within a phrase based on the theory of movement together with the assumption that the smallest building block is not a morpheme, as it has been the case in various generative approaches, but a feature. What follows, elements in phrases occurring in positions to which structural cases, i.e. Nominative and Accusative, or oblique cases, i.e. and Genitive or Dative etc. are assigned, move to the position within a maximal projection of a given Case. The proposed model seems to provide tools to explain the homogenous and heterogeneous syntax of numerals, the intricate patterns of case marking of modifiers in a pre-numeral and pre-nominal position as well as signals new avenues to explore in the syntax of agreement with quantified subjects