Set Of Stable Models Research Articles

Splitting Epistemic Logic Programs

AbstractEpistemic logic programs constitute an extension of the stable model semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some objective literal is true in all or some stable models. As it can be imagined, the associated semantics has proved to be non-trivial, since the truth of subjective literals may interfere with the set of stable models it is supposed to query. As a consequence, no clear agreement has been reached and different semantic proposals have been made in the literature. Unfortunately, comparison among these proposals has been limited to a study of their effect on individual examples, rather than identifying general properties to be checked. In this paper, we propose an extension of the well-known splitting property for logic programs to the epistemic case. We formally define when an arbitrary semantics satisfies the epistemic splitting property and examine some of the consequences that can be derived from that, including its relation to conformant planning and to epistemic constraints. Interestingly, we prove (through counterexamples) that most of the existing approaches fail to fulfill the epistemic splitting property, except the original semantics proposed by Gelfond 1991 and a recent proposal by the authors, called Founded Autoepistemic Equilibrium Logic.

Identification of Models of Geomagnetic Activity and Space Weather Prediction

The problem of prediction of geomagnetic activity by the example of the method of Dst-index is considered. For its solving we suggested to use a nonlinear discrete dynamical system, which is obtained by decomposition of perturbations into series relative to correlation functions. Identification of structure and model parameters is defined by solving the corresponding problems of mathematical programming on bounded, but large enough set of stable models. On identification of model structure we took into account the assumption that model describes the state of magnetic-spherical-plasma medium, which is to great extent caused by influence of velocities of solar wind and south magnetic component of interplanetary magnetic field. The principal result of the work consists in numerical substantiation of existence of common stable model of minimal complexity, which provides the best prediction.

Locally Determined Logic Programs and Recursive Stable Models

In general, the set of stable models of a recursive logic program can be quite complex. For example, it follows from results of Marek, Nerode, and Remmel [Ann. Pure and Appl. Logic (1992)] that there exists finite predicate logic programs and recursive propositional logic programs which have stable models but no hyperarithmetic stable models. In this paper, we shall define several conditions which ensure that recursive logic program P has a stable model which is of low complexity, e.g., a recursive stable model, a polynomial time stable model, or a stable model which lies in a low level of the polynomial time hierarchy.