In this thesis, the notion of the derivation spaces is introduced. In a suitable two-sorted language, the first order theory of these structures is studied. In particular, it is shown that the theory is not companionable. In the last section, the language is expanded by predicate symbols for a dependence relation. In this language it is shown that the extension of the corresponding theory has a model companion. It is shown that the model companion is a complete, unstable theory which does not eliminate quantifiers.

A difference field M , is a field with a distinguished endomorphism, is called a generic difference field if it is existentially closed among the models of the theory of difference fields. In the language Ld, by a theorem of Hrushovski, it is characterized by the following: M is an algebraically closed field, s is an automorphism of M, and if W and V are varieties defined over M such that W is a subset of VU s (V ) and the projection maps W to V and W to s(V ) are generically onto, then there is a tuple a in M such that (a, s ( a)) in W. This thesis is a survey on the theory of generic difference fields, called ACFA, which has been studied by Angus Macintyre, Van den Dries, Carol Wood, Ehud Hrushovski and Zoe Chatzidakis. ACFA is the model completion of the theory of algebraically closed difference fields. It is very close to having full quantifier elimination, but it doesn&#039 / t. We can eliminate quantifiers down to formulas with one quantifier and hence obtain the completions of ACFA. This entails the decidability of the theory ACFA as well as its extensions obtained by specifying the characteristic. The fixed field of s is a pseudo-finite field

As the Web Services proliferate and complicate it is becoming an overwhelming job to manually prepare the Web Service Compositions which describe the communication and integration between Web Services. This thesis analyzes the usage of Event Calculus, which is one of the logical action-effect definition languages, for the automated preparation and execution of Web Service Compositions. In this context, planning capabilities of Event Calculus are utilized. Translations from Planning Domain Description Language and DARPA Agent Markup Language to Event Calculus are provided to show that Web Services can be composed with the help of Event Calculus. Also comparisons between Event Calculus and other planning languages used for the same purposes are presented.

Answer set programming (ASP) is a declarative approach to solving search problems. Logic programming constitutes the foundation of ASP. ASP is not a proof-theoretical approach where you get solutions by answer substitutions. Instead, the problem is represented by a logic program in such a way that models of the program according to the answer set semantics correspond to solutions of the problem. Answer set solvers (Smodels, Cmodels, Clasp, and Dlv) are used for finding answer sets of a given program. Although users can write programs with variables for convenience, current answer set solvers work on ground logic programs where there are no variables. The grounding step of ASP generates a propositional instance of a logic program with variables. It may generate a huge propositional instance and make the search process of answer set solvers more difficult. Model generation theorem provers (Paradox, Darwin, and FM-Darwin) have the capability of producing a model when the first-order input theory is satisfiable. This work proposes the use of model generation theorem provers as computational engines for ASP. The main motivation is to eliminate the grounding step of ASP completely or to perform it more intelligently using the model generation system. Additionally, regardless of grounding, model generation systems may display better performance than the current solvers. The proposed method can be seen as lifting SAT-based ASP, where SAT solvers are used to compute answer sets, to the first-order level for tight programs. A completion procedure which transforms a logic program to formulas of first-order logic is utilized. Besides completion, other transformations which are necessary for forming a firstorder theory suitable for model generation theorem provers are investigated. A system called Completor is implemented for handling all the necessary transformations. The empirical results demonstrate that the use of Completor and the theorem provers together can be an eective way of computing answer sets. Especially, the run time results of Paradox in the experiments has showed that using Completor and Paradox together is favorable compared to answer set solvers. This advantage has been more clearly observed for programs with large propositional instances, since grounding can be a bottleneck for such programs.