On the Termination of Logic Programs with Function Symbols

Recently there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The main problem due to the presence of functional symbols in the head of rules is that the corresponding ground program could be infinite and that finiteness of models and termination of the evaluation procedure is not guaranteed. This paper introduces, by deeply analyzing program structure, new decidable criteria, called safety and Gamma-acyclicity, for checking termination of logic programs with function symbols under bottom-up evaluation. These criteria guarantee that stable models are finite and computable, as it is possible to generate a finitely ground program equivalent to the source program. We compare new criteria with other decidable criteria known in the literature and show that the Gamma-acyclicity criterion is the most general one. We also discuss its application in answering bound queries

Detecting Decidable Classes of Finitely Ground Logic Programs with Function Symbols

In this article, we propose a new technique for checking whether the bottom-up evaluation of logic programs with function symbols terminates. The technique is based on the definition of mappings from arguments to strings of function symbols, representing possible values which could be taken by arguments during the bottom-up evaluation. Starting from mappings, we identify mapping-restricted arguments, a subset of limited arguments, namely arguments that take values from finite domains. Mapping-restricted programs, consisting of rules whose arguments are all mapping restricted, are terminating under the bottom-up computation, as all of its arguments take values from finite domains. We show that mappings can be computed by transforming the original program into a unary logic program: this allows us to establish decidability of checking if a program is mapping restricted. We study the complexity of the presented approach and compare it to other techniques known in the literature. We also introduce an extension of the proposed approach that is able to recognize a wider class of logic programs. The presented technique provides a significant improvement, as it can detect terminating programs not identified by other criteria proposed so far. Furthermore, it can be combined with other techniques to further enlarge the class of programs recognized as terminating under the bottom-up evaluation. </jats:p

Statistical properties of solar wind discontinuities, intermittent turbulence, and rapid emergence of non-Gaussian distributions

Recent studies have compared properties of the magnetic field in simulations of Hall MHD turbulence with spacecraft data, focusing on methods used to identify classical discontinuities and intermittency statistics. Comparison of ACE solar wind data and simulations of 2D and 3D turbulence shows good agreement in waiting‐time analysis of magnetic discontinuities, and in the related distribution of magnetic field increments. This supports the idea that the magnetic structures in the solar wind may emerge fast and locally from nonlinear dynamics that can be understood in the framework of nonlinear MHD theory. The analysis suggests that small scale current sheets form spontaneously and rapidly enough that some of the observed solar wind discontinuities may be locally generated, representing boundaries between interacting flux tubes