Parameterizing the semantics of fuzzy attribute implications by systems of isotone Galois connections

We study the semantics of fuzzy if-then rules called fuzzy attribute implications parameterized by systems of isotone Galois connections. The rules express dependencies between fuzzy attributes in object-attribute incidence data. The proposed parameterizations are general and include as special cases the parameterizations by linguistic hedges used in earlier approaches. We formalize the general parameterizations, propose bivalent and graded notions of semantic entailment of fuzzy attribute implications, show their characterization in terms of least models and complete axiomatization, and provide characterization of bases of fuzzy attribute implications derived from data

Rethinking Hart : From Open Texture to Prototype Theory - Analytic Philosophy Meets Cognitive Linguistics

The article is based on an observation that there are significant and non-arbitrary similarities between two, seemingly quite distant, theories that address the problem of linguistic categorization. One is the theory of open texture put forward by a prominent legal philosopher, Herbert L.A Hart. The other is the theory of prototypes, originated from psychological research by Eleanor Rosch and developed by cognitively- oriented linguists, most notably Charles Fillmore, George Lakoff, and Ronald Langacker. Firstly, the origins of the open texture theory are presented, including the discussion of Friedrich Waismann’s and Ludwig Wittgenstein’s ideas and their impact on Hart’s theory. Secondly, Hart’s theory of open texture is examined, based on several articles and his masterpiece: The Concept of Law (Oxford: Oxford University Press 1961). Thirdly, a brief introduction to the prototype theory is provided, focusing on its reception in Cognitive Linguistics. Fourthly, a comparison of both theories is presented, including a sketch of a broader philosophical and historical background, as well as a detailed analysis of similarities and dissimilarities between them. The comparison results in a conclusion that, on linguistic grounds, the open texture theory can be viewed as an anticipation of prototype theory. Finally, several reservations are made in order to avoid possible confusions and some obvious objections

TEORIA PROTOTYPU W PRAKTYCE ORZECZNICZEJ TRYBUNAŁU SPRAWIEDLIWOŚCI UNII EUROPEJSKIEJ - STUDIUM PRZYPADKU

Prototype theory is a semantic theory according to which the membership of conceptual categories is based not on a list of criterial features, but rather on the similarity to the most representative member of the category. Consequently, conceptual categories may lack classical definitions and rigid boundaries. This article supports the claims, already made by other scholars working in the field, that prototype theory may greatly augment our understanding of legal (i.e. statutory, judicial) interpretation. Legal provisions are traditionally written as classical definitions, but they are rarely applied that way. Statutory concepts tend to be interpreted with a great deal of flexibility, using a wide array of extra-textual factors. This is especially true for the case law of the Court of Justice of the European Union, which has to deal with the challenges of the multilingual, supranational law of the European Union.Teoria prototypu jest teorią semantyczną, zgodnie z którą przynależność do kategorii pojęciowych nie opiera się na zestawie określonych cech, lecz na podobieństwie do najbardziej reprezentatywnego egzemplarza danej kategorii. W związku z tym kategorie pojęciowe mogą nie poddawać się klasycznemu definiowaniu, a ich granice bywają rozmyte. Artykuł ten wspiera twierdzenia innych autorów, że teoria prototypów może znacząco pogłębić nasze rozumienie interpretacji prawniczej. Przepisy prawne są tradycyjnie formułowane jak klasyczne definicje, jednak rzadko są stosowane w ten sposób. Pojęcia ustawowe są często interpretowane z dużą elastycznością, przy wykorzystaniu szerokiej palety czynników pozatekstowych. Jest to szczególnie aktualne w przypadku orzecznictwa Trybunału Sprawiedliwości Unii Europejskiej, który stoi przed wyzwaniem stosowania wielojęzycznego, ponadnarodowego prawa Unii Europejskiej

Staying Faithful to the Standards of Proof

Academics have never quite understood the standards of proof or, indeed, much about the theory of proof Their formulations beget probabilistic musings, which beget all sorts of paradoxes, which in turn beget radical reconceptions and proposals for reform. The theoretical radicals argue that the law needs some basic reconception such as recognizing the aim of legal proof as not at all a search for truth but rather the production of an acceptable result, or that the law needs some shattering reform such as greatly heightening the civil standard of proof on each part of the case to ensure a more-likely than- not overall result. This Article refutes all those baroque rereadings. It shows that the standards of proof properly understood on the law\u27s own terms without a probabilistic overlay, work just fine. The law tells factfinders to compare their degree of belief in the alleged fact to their degree of contradictory disbelief. Obeying that instruction resolves mathematically the paradoxes that traditional probability theory creates for itself Most surprising, the burden of proof by which the proponent must prove all the elements and the opponent need disprove only one, does not produce an asymmetry between the parties. The law\u27s standards of proof need no drastic reconception or reform, because the law knew what it was doing all along. It deals with factual beliefs in a world that will remain uncertain, not with the odds of the facts becoming certain. And the well-established mathematics of beliefs are not the mathematics of odds

Computer science: the hardware software and heart of IT

1st edition, 201

Conjuntos construibles en modelos valuados en retículos

We investigate different set-theoretic constructions in Residuated Logic based on Fitting’s work on Intuitionistic Kripke models of Set Theory. Firstly, we consider constructable sets within valued models of Set Theory. We present two distinct constructions of the constructable universe: L B and L B , and prove that the they are isomorphic to V (von Neumann universe) and L (Gödel’s constructible universe), respectively. Secondly, we generalize Fitting’s work on Intuitionistic Kripke models of Set Theory using Ono and Komori’s Residuated Kripke models. Based on these models, we provide a general- ization of the von Neumann hierarchy in the context of Modal Residuated Logic and prove a translation of formulas between it and a suited Heyting valued model. We also propose a notion of universe of constructable sets in Modal Residuated Logic and discuss some aspects of it.Investigamos diferentes construcciones de la teoría de conjuntos en Lógica Residual basados en el trabajo de Fitting sobre los modelos intuicionistas de Kripke de la Teoría de Conjuntos. En primer lugar, consideramos conjuntos construibles dentro de modelos valuados de la Teoría de Conjuntos. Presentamos dos construcciones distintas del universo construible: L B y L B , y demostramos que son isomorfos a V (universo von Neumann) y L (universo construible de Gödel), respectivamente. En segundo lugar, generalizamos el trabajo de Fitting sobre los modelos intuicionistas de Kripke de la teoría de conjuntos utilizando los modelos residuados de Kripke de Ono y Komori. Con base en estos modelos, proporcionamos una generalización de la jerarquía de von Neumann en el contexto de la Lógica Modal Residuada y demostramos una traducción de fórmulas entre ella y un modelo Heyting valuado adecuado. También proponemos una noción de universo de conjuntos construibles en Lógica Modal Residuada y discutimos algunos aspectos de la misma. (Texto tomado de la fuente)MaestríaMagíster en Ciencias - MatemáticasLógica matemática, teoría de conjunto