A quantitative-informational approach to logical consequence

In this work, we propose a definition of logical consequence based on the relation between the quantity of information present in a particular set of formulae and a particular formula. As a starting point, we use Shannon‟s quantitative notion of information, founded on the concepts of logarithmic function and probability value. We first consider some of the basic elements of an axiomatic probability theory, and then construct a probabilistic semantics for languages of classical propositional logic. We define the quantity of information for the formulae of these languages and introduce the concept of informational logical consequence, identifying some important results, among them: certain arguments that have traditionally been considered valid, such as modus ponens, are not valid from the informational perspective; the logic underlying informational logical consequence is not classical, and is at the least paraconsistent sensu lato; informational logical consequence is not a Tarskian logical consequence

Estimating a pressure dependent thermal conductivity coefficient with applications in food technology

In this paper we introduce a method to estimate a pressure dependent thermal conductivity coefficient arising in a heat diffusion model with applications in food technology. To address the known smoothing effect of the direct problem, we model the uncertainty of the conductivity coefficient as a hierarchical Gaussian Markov random field (GMRF) restricted to uniqueness conditions for the solution of the inverse problem established in Fraguela et al. Furthermore, we propose a Single Variable Exchange Metropolis-Hastings algorithm to sample the corresponding conditional probability distribution of the conductivity coefficient given observations of the temperature. Sensitivity analysis of the direct problem suggests that large integration times are necessary to identify the thermal conductivity coefficient. Numerical evidence indicates that a signal to noise ratio of roughly 1000 suffices to reliably retrieve the thermal conductivity coefficient

A Note on the Pseudo-Spectra and the Pseudo-Covariance Generating Functions of ARMA Processes

Although the spectral analysis of stationary stochastic processes has solid mathematical foundations, this is not the case for non-stationary stochastic processes. In this paper, the algebraic foundations of the spectral analysis of non-stationary ARMA processes are established. For this purpose the Fourier Transform is extended to the field of fractions of polynomials. Then, the Extended Fourier Transform pair pseudo-covariance generating function / pseudo-spectrum, analogous to the Fourier Transform pair covariance generating function / spectrum,is defined. The new transform pair is well defined for stationary and non-stationary ARMA processes. This new approach can be viewed as an extension of the classical spectral analysis. It is shown that the frequency domain has some additional algebraic advantages over the time domain.

Solvability of the G_2 Integrable System

It is shown that the 3-body trigonometric G_2 integrable system is exactly-solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, for arbitrary values of the coupling constants, the Hamiltonian can be expressed as a quadratic polynomial in the generators of some Lie algebra of differential operators in a finite-dimensional representation. Four infinite families of eigenstates, represented by polynomials, and the corresponding eigenvalues are described explicitly.Comment: 18 pages, LaTeX, some minor typos correcte

Timor leste collaborative project: a short report

This report discusses findings from a small-scale scoping study, which is part of a larger curriculum project—a collaborative venture between staff from the Universidade Nacional Timor Lorosa'e (UNTL) and a New Zealand university. The aim of the wider project is to develop a context-sensitive English language curriculum for students at UNTL who are undergoing pre-service training to be teachers of English as a foreign language in local secondary schools. (Details of the institutional and linguistic context are provided in the appendix.) According to Norton (2000), investment by learners is a key factor in the successful implementation of a new curriculum: "if learners invest in a second language, they do so with the understanding that they will acquire a wider range of symbolic and material resources, which will increase their value in the social world" (Norton, 2000, pp. 165-166). Thus, when designing the curriculum, it is important to ensure that the students will not only understand how to use the specific learning tasks but that it also expands their repertoire of skills and knowledge for application in their subsequent professional and social lives. The report begins by outlining the history and objectives of the project before explaining the specific research questions posed for the scoping study. The means of collecting data will be outlined and examples of the participants' attitudes will be presented based on open-ended questionnaire responses. These findings will be discussed in terms of how they might lead to the design of a curriculum which is internationally-framed and context-sensitive in terms both of its content and implementation. The report will conclude with the further steps that are being taken to move the project to its next phase

Development of Technologies for Local Composting of Food Waste From Universities

[Abstract] The amount of biowaste generated by university canteens (BWUC) in the faculties of the University of A Coruña (UDC) varies between 6 and 100 kg/day. In addition, the gardening services of the campus generate even higher amounts of garden waste (GrW), including pruning, which, once crushed, serves as bulking material for composting the biowaste from the canteens. Decentralized composting has been chosen with the aim of producing high quality organic fertilizers for university urban gardens while reducing the environmental burdens of both waste management and agricultural practice. Small static home composters of 340 L (SHC) for smaller amounts of generation (up to 20 kg BWUC/day) were used, while, for faculties of higher generation (up to 40 kg BWUC/day on average), the first composting stage was carried out in a closed and dynamic composter (DC). The dynamic composter was designed and built specifically for this project and its features were improved and optimized throughout the study. The pilot project was carried out in two centers of the UDC, which are known as the Philology Faculty (PF) and the School of Architecture (SA). All the organic waste generated by the canteens of these two colleges from January 2011 to July 2011 (approximately 3000 kg) was treated. Composting in SHC included a thermophilic phase that extended one month beyond the loading period for which thermophilic temperatures were also recorded. The use of the DC as the first stage in combination with static composters (SC) for the maturation stage reduced the overall thermophilic phase to 6–8 weeks. The complete maturation (Rottegrade class IV-V) was achieved after about four months in SHC and after two months when using the combined DC-SC system, if the right conditions of moisture were maintained. The chemical quality of the compost produced was compatible with Class A of Spanish legislation (equivalent to organic farmer quality) and the C/N ratio ranged from 9 to 15 depending on the relation BWUC:GrW