14 research outputs found

    The semiring-theoretic approach to MV-algebras: a survey

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    In this paper we review some of the main achievements of the semiring-theoretic approach to MV-algebras initiated and pursued mainly by the present authors and their collaborators. The survey focuses mainly on the connections between MV-algebras and other theories that such a semiringbased approach enabled, and on an application of such a framework to Digital Image Processing. We also give some suggestions for further developments by stating several open problems and possible research lines.Comment: Published versio

    Fuzzy Sets, Fuzzy Logic and Their Applications 2020

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    The present book contains the 24 total articles accepted and published in the Special Issue ā€œFuzzy Sets, Fuzzy Logic and Their Applications, 2020ā€ of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity

    Weighted programming: A programming paradigm for specifying mathematical models

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    We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic branching and (2) weighting execution traces. Weights can be numbers but also other objects like words from an alphabet, polynomials, formal power series, or cardinal numbers. We argue that weighted programming as a paradigm can be used to specify mathematical models beyond probability distributions (as is done in probabilistic programming). We develop weakest-precondition- and weakest-liberal-precondition-style calculi Ć  la Dijkstra for reasoning about mathematical models specified by weighted programs. We present several case studies. For instance, we use weighted programming to model the ski rental problem - an optimization problem. We model not only the optimization problem itself, but also the best deterministic online algorithm for solving this problem as weighted programs. By means of weakest-precondition-style reasoning, we can determine the competitive ratio of the online algorithm on source code level

    19th Brazilian Logic Conference: Book of Abstracts

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    This is the book of abstracts of the 19th Brazilian Logic Conferences. The Brazilian Logic Conferences (EBL) is one of the most traditional logic conferences in South America. Organized by the Brazilian Logic Society (SBL), its main goal is to promote the dissemination of research in logic in a broad sense. It has been occurring since 1979, congregating logicians of different fields ā€” mostly philosophy, mathematics and computer science ā€” and with different backgrounds ā€” from undergraduate students to senior researchers. The meeting is an important moment for the Brazilian and South American logical community to join together and discuss recent developments of the field. The areas of logic covered in the conference spread over foundations and philosophy of science, analytic philosophy, philosophy and history of logic, mathematics, computer science, informatics, linguistics and artificial intelligence. Previous editions of the EBL have been a great success, attracting researchers from all over Latin America and elsewhere. The 19th edition of EBL takes place from May 6-10, 2019, in the beautiful city of JoĆ£o Pessoa, at the northeast coast of Brazil. It is conjointly organized by Federal University of ParaĆ­ba (UFPB), whose main campus is located in JoĆ£o Pessoa, Federal University of Campina Grande (UFCG), whose main campus is located in the nearby city of Campina Grande (the second-largest city in ParaĆ­ba state) and SBL. It is sponsored by UFPB, UFCG, the Brazilian Council for Scientific and Technological Development (CNPq) and the State Ministry of Education, Science and Technology of ParaĆ­ba. It takes place at Hotel Luxxor Nord TambaĆŗ, privileged located right in front TambaĆŗ beach, one of JoĆ£o Pessoaā€™s most famous beaches

