Superposition modulo theory

This thesis is about the Hierarchic Superposition calculus SUP(T) and its application to reasoning in hierarchic combinations FOL(T) of the free first-order logic FOL with a background theory T where the hierarchic calculus is refutationally complete or serves as a decision procedure. Particular hierarchic combinations covered in the thesis are the combinations of FOL and linear and non-linear arithmetic, LA and NLA resp. Recent progress in automated reasoning has greatly encouraged numerous applications in soft- and hardware verification and the analysis of complex systems. The applications typically require to determine the validity/unsatisfiability of quantified formulae over the combination of the free first-order logic with some background theories. The hierarchic superposition leverages both (i) the reasoning in FOL equational clauses with universally quantified variables, like the standard superposition does, and (ii) powerful reasoning techniques in such theories as, e.g., arithmetic, which are usually not (finitely) axiomatizable by FOL formulae, like modern SMT solvers do. The thesis significantly extends previous results on SUP(T), particularly: we introduce new substantially more effective sufficient completeness and hierarchic redundancy criteria turning SUP(T) to a complete or a decision procedure for various FOL(T) fragments; instantiate and refine SUP(T) to effectively support particular combinations of FOL with the LA and NLA theories enabling a fully automatic mechanism of reasoning about systems formalized in FOL(LA) or FOL(NLA).Diese Arbeit befasst sich mit dem hierarchischen Superpositionskalkül SUP(T) und seiner Anwendung auf hierarchischen Kombinationen FOL(T) der freien Logik erste Stufe FOL und einer Hintergrundtheorie T, deren hierarchischer Kalkül widerlegungsvollständig ist oder als Entscheidungsverfahren dient. Die behandelten hierarchischen Kombinationen sind im Besonderen die Kombinationen von FOL und linearer und nichtlinearer Arithmetik, LA bzw. NLA. Die jüngsten Fortschritte in dem Bereich des automatisierten Beweisens haben zahlreiche Anwendungen in der Soft- und Hardwareverifikation und der Analyse komplexer Systeme hervorgebracht. Die Anwendungen erfordern typischerweise die Gültigkeit/Unerfüllbarkeit quantifizierter Formeln über Kombinationen der freien Logik erste Stufe mit Hintergrundtheorien zu bestimmen. Die hierarchische Superposition verbindet beides: (i) das Beweisen über FOL-Klauseln mit Gleichheit und allquantifizierten Variablen, wie in der Standardsuperposition, und (ii) mächtige Beweistechniken in Theorien, die üblicherweise nicht (endlich) axiomatisierbar durch FOL-Formeln sind (z. B. Arithmetik), wie in modernen SMT-Solvern. Diese Arbeit erweitert frühere Ergebnisse über SUP(T) signifikant, im Besonderen führen wir substantiell effektiverer Kriterien zur Bestimmung der hinreichenden Vollständigkeit und der hierarchischen Redundanz ein. Mit diesen Kriterien wird SUP(T) widerlegungsvollständig beziehungsweise ein Entscheidungsverfahren für verschiedene FOL(T)-Fragmente. Weiterhin instantiieren und verfeinern wir SUP(T), um effektiv die Kombinationen von FOL mit der LA- und der NLA-Theorie zu unterstützen, und erhalten eine vollautomatische Beweisprozedur auf Systemen, die in FOL(LA) oder FOL(NLA) formalisiert werden können

Clause union and verb raising phenomena in German

In this paper we discuss a class of constructions in German syntax which have been known as coherent infinitive, clause union or verb raising constructions. These data run against the predictions of strictly configurational theories by apparently having a syntactic structure where the subcategorization frames of two or more verbal heads are merged into one. Thus, in addition to a fully bi-clausal structure with two clearly separated verbal heads, we also have to envisage the case where a verb is apparently raised from an embedded to form a verb cluster together with its governing verb, while the sets of their arguments are merged into a single set, representing the case of clause union. In addition, there are constructions where there is no evidence for clause union, but where one could nevertheless argue for the formation of a verb cluster. We investigate these data by looking at a series of constructions which bear evidence on the issue. Among these are extraposition, which appears a reliable test for nonobligatory verb raising; subjectless constructions, which are possible only as the complements of so-called raising verbs but not of control verbs; S-pronominalization, which seems to be limited to equi-verbs; scrambling and long reflexivization, which we can take as evidence for clause union; the scope of adjuncts and negation which argues in favour of verb raising, but does not necessarily presuppose clause union; and finally certain topicalization phenomena which appear to violate almost any of the generalizations set up so far by configurational theories

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Proceedings of the workshop on Syntax of Predication, Nov 2-3, 2001, ZAS-Berlin / Edited by Niina Zhang

This volume presents working versions of presentations heard at and selected for the Workshop on Syntax of Predication, held at ZAS, Berlin, on November 2-3, 2001 (except the editor’s own paper). Predication is a many-faceted topic which involves both syntax and semantics and the interface between them. This is reflected in the papers of the volume

Cappadocian kinship

Cappadocian kinship systems are very interesting from a sociolinguistic and anthropological perspective because of the mixture of inherited Greek and borrowed Turkish kinship terms. Precisely because the number of Turkish kinship terms differs from one variety to another, it is necessary to talk about Cappadocian kinship systems in the plural rather than about the Cappadocian kinship system in the singular. Although reference will be made to other Cappadocian varieties, this paper will focus on the kinship systems of Mišotika and Aksenitika, the two Central Cappadocian dialects still spoken today in several communities in Greece. Particular attention will be given to the use of borrowed Turkish kinship terms, which sometimes seem to co-exist together with their inherited Greek counterparts, e.g. mána vs. néne ‘mother’, ailfó/aelfó vs. γardáš ‘brother’ etc. In the final part of the paper some kinship terms with obscure or hitherto unknown etymology will be discussed, e.g. káka ‘grandmother’, ižá ‘aunt’, lúva ‘uncle (father’s brother)’ etc