A notion of quantified conditional logics is provided that includes quantification over individual and propositional variables. The former is supported with respect to constant and variable domain semantics. In addition, a sound and complete embedding of this framework in classical higher-order logic is presented. Using prominent examples from the literature it is demonstrated how this embedding enables effective automation of reasoning within (object-level) and about (meta-level) quantified conditional logics with off-the-shelf higher-order theorem provers and model finders.

Among the many approaches for reasoning about degrees of belief inthe presence of noisy sensing and acting, the logical accountproposed by Bacchus, Halpern, and Levesque is perhaps the most expressive.While their formalism is quite general, it is restricted to fluentswhose values are drawn from discrete countable domains, as opposed tothe continuous domains seen in many robotic applications. In thispaper, we show how this limitation in their approach can be lifted.By dealing seamlessly with both discrete distributions and continuousdensities within a rich theory of action, we provide a very generallogical specification of how belief should change after acting andsensing in complex noisy domains.

Recently there has been an increasing interest in incorporating "intensional" functions in answer set programming. Intensional functions are those whose values can be described by other functions and predicates, rather than being pre-defined as in the standard answer set programming. We demonstrate that the functional stable model semantics plays an important role in the framework of "Answer Set Programming Modulo Theories (ASPMT)" — a tight integration of answer set programming and satisfiability modulo theories, under which existing integration approaches can be viewed as special cases where the role of functions is limited. We show that "tight" ASPMT programs can be translated into SMT instances, which is similar to the known relationship between ASP and SAT.

While function symbols are widely acknowledged as an important feature in logic programming, they make common inference tasks undecidable. To cope with this problem, recent research has focused on identifying classes of logic programs imposing restrictions on the use of function symbols, but guaranteeing decidability of common inference tasks. This has led to several criteria, called termination criteria, providing sufficient conditions for a program to have finitely many stable models, each of finite size.This paper introduces the new class of bounded programs which guarantees the aforementioned property and strictly includes the classes of programs determined by current termination criteria. Different results on the correctness, the expressiveness, and the complexity of the class of bounded programs are presented.

Update semantics for Answer-Set Programming assign models to sequences of answer-set programs which result from the iterative process of updating programs by programs. Each program in the sequence represents an update of the preceding ones. One of the enduring problems in this context is state condensing, or the problem of determining a single logic program that faithfully represents the sequence of programs. Such logic program should 1) be written in the same alphabet, 2) have the same stable models, and 3) be equivalent to the sequence of programs when subject to further updates. It has been known for more than a decade that update semantics easily lead to non-minimal stable models, so an update sequence cannot be represented by a single non-disjunctive program. On the other hand, more expressive classes of programs were never considered, mainly because it was not clear how they could be updated further. In this paper we solve the state condensing problem for two foundational rule update semantics, using nested logic programs. Furthermore, we also show that disjunctive programs with default negation in the head can be used for the same purpose.

In dynamic systems, state constraints are formulas that hold in every reachable state. It has been shown that state constraints can be used to greatly reduce the planning search space. They are also useful in program verification. In this paper, we propose a sound but incomplete method for automatic verification and discovery of state constraints for a class of action theories that include many planning benchmarks. Our method is formulated in the situation calculus, theoretically based on Skolemization and Herbrand Theorem, and implemented with SAT solvers. Basically, we verify a state constraint by strengthening it in a novel and smart way so that it becomes a state invariant. We experimented with the blocks world, logistics and satellite domains, and the results showed that, almost all known state constraints can be verified in a reasonable amount of time, and meanwhile succinct and intuitive related state constraints are discovered.

Since it is a relatively new concept, little is known about the computational complexity of fuzzy answer set programming (FASP) and almost no techniques are available to compute answer sets of FASP programs. Furthermore, the connections of FASP to other paradigms of nonmonotonic reasoning with continuous values are largely unexplored. In our disertation, we contribute to the ongoing research on FASP on two different levels: complexity and connections to fuzzy modal logics.

Wastl introduced for first time a tableaux-like method based on an inference system for deriving all minimal keys from a relational schema. He introduced two inference rules and built an automated method over them.In this work we tackle the key finding problem with a tableaux method, but we will use two inference rules inspired by the Simplification Logic for Functional Dependencies. Wastl's method requires the input to be a set of functional dependencies with atomic right hand sides. Therefore, it is necessary to apply fragmentation rule with the consequent increasing of the input.The main novelty of our rules is that they deal with generalized formulas, avoiding the fragmentation needed in the former tableaux. Finally we illustrate the advantages of our new tableaux method with an experiment.

Artifact-Centric Systems are a novel paradigm in service-oriented computing. In the present contribution we show that model checking bounded, non-uniform artifact-centric systems is undecidable. We provide a partial model checking procedure for artifact-centric systems against the universal fragment of a first-order version of the logic CTL. We obtain this result by introducing a counterpart semantics and developing an abstraction methodology operating on these structures. This enables us to generate finite abstractions of infinite artifact-centric systems, hence perform verification on abstract models.

We introduce a new approach to disjunctive ASP solving that aims at an equitable interplay between "generating" and "testing" solver units. To this end, we develop novel characterizations of answer sets and unfounded sets allowing for a bidirectional dynamic information exchange between solver units for orthogonal tasks. This results in the new multi-threaded disjunctive ASP solver claspD-2, greatly improving the performance of existing systems.