On formal aspects of the epistemic approach to paraconsistency

This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for both BLE and LET J . The meanings of the connectives of BLE and LET J , from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LET J is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed

A toolbox to solve coupled systems of differential and difference equations

We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter \ep (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t.\ \ep and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package \texttt{SolveCoupledSystem} which is based on the packages \texttt{Sigma}, \texttt{HarmonicSums} and \texttt{OreSys}. In all applications the representation in $x$-space is obtained as an iterated integral representation over general alphabets, generalizing Poincar\'{e} iterated integrals

Aves españolas con nombres de persona (IV): la terrera marismeña de Apetz

En el año 1856, durante el viaje ornitológico de los hermanos Alfredo y Reinaldo Brehm a la península Ibérica, se descubría una nueva especie de ave, la terrera marismeña de Apetz (Melanocorypha Apetzii; Brehm, 1857 [1858]). En esta nueva entrega de la serie Aves españolas con nombres de persona se revisa la historia del descubrimiento de esta especie, su redescubrimiento como Calandrella baetica, o su reaparición como subespecie, para terminar con un breve apunte biográfico de la persona a la que se honró con el epónimo apetzii, el médico y entomólogo alemán Dr. Theodor Apetz (1834-1898)

José Antonio Valverde Gómez (1926-2003) y el quebrantahuesos (Gypaetus barbatus)

Hace diez años fallecía, en su domicilio sevillano, el naturalista vallisoletano José Antonio Valverde Gómez. En homenaje a su memoria, me propongo en este trabajo revisitar, y en lo posible también revisar, la relación que este biólogo mantuvo con nuestra ave más impresionante y bella, con esa joya de nuestro patrimonio natural y cultural, el quebrantahuesos. Para ello, se aporta documentación inédita, se añaden datos nuevos, y se corrigen viejos errores

Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory

We present the two-loop helicity amplitudes for the scattering of two gluons into two gluons in QCD, which are relevant for next-to-next-to-leading order corrections to jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity variants of dimensional regularization. Summing our expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Glover, Oleari and Tejeda-Yeomans. We also present the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric Yang-Mills theory.Comment: 55 pages, 3 figures, corrected remark below eq. (4.33), other minor changes, version appearing in JHE

Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations

We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in $\epsilon$ if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the $\epsilon$-expansion of a ladder graph with 6 massive fermion lines