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.

Answer Set Programming Modulo Theories (ASPMT) is a new framework of tight integration of answer set programming (ASP) and satisfiability modulo theories (SMT). Similar to the relationship between first-order logic and SMT, it is based on a recent proposal of the functional stable model semantics by fixing interpretations of background theories. Analogously to a known relationship between ASP and SAT, "tight'' ASPMT programs can be translated into SMT instances. We demonstrate the usefulness of ASPMT by enhancing action language C+ to handle continuous changes as well as discrete changes. We reformulate the semantics of C+ in terms of ASPMT, and show that SMT solvers can be used to compute the language. We also show how the language can represent cumulative effects on continuous resources.

The action description languages B and C have significant common core. Nevertheless, some expressive possibilities of B are difficult or impossible to simulate in C, and the other way around. The main advantage of B is that it allows the user to give Prolog-style recursive definitions, which is important in applications. On the otherhand, B solves the frame problem by incorporating the commonsense law of inertia in its semantics, which makes it difficult to talk about fluents whose behavior is described by defaults other than inertia. In C and in its extension C+, the inertia assumption is expressed by axioms that the user is free to include or not to include, and other defaults can be postulated as well. This paper defines a new action description language, called BC, that combines the attractive features of B and C. Examples of formalizing commonsense domains discussed in the paper illustrate the expressive capabilities of BC and the use of answer set solvers for the automation of reasoning about actions described inthis language.

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.

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.

We study a logical system FQHT that is appropriate for reasoning about nonmonotonic theories with intensional functions as treated in the approach of Bartholomew and Lee (2012). We provide a logical semantics, a Gentzen style proof theory and establish completeness results. The adequacy of the approach is demonstrated by showing that it captures the Bartholemew/Lee semantics and satisfies a strong equivalence property.

We define the class of e-bounded theories in the epistemic situation calculus, where the number of fluent atoms that the agent thinks may be true is bounded by a constant. Such theories can still have an infinite domain and an infinite set of states. We show that for them verification of an expressive class of first-order mu-calculus temporal epistemic properties is decidable. We also show that if the agent’s knowledge in the initial situation is e-bounded and the objective part of an action theory maintains boundedness, then the entire epistemic theory is e-bounded.

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.

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.