Abduction in Well-Founded Semantics and Generalized Stable Models

Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that provides a level of declarativity superior to that of Prolog, and which has supported successful applications in fields such as parsing, program analysis, and model checking. In this paper we show how to use tabled logic programming to evaluate queries to abductive frameworks with integrity constraints when these frameworks contain both default and explicit negation. The result is the ability to compute abduction over well-founded semantics with explicit negation and answer sets. Our approach consists of a transformation and an evaluation method. The transformation adjoins to each objective literal $O$ in a program, an objective literal $not(O)$ along with rules that ensure that $not(O)$ will be true if and only if $O$ is false. We call the resulting program a {\em dual} program. The evaluation method, \wfsmeth, then operates on the dual program. \wfsmeth{} is sound and complete for evaluating queries to abductive frameworks whose entailment method is based on either the well-founded semantics with explicit negation, or on answer sets. Further, \wfsmeth{} is asymptotically as efficient as any known method for either class of problems. In addition, when abduction is not desired, \wfsmeth{} operating on a dual program provides a novel tabling method for evaluating queries to ground extended programs whose complexity and termination properties are similar to those of the best tabling methods for the well-founded semantics. A publicly available meta-interpreter has been developed for \wfsmeth{} using the XSB system.Comment: 48 pages; To appear in Theory and Practice in Logic Programmin

Analysis of the causes of price fluctuations of dairy products at individual levels of the product vertical

The paper analyzes the reasons for the prices of milk and milk products in the Czech Republic for the period 2008 – 2009. In January 2008, the purchase price of raw milk was 10.08 CZK/l, and in the subsequent period it began to decline. At the end of 2008, the price was more than 3 crowns lower, and still the decrease continued. The research determined that the essential reason for the price fluctuations is the impact of the economic crisis. A substantial portion of the article was devoted to analyzing the behavior of supermarket chains toward their suppliers. It was discovered that even here there is a lot of room for the creation of pricing policy. Margin trading networks up to 25% of the delivered goods. Price negotiations affect the position papers in the manufacturing vertical. The power of suppliers and processors is based on the establishment of a strong integration unit. In the conclusion the author discusses possible future developments in price, sales policy, and the self-sufficiency of milk production in the Czech Republic. The paper was processed within the framework of the Research Project of MSM 6046070906 "The economics of Czech agricultural resources and their effective use within the framework of multifunctional agri-food systems".Milk, price depression, price scissors, chain store, retail revenues from food, self-sufficiency., Food Consumption/Nutrition/Food Safety, Production Economics, GA, IN,

Demonstration of a robust pseudogap in a three-dimensional correlated electronic system

We outline a partial-fractions decomposition method for determining the one-particle spectral function and single-particle density of states of a correlated electronic system on a finite lattice in the non self-consistent T-matrix approximation to arbitrary numerical accuracy, and demonstrate the application of these ideas to the attractive Hubbard model. We then demonstrate the effectiveness of a finite-size scaling ansatz which allows for the extraction of quantities of interest in the thermodynamic limit from this method. In this approximation, in one or two dimensions, for any finite lattice or in the thermodynamic limit, a pseudogap is present and its energy diverges as Tc is approached from above; this is an unphysical manifestation of using an approximation that predicts a spurious phase transition in one or two dimensions. However, in three dimensions one expects the transition predicted by this approximation to represent a true continuous phase transition, and in the thermodynamic limit any pseudogap predicted by this formulation will remain finite. We have applied our method to the attractive Hubbard model on a three-dimensional simple cubic lattice, and find that for intermediate coupling a prominent pseudogap is found in the single-particle density of states, and this gap persists over a large temperature range. In addition, we also show that for weak coupling a pseudogap is also present. The pseudogap energy at the transition temperature is almost a factor of three larger than the T=0 BCS gap for intermediate coupling, whereas for weak coupling the pseudogap and BCS gap energies are essentially equal.Comment: 28 pages, 9 figure

Commonsense axiomatizations for logic programs

AbstractVarious semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second-order formulas. The semantics of Clark, Fitting, and Kunen are characterized in this framework, and a finite first-order presentation of Kunen's semantics is described. A new axiom to represent “commonsense” reasoning is proposed for logic programs. It is shown that the well-founded semantics and stable models are definable with this axiom. The roles of domain augmentation and domain closure are examined. A “domain foundation” axiom is proposed to replace the domain closure axiom

A NEW APPROACH TO NEUTRAL MONISM AND THE MIND-MATTER CONTROVERSY.

Neutral monism claims that both mind and matter are categories derived froma single underlying realit y that is univocally identified with none of them. In this paper atheoretical outline is presented from the neutral-monism perspective on the different configurations of reality referred to as “mind” and “matter”, while also discussing its consequences and the approaches it could give raise

An Overview of Schema Theory

The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a mathematician, to point out some related open problems, and to suggest some large-scale projects. Schema theory seeks to give a theoretical justification for the efficacy of the field of genetic algorithms, so readers who have studied genetic algorithms stand to gain the most from this paper. However, nothing beyond basic probability theory is assumed of the reader, and for this reason we write in a fairly informal style. Because the mathematics behind the theorems in schema theory is relatively elementary, we focus more on the motivation and philosophy. Many of these results have been proven elsewhere, so this paper is designed to serve a primarily expository role. We attempt to cast known results in a new light, which makes the suggested future directions natural. This involves devoting a substantial amount of time to the history of the field. We hope that this exposition will entice some mathematicians to do research in this area, that it will serve as a road map for researchers new to the field, and that it will help explain how schema theory developed. Furthermore, we hope that the results collected in this document will serve as a useful reference. Finally, as far as the author knows, the questions raised in the final section are new.Comment: 27 pages. Originally written in 2009 and hosted on my website, I've decided to put it on the arXiv as a more permanent home. The paper is primarily expository, so I don't really know where to submit it, but perhaps one day I will find an appropriate journa

A Yabloesque paradox in epistemic game theory

The Brandenburger–Keisler paradox is a self-referential paradox in epistemic game theory which can be viewed as a two-person version of Russell’s Paradox. Yablo’s Paradox, according to its author, is a non-self referential paradox, which created a significant impact. This paper gives a Yabloesque, non-self-referential paradox for infinitary players within the context of epistemic game theory. The new paradox advances both the Brandenburger–Keisler and Yablo results. Additionally, the paper constructs a paraconsistent model satisfying the paradoxical statement

Economy, Technology and the Environment: The Islamic Middle Way

Dr. Ahmad considers some specifics of the ways in which the Qur\'an, the Prophetic traditions and Islamic law lead toward a path of moderation between extremes, in terms of both belief and behavior: in favor of free markets, but with property rights clearly defined to prevent fraud and unfairness; in favor of technology, but not materialism; and with a concept of trusteeship of the environment that accommodates both development and stewardship