Undecidability of the Logic of Partial Quasiary Predicates

We obtain an effective embedding of the classical predicate logic into the logic of partial quasiary predicates. The embedding has the property that an image of a non-theorem of the classical logic is refutable in a model of the logic of partial quasiary predicates that has the same cardinality as the classical countermodel of the non-theorem. Therefore, we also obtain an embedding of the classical predicate logic of finite models into the logic of partial quasiary predicates over finite structures. As a consequence, we prove that the logic of partial quasiary predicates is undecidable—more precisely, $\varSigma ^0_1$-complete—over arbitrary structures and not recursively enumerable—more precisely, $\varPi ^0_1$-complete—over finite structures.

Employees balance and stability as key points in organizational performance

System analyses deal with interrelationships between different variables that keep the system in balance. In many analysis of complex thinking, a system is viewed as a complex unit in which the ‘whole’ is not reduced to the ‘sum’ of its parts; the system becomes an ambiguous item because it consists of several entities that interact with unforeseen results or, in other words, it is situated at a transdisciplinary level, it is impossible for an area to have a complete reading of its complexity. It was also mentioned that the concept of the open system best describes complexity by stating that ‘the laws of the organization are not equilibrium, but an imbalance that is restored or compensated for by stabilized dynamics’. This idea originated from the field of thermodynamics and the second law, in which the imbalance that it maintains allows the system for an apparent balance. This fragile steady state has something of a paradox, since the structures remain the same, but their constituents are changeable. The concept of open system undoes the door to a theory of evolution that can only derive from the interactions between a system and its ecosystem. Within this systemic approach, the focus of the analysis takes into account the ambiguity, multidisciplinary and complexity associated with system adjustment, i.e. it is intended to qualify an employee job based on their experience and knowledge as a measure of their impact on the organization performance.

Deep Convolutional Neural Networks on Automatic Classification for Skin Tumour Images

The skin, uniquely positioned at the interface between the human body and the external world, plays a multifaceted immunologic role in human life. In medical practice, early accurate detection of all types of skin tumours is essential to guide appropriate management and improve patients’ survival. The most important issue is to differentiate between malignant skin tumours and benign lesions. The aim of this research is the classification of skin tumours by analysing medical skin tumour dermoscopy images. This paper is focused on a new strategy based on deep convolutional neural networks which have recently shown a state-of-the-art performance to define strategy to automatic classification for skin tumour images. The proposed system is tested on well-known HAM10000 data set. For experimental results, verification is performed and the results are compared with similar researches.

Proof Systems for 3-valued Logics Based on Gödel’s Implication

The logic $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ was introduced in Robles and Mendéz (2014, Logic Journal of the IGPL, 22, 515–538) as a paraconsistent logic which is based on Gödel’s 3-valued matrix, except that Kleene–Łukasiewicz’s negation is added to the language and is used as the main negation connective. We show that $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ is exactly the intersection of $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ and $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$, the two truth-preserving 3-valued logics which are based on the same truth tables. (In $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ the set ${\cal D}$ of designated elements is $\{1\}$, while in $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ ${\cal D}=\{1,0.5\}$.) We then construct a Hilbert-type system which has (MP) for $\to $ as its sole rule of inference, and is strongly sound and complete for $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$. Then we show how, by adding one axiom (in the case of $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$) or one new rule of inference (in the case of $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$), we get strongly sound and complete systems for $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ and $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$. Finally, we provide quasi-canonical Gentzen-type systems which are sound and complete for those logics and show that they are all analytic, by proving the cut-elimination theorem for them.

On bivalent semantics and natural deduction for some infectious logics

In this work, we propose a variant of so-called informational semantics, a technique elaborated by Voishvillo, for two infectious logics, Deutsch’s ${\mathbf{S}_{\mathbf{fde}}}$ and Szmuc’s $\mathbf{dS}_{\mathbf{fde}}$. We show how the machinery of informational semantics can be effectively used to analyse truth and falsity conditions of disjunction and conjunction. Using this technique, it is possible to claim that disjunction and conjunction can be rightfully regarded as such, a claim which was disputed in the recent literature. Both ${\mathbf{S}_{\mathbf{fde}}}$ and $\mathbf{dS}_{\mathbf{fde}}$ are formalized in terms of natural deduction. This allows us to solve several problems: to develop a natural deduction calculus for ${\mathbf{S}_{\mathbf{fde}}}$ containing the standard form of disjunction elimination (in contrast to the calculus by Petrukhin), to introduce the first natural deduction calculus for $\mathbf{dS}_{\mathbf{fde}}$ and to reflect the fundamental symmetry between ${\mathbf{S}_{\mathbf{fde}}}$ and $\mathbf{dS}_{\mathbf{fde}}$ on proof-theoretical level forming a convenient basis for obtaining their well-known extensions $\mathbf{K}^{\mathbf{w}}_{\mathbf{3}}$ and $\mathbf{PWK}$.

Parsimonious Modelling for Estimating Hospital Cooling Demand to Improve Energy Efficiency

Of all the different types of public buildings, hospitals are the biggest energy consumers. Cooling systems for air conditioning and healthcare uses are particularly energy intensive. Forecasting hospital thermal-cooling demand is a remarkable and innovative method capable of improving the overall energy efficiency of an entire cooling system. Predictive models allow users to forecast the activity of water-cooled generators and adapt power generation to the real demand expected for the day ahead, while avoiding inefficient subcooling. In addition, the maintenance costs related to unnecessary starts and stops and power-generator breakdowns occurring over the long term can be reduced. This study is based on the operations of a real hospital facility and details the steps taken to develop an optimal and efficient model based on a genetic methodology that searches for low-complexity models through feature selection, parameter tuning and parsimonious model selection. The methodology, called GAparsimony, has been tested with neural networks, support vector machines and gradient boosting techniques. Finally, a weighted combination of the three best models was created. The new operational method employed herein can be replicated in similar buildings with similar water-cooled generators.