Data exchange, the problem of transferring data from a source schema to a target schema, has been studied for several years. The semantics of answering positive queries over the target schema has been defined in early work, but little attention has been paid to more general queries. A few proposals of semantics for more general queries exist but they either do not properly extend the standard semantics under positive queries, giving rise to counterintuitive answers, or they make query answering undecidable even for the most important data exchange settings, for example, with weakly-acyclic dependencies.

The goal of this paper is to provide a new semantics for data exchange that is able to deal with general queries. At the same time, we want our semantics to coincide with the classical one when focusing on positive queries, and to not trade-off too much in terms of complexity of query answering. We show that query answering is undecidable in general under the new semantics, but it is $\text{co}\text{NP}\text{-complete}$ when the dependencies are weakly-acyclic. Moreover, in the latter case, we show that exact answers under our semantics can be computed by means of logic programs with choice, thus exploiting existing efficient systems. For more efficient computations, we also show that our semantics allows for the construction of a representative target instance, similar in spirit to a universal solution, that can be exploited for computing approximate answers in polynomial time.

Recently there has been an increasing interest in frameworks extending Dung’s abstract Argumentation Framework (AF). Popular extensions include bipolar AFs and AFs with recursive attacks and necessary supports. Although the relationships between AF semantics and Partial Stable Models (PSMs) of logic programs has been deeply investigated, this is not the case for more general frameworks extending AF.

In this paper we explore the relationships between AF-based frameworks and PSMs. We show that every AF-based framework Δ can be translated into a logic program PΔ so that the extensions prescribed by different semantics of Δ coincide with subsets of the PSMs of PΔ. We provide a logic programming approach that characterizes, in an elegant and uniform way, the semantics of several AF-based frameworks. This result allows also to define the semantics for new AF-based frameworks, such as AFs with recursive attacks and recursive deductive supports.

It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modelling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their introduction is that the evaluation of a program might not terminate and checking whether it terminates or not is undecidable. To cope with this problem, several classes of logic programs have been proposed where the use of function symbols is restricted but the program evaluation termination is guaranteed. Despite the significant body of work in this area, current approaches do not include many simple practical programs whose evaluation terminates. In this paper, we present the novel classes of rule-bounded and cycle-bounded programs, which overcome different limitations of current approaches by performing a more global analysis of how terms are propagated from the body to the head of rules. Results on the correctness, the complexity, and the expressivity of the proposed approach are provided.

Recently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness of models and termination of the evaluation procedure, in the general case, are not guaranteed anymore. Since the program termination problem is undecidable in the general case, several decidable criteria (called program termination criteria) have been recently proposed. However, current conditions are not able to identify even simple programs, whose bottom-up execution always terminates. The paper introduces new decidable criteria for checking termination of logic programs with function symbols under bottom-up evaluation, by deeply analyzing the program structure. First, we analyze the propagation of complex terms among arguments by means of the extended version of the argument graph called propagation graph. The resulting criterion, called acyclicity, generalizes most of the decidable criteria proposed so far. Next, we study how rules may activate each other and define a more powerful criterion, called safety. This criterion uses the so-called safety function able to analyze how rules may activate each other and how the presence of some arguments in a rule limits its activation. We also study the application of the proposed criteria to bound queries and show that the safety criterion is well-suited to identify relevant classes of programs and bound queries. Finally, we propose a hierarchy of classes of terminating programs, called k-safety, where the k-safe class strictly includes the (k-1)-safe class.

Recent years have witnessed an increasing interest in enhancing answer set solvers by allowing function symbols. Since the introduction of function symbols makes common inference tasks undecidable, research has focused on identifying classes of programs allowing only a restricted use of function symbols while ensuring decidability of common inference tasks. Finitely-ground programs, introduced in Calimeri et al. (2008), are guaranteed to admit a finite number of stable models with each of them of finite size. Stable models of such programs can be computed and thus common inference tasks become decidable. Unfortunately, checking whether a program is finitely-ground is semi-decidable. This has led to several decidable criteria, called termination criteria, providing sufficient conditions for a program to be finitely-ground. This paper presents a new technique that, used in conjunction with current termination criteria, allows us to detect more programs as finitely-ground. Specifically, the proposed technique takes a logic program ${\cal P}$ and transforms it into an adorned program ${{\cal P}}$μ with the aim of applying termination criteria to ${{\cal P}}$μ rather than ${\cal P}$. The transformation is sound in that if the adorned program satisfies a certain termination criterion, then the original program is finitely-ground. Importantly, applying termination criteria to adorned programs rather than the original ones strictly enlarges the class of programs recognized as finitely-ground.