    Knowledge Accumulation of Microbial Data Aiming at a Dynamic Taxonomic Framework

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    Deze thesis is een poging om precies dit onderzoeksgebied te overbruggen dat ligt tussen ruw gegeven en abstract concept, tussen praktijk en theorie, binnen het kader van de hedendaagse bacteriĆ«le taxonomie. Als gevolg hiervan is het een kruisbestuiving geworden tussen microbiologie, wiskunde en computerwetenschappen. De kunst om het landschap van de bacteriĆ«le diversiteit uit te tekenen, gebruikt als een metafoor voor het modelleren van de taxonomie, vereist het bepalen van een representatieve waaier aan reproduceerbare en vergelijkbare experimentele kenmerken van een verzameling bacteriĆ«n (microbiologie/taxonomie), het ontwerpen en implementeren van objectieve classificatiemethodes voor het groeperen van gegevens op een niet gecoƶrdineerde manier (wiskunde/classificatie) en het consolideren van experimentele gegevens en hun verschillende onderverdelingen via een uniforme en weldoordachte aanpak (computerwetenschappen/kennisbeheer). Men kan zich gemakkelijk een globaal kennissysteem voor de geest halen dat de vellen vol experimentele gegevens die voortspruiten uit de microbiologische onderzoeksverrichtingen op een gestructureerde en geĆ¼niformiseerde manier kan absorberen. Een dergelijk kennisbeheersysteem zou een ongelofelijke vooruitgang betekenen voor de mogelijke toepassing van intelligente en goed gefundeerde methodes voor het ontginnen van de gegevens, ingezet als hulpmiddel om het afbakenen van objectieve en universele taxonomische consensusmodellen op een betere manier te stroomlijnen en te automatiseren. Bovendien kunnen dergelijke inferentiesystemen in staat worden geacht om ogenblikkelijk te reageren op een toevloed van nieuwe gegevens en interactief te communiceren met de buitenwereld indien noodzakelijke stukken voor het vervolledigen van de taxonomische puzzel zouden ontbreken. De geldigheid van nieuwe inzichten of hypothesen omtrent het leven en de evolutie van bacteriĆ«n zou onmiddellijk kunnen getoetst worden aan deze vergaarbakken vol kennis, mogelijks met een directe aanpassing van bestaande taxonomische modellen tot gevolg. Vooraleer de betrachtingen van een autodidactisch inferentiesysteem voor het uittekenen van het landschap van de bacteriĆ«le diversiteit kunnen gerealiseerd worden, moeten belangrijke technische en organisatorische hindernissen overwonnen worden. Dit vraagt het verleggen van de grenzen van een mondiale uitwisseling van gegevens, het nasporen en invullen van de hiaten in de waarnemingen, en het verkennen van de mogelijkheden van nieuwe technieken voor het ontginnen van gegevens, ten voordele van een beter inzicht in het leven en de evolutie van bacteriĆ«n. Spijts de nog vele onopgeloste kwesties, kunnen de ideeĆ«n die worden aangebracht in deze verhandeling als stimulans en leidraad dienen bij het integreren en exploiteren van microbiĆ«le gegevens, in plaats van het blijvend koesteren van een ijdele hoo

    Vector Semantics

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    This open access book introduces Vector semantics, which links the formal theory of word vectors to the cognitive theory of linguistics. The computational linguists and deep learning researchers who developed word vectors have relied primarily on the ever-increasing availability of large corpora and of computers with highly parallel GPU and TPU compute engines, and their focus is with endowing computers with natural language capabilities for practical applications such as machine translation or question answering. Cognitive linguists investigate natural language from the perspective of human cognition, the relation between language and thought, and questions about conceptual universals, relying primarily on in-depth investigation of language in use. In spite of the fact that these two schools both have ā€˜linguisticsā€™ in their name, so far there has been very limited communication between them, as their historical origins, data collection methods, and conceptual apparatuses are quite different. Vector semantics bridges the gap by presenting a formal theory, cast in terms of linear polytopes, that generalizes both word vectors and conceptual structures, by treating each dictionary definition as an equation, and the entire lexicon as a set of equations mutually constraining all meanings

    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum

    Vector Semantics

    Get PDF
    This open access book introduces Vector semantics, which links the formal theory of word vectors to the cognitive theory of linguistics. The computational linguists and deep learning researchers who developed word vectors have relied primarily on the ever-increasing availability of large corpora and of computers with highly parallel GPU and TPU compute engines, and their focus is with endowing computers with natural language capabilities for practical applications such as machine translation or question answering. Cognitive linguists investigate natural language from the perspective of human cognition, the relation between language and thought, and questions about conceptual universals, relying primarily on in-depth investigation of language in use. In spite of the fact that these two schools both have ā€˜linguisticsā€™ in their name, so far there has been very limited communication between them, as their historical origins, data collection methods, and conceptual apparatuses are quite different. Vector semantics bridges the gap by presenting a formal theory, cast in terms of linear polytopes, that generalizes both word vectors and conceptual structures, by treating each dictionary definition as an equation, and the entire lexicon as a set of equations mutually constraining all meanings
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