Student Name: Amena Assem Abd-AlQader Mahmoud. Title of the Thesis: The Power of the Depth of Iteration in Defining Relations by Induction. Degree: M.Sc. (Pure Mathematics). In this thesis we study inductive definitions over finite structures, particularly, the depth of inductive definitions. We also study infinitary finite variable logic which contains fixed-point logic and we introduce a new ...

In this paper we present an algorithm to anchor floating quantifiers in Japanese, a language in which quantificational nouns and numeralclassifier combinations can appear separated from the noun phrase they quantify. The algorithm differentiates degree and event modifiers from nouns that quantify noun phrases. It then finds a suitable anchor for such floating quantifiers. To do this, the algori...

Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any LF -sentence φ containing only bounded quantifiers, and any positive rational number δ, decides either “φ is true”, or “a δ-strengthening of φ is false”’. Under mild assumptions, for a C-computable signature F , the δ-decision problem for bounded Σk-sentences in LF resides in (Σ...

We develop a translation-based view dual of modal logic as the study of intensional languages that are at the same time interesting expressive and decidable parts of standard logical systems. This tandem approach improves our understanding of modal logic – while at the same time, it extends the range of modal notions and techniques into broader areas of standard logic. 1 Translation as a Way of...

In this paper, I shall explore a determiner in natural language which is ambivalent as to whether it should be classified as quantificational or object-denoting: the determiner both. Both in many ways appears to be a paradigmatic quantifier; and yet, I shall argue, it can be interpreted as having an individual—an object—as semantic value. To show the significance of this, I shall discuss two wa...

We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets”. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order. Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over ...

The logic of quantified Boolean formulae (QBF) extends propositional logic with universal quantification over propositional variables. The presence of universal quantifiers in QBF does not add expressiveness, but often allows for more compact encodings of problems. From a theoretical point of view, the decision problems of propositional logic (SAT) and QBF are NP-complete and PSPACE-complete, r...

We show that the Cantor-Bendixon rank of limit groups is finite as well as that of limit groups of linear groups. Let T be an universal theory. In what follows this will be just the universal theory of some linear group. If T has at most countably many finitely generated models, then one can associate to each finitely generated model M of T an ordinal rank, denoted Rk(M), as defined in [2]. We ...