In recent analyses of numerical simulation and solar wind dataset, the idea that the magnetic discontinuities may be related to intermittent structures that appear spontaneously in MHD turbulence has been explored in details. These studies are consistent with the hypothesis that discontinuity events founds in the solar wind might be of local origin as well, i.e. a by-product of the turbulent evolution of magnetic fluctuations.

Using simulations of 2D MHD turbulence, we are exploring a possible link between tangential discontinuities and magnetic reconnection. The goal is to develop numerical algorithms that may be useful for solar wind applications.

This paper presents a logic language for expressing search and optimization problems. Specifically, first a language obtained by extending (positive) DATALOG with intuitive and efficient constructs (namely, stratified negation, constraints, and exclusive disjunction) is introduced. Next, a further restricted language only using a restricted form of disjunction to define (nondeterministically) subsets (or partitions) of relations is investigated. This language, called atalog, captures the power of DATALOG¬ in expressing search and optimization problems. A system prototype implementing atalog is presented. The system translates atalog queries into Optimization Programming Language (OPL) programs which are executed by the ILOG OPL Development Studio. Our proposal combines easy formulation of problems, expressed by means of a declarative logic language, with the efficiency of the ILOG System. Several experiments show the effectiveness of this approach.

This paper presents a technique for the optimization of bound queries over disjunctive deductive databases with constraints. The proposed approach is an extension of the well-known Magic-Set technique and is well-suited for being integrated in current bottom-up (stable) model inference engines. More specifically, it is based on the exploitation of binding propagation techniques which reduce the size of the data relevant to answer the query and, consequently, reduces both the complexity of computing a single model and the number of models to be considered. The motivation of this work stems from the observation that traditional binding propagation optimization techniques for bottom-up model generator systems, simulating the goal driven evaluation of top-down engines, are only suitable for positive (disjunctive) queries, while hard problems are expressed using unstratified negation. The main contribution of the paper consists in the extension of a previous technique, defined for positive disjunctive queries, to queries containing both disjunctive heads and constraints (a simple and expressive form of unstratified negation). As the usual way of expressing declaratively hard problems is based on the guess-and-check technique, where the guess part is expressed by means of disjunctive rules and the check part is expressed by means of constraints, the technique proposed here is highly relevant for the optimization of queries expressing hard problems. The value of the technique has been proved by several experiments.

In this paper, we propose a variant of stable model semantics for disjunctive logic programming and deductive databases. The semantics, called minimal founded, generalizes stable model semantics for normal (i.e. non-disjunctive) programs, but differs from disjunctive stable model semantics (the extension of stable model semantics for disjunctive programs). Compared with disjunctive stable model semantics, minimal founded semantics seems to be more intuitive, it gives meaning to programs which are meaningless under stable model semantics and is no harder to compute. More specifically, minimal founded semantics differs from stable model semantics only for disjunctive programs having constraint rules or rules working as constraints. We study the expressive power of the semantics, and show that for general disjunctive datalog programs it has the same power as disjunctive stable model semantics.

In the design of algorithms, the greedy paradigm provides a powerful tool for solving efficiently classical computational problems, within the framework of procedural languages. However, expressing these algorithms within the declarative framework of logic-based languages has proven a difficult research challenge. In this paper, we extend the framework of Datalog-like languages to obtain simple declarative formulations for such problems, and propose effective implementation techniques to ensure computational complexities comparable to those of procedural formulations. These advances are achieved through the use of the choice construct, extended with preference annotations to effect the selection of alternative stable-models and nondeterministic fixpoints. We show that, with suitable storage structures, the differential fixpoint computation of our programs matches the complexity of procedural algorithms in classical search and optimization problems.

In this paper we analyze declarative deterministic and non-deterministic semantics for active rules. In particular, we consider several (partial) stable model semantics, previously defined for deductive rules, such as well-founded, max deterministic, unique total stable model, total stable model and maximal stable model semantics. The semantics of an active program [Ascr ][Pscr ] is given by first rewriting it into a deductive program [Lscr ][Pscr ], then computing a model M defining the declarative semantics of [Lscr ][Pscr ] and, finally, applying ‘consistent’ updates contained in M to the source database. The framework we propose permits a natural integration of deductive and active rules and can also be applied to queries with function symbols or to queries over infinite databases.