Loop Formulas for Description Logic Programs

Description Logic Programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the {\em canonical answer set semantics}, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored.Comment: 29 pages, 1 figures (in pdf), a short version appeared in ICLP'1

General one-loop formulas for decay h→Zγh\rightarrow Z\gamma

Radiative corrections to the $h\rightarrow Z\gamma$ are evaluated in the one-loop approximation. The unitary gauge gauge is used. The analytic result is expressed in terms of the Passarino-Veltman functions. The calculations are applicable for the Standard Model as well for a wide class of its gauge extensions. In particular, the decay width of a charged Higgs boson $H^\pm \rightarrow W^\pm\gamma$ can be derived. The consistence of our formulas and several specific earlier results is shown.Comment: 33 pages, 3 figures, a new section (V) and references were improved in the published versio

On Loop Formulas with Variables

Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary first-order sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop formulas to disjunctive programs and to arbitrary first-order sentences. We also extend the syntax of logic programs to allow explicit quantifiers, and define its semantics as a subclass of the new language of stable models by Ferraris et al. Such programs inherit from the general language the ability to handle nonmonotonic reasoning under the stable model semantics even in the absence of the unique name and the domain closure assumptions, while yielding more succinct loop formulas than the general language due to the restricted syntax. We also show certain syntactic conditions under which query answering for an extended program can be reduced to entailment checking in first-order logic, providing a way to apply first-order theorem provers to reasoning about non-Herbrand stable models.Comment: 10 pages. In Proc. Eleventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), pages 444-453. arXiv admin note: text overlap with arXiv:1401.389

New Formulas and Predictions for Running Masses at Higher Scales in MSSM

Including contributions of scale-dependent vacuum expectation values of Higgs scalars, we derive new one-loop formulas analytically for running quark-lepton masses at higher scales in MSSM. Apart from the gauge-coupling dependence being different from earlier formulas, the third-generation- Yukawa-coupling effects are absent in the masses of the first two generations. While predicting the masses and $\tan\beta$ numerically, we also include two-loop effects.Comment: 9 pages Latex.Typos correcte

Computing Loops With at Most One External Support Rule

If a loop has no external support rules, then its loop formula is equivalent to a set of unit clauses; and if it has exactly one external support rule, then its loop formula is equivalent to a set of binary clauses. In this paper, we consider how to compute these loops and their loop formulas in a normal logic program, and use them to derive consequences of a logic program. We show that an iterative procedure based on unit propagation, the program completion and the loop formulas of loops with no external support rules can compute the same consequences as the “Expand ” operator in smodels, which is known to compute the well-founded model when the given normal logic program has no constraints. We also show that using the loop formulas of loops with at most one external support rule, the same procedure can compute more consequences, and these extra consequences can help ASP solvers such as cmodels to find answer sets of certain logic programs

Many-body effects in graphene beyond the Dirac model with Coulomb interaction

This paper is devoted to development of perturbation theory for studying the properties of graphene sheet of finite size, at nonzero temperature and chemical potential. The perturbation theory is based on the tight-binding Hamiltonian and arbitrary interaction potential between electrons, which is considered as a perturbation. One-loop corrections to the electron propagator and to the interaction potential at nonzero temperature and chemical potential are calculated. One-loop formulas for the energy spectrum of electrons in graphene, for the renormalized Fermi velocity and also for the dielectric permittivity are derived.Comment: 11 pages, 11 figure

Six and seven loop Konishi from Luscher corrections

In the present paper we derive six and seven loop formulas for the anomalous dimension of the Konishi operator in N=4 SYM from string theory using the technique of Luscher corrections. We derive analytically the integrand using the worldsheet S-matrix and evaluate the resulting integral and infinite sum using a combination of high precision numerical integration and asymptotic expansion. We use this high precision numerical result to fit the integer coefficients of zeta values in the final analytical answer. The presented six and seven loop results can be used as a cross-check with FiNLIE on the string theory side, or with direct gauge theory computations. The seven loop level is the theoretical limit of this Luscher approach as at eight loops double-wrapping corrections will appear.Comment: 18 pages, typos correcte