Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as N4-lattices which (...) correspond to the paraconsistent version of Nelson's logic, as well as their applications to other areas of interest to logicians, such as duality and rough set theory. A general representation theorem states that each Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson logic if and only if it is valid in every finite Nelson algebra induced by a quasiorder. (shrink)

A systematic introduction to mathematical logic which does not take classical logic for granted. The books develops a system of contradictorial gradualistic logic.

We understand by data analysis the full set of methods which are used to point out the structural relations between certain objects and the characteristics observed in them. In the case where these characteristics admit a process of dichotomy, the relations can be expressed in terms of propositional logic.In the present paper, we endeavour to make clear the opposition between the problems of propositional logic and those of certain model utilised in data analysis: in propositional logic, we look for a (...) solution verified by a given set of propositions; as long as we are concerned with data analysis, we look for a solution in terms of propositions which include as proper parts the observed objects.Finally, we draw the main lines of two very used methods which can be relevant with the aid of computer: the factor analysis and the automatic classification (cluster analysis). (shrink)

Synchronic and diachronic philology is a necessary but insufficient condition for studying rhetoricians and philosophers of the Ancient world. Knowledge of formal logic in order to understand their works is also required. As a rhetorician-turned-philosopher Augustine not only utilized Stoic and Aristotelian logic but also exceeded the boundary of such formal languages using both original inference patterns unknown to such formal systems and disclosing new horizons to Western philosophy.

John Wyclif’s logical works have lain under a kind of fog since they were first published in the 1890s. My first aim is to clear up some long-standing confusions by dispelling this fog once and for all. A partial identification of Wyclif’s source material then allows me to make a more dramatic claim about persistent misunderstandings of what is thought to be his earliest work.

Standardly, the usual approach to rationality is based on the notion of ‘being a reason for’. Honouring the traditional distinction between practical and theoretical philosophy, reasons are classified as justificative and explicative. In both cases, a reason-statement has the form ‘’. For reasons of type , ‘A’ is a factual statement and ‘B’ is a statement which describes an action of the agent. The reason-statement has a prescriptive sense because ‘A is a reason for doing B’ means ‘A is a (...) reason an agent ought to do B’. So, it is advisable to schematize that kind of statements as ‘’, where ‘OB’ is a deontic statement prescribing the duty to do B. Reasons of type have a descriptive sense and do not require the above-mentioned constraint. But ‘being a reason for’ has different senses according to context, even when the distinction between justificative and explicative reasons is drawn. Accordingly, it is important to distinguish two basic types of reasons: sufficient and necessary, and two subordinate types of reasons: contributing and substitutive . A lot of attention has been paid, lately, to a sense of contributive reasons: prima facie reasons . The paper will deal with that kind of reasons. Its main thesis are: 1) prima facie reason-statements are defeasible conditionals ‘’ pointing out that A is a contributing condition of B, 2) a defeasible conditional has the properties of ‘’, where ‘ =>’ is a strict implication and ‘f’’ a revision-operator satisfying the conditions set up by the theory AGM on the rational change of theories. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

In quanto segue si d× in poche pagine un'idea del paradigma classico della logica assiomatica; Ë un richiamo alla terminologia e ai simboli che si useranno in seguito. I due successivi capitoli presentano i problemi ce hanno segnato la nascita del paradigma classico e un confronto con il paradigma tradizionale della logica aristotelica.

Este trabajo orienta su contenido a las aplicaciones de la lógica borrosa, pero no desde una aproximación que trate de abordar ciertas caracterrsticas relevantes de algunas de ellas y/o comentar sus coincidencias y discrepancias desde el punto de vista dei soporte dado por la lógica borrosa. Existen excelentes y abundantes revisiones de este estilo, por lo que nosotros hemos optado por introducir algunas reflexiones a modo de respuesta a preguntas formuladas al hilo de la más general que da (...) trtulo al trabajo. Contestar a algunas de ellas es, sin duda, uncometido realmente arriesgado, como ocurre al tratar de plasmar, por ejemplo, y aunque sea con trazos “borrosos”, cuáles serán las aplicaciones futuras de la lógica borrosa. Esperamos que se nos disculpe si el acierto torna a ser escaso.This paper discusses about the field of fuzzy logic applications, but not from the point of view of its importance or commenting their main features and how they are formally supported by fuzzy logic. Very good, exist in this field, and so we decided to present some reflections trying to answer very general questions about this issue. Answering, for example, to the question about possible futureapplications of fuzzy logic is, no doubts, a very risky task. We look forward to be forgiven if our approach proves not to be very successful. (shrink)