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However, these languages have important expressive limits, since none of them reaches the full expressive power of a first-order language. As a result, large parts of our knowledge\u2014in particular, mathematical and scientific theories\u2014cannot currently be made available on the Semantic Web as linked data, not even in principle. In this work, we are going to define FOOL (first-order ontology language), a new ontological language compatible with RDF, which allows the expression of any formula of a first-order language as a connected RDF graph. FOOL is as expressive as a first-order language, but unlike it, its statements do not have a serialized form. Instead, like a RDF statement, each statement of a FOOL knowledge base is a connected graph, and different statements link to each other through the meaningful nodes they share. In this way, the semantic relationships between statements are made explicit, and given FOOL\u2019s compatibility with RDF, virtually the entire complex of our knowledge can in principle be made available on the Semantic Web as linked data. The semantic relationships made explicit by a FOOL ontology are not those of logical consequence, but they are meaning connections between statements represented as graphs. It is not far-fetched to think that, by devising appropriate measures of the linking patterns between statements, such relations can be mechanized, thus opening the way to new and possibly unforeseen results and applications.<\/jats:p>","DOI":"10.1093\/jigpal\/jzae085","type":"journal-article","created":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T19:09:39Z","timestamp":1718910579000},"source":"Crossref","is-referenced-by-count":0,"title":["Expressing knowledge as linked data by FOOL"],"prefix":"10.1093","volume":"34","author":[{"given":"Marco","family":"Giunti","sequence":"first","affiliation":[{"name":"Dip. di Pedagogia Psicologia Filosofia Universit\u00e0 di Cagliari, , via Is Mirrionis 1, 09123 Cagliari, , giunti@unica.it","place":["Italy"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simone","family":"Pinna","sequence":"additional","affiliation":[{"name":"Dip. di Pedagogia Psicologia Filosofia Universit\u00e0 di Cagliari, , via Is Mirrionis 1, 09123 Cagliari, , simone.pinna@unica.it","place":["Italy"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,11,11]]},"reference":[{"key":"2026032700502790000_ref1","article-title":"World wide web future directions","author":"Berners-Lee","year":"1994","journal-title":"Plenary talk,"},{"key":"2026032700502790000_ref2","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1038\/scientificamerican0501-34","article-title":"The semantic web","volume":"284","author":"Berners-Lee","year":"2001","journal-title":"Scientific American"},{"key":"2026032700502790000_ref3","article-title":"Linked data,","author":"Berners-Lee","year":"2006"},{"key":"2026032700502790000_ref4","first-page":"191","article-title":"On the epistemological status of semantic networks","volume-title":"Readings in Knowledge Representation","author":"Brachman","year":"1985"},{"key":"2026032700502790000_ref5","volume-title":"Knowledge Representation and Reasoning","author":"Brachman","year":"2004"},{"key":"2026032700502790000_ref6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3390\/info14030154","article-title":"LPG-based knowledge graphs: a survey, a proposal and current trends","volume":"14","author":"Di Pierro","year":"2023","journal-title":"Information"},{"key":"2026032700502790000_ref7","first-page":"56","article-title":"On sense and reference","volume-title":"Translations from the Philosophical Writings of Gottlob Frege","author":"Frege","year":"1960"},{"key":"2026032700502790000_ref8","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1093\/jigpal\/jzz047","article-title":"Representing $n$-ary relations in the semantic web","volume":"29","author":"Giunti","year":"2021","journal-title":"Logic Journal of the IGPL"},{"key":"2026032700502790000_ref9","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s11023-011-9230-6","article-title":"Sense and reference on the web","volume":"21","author":"Halpin","year":"2011","journal-title":"Minds and Machines"},{"key":"2026032700502790000_ref10","volume-title":"Fundamentals of Concept Formation in Empirical Science","author":"Hempel","year":"1952"},{"key":"2026032700502790000_ref11","article-title":"Linked Data: Evolving the Web into a Global Data Space (1st edition)","volume-title":"Synthesis Lectures on the Semantic Web: Theory and Technology, 1:1, 1\u2013136","author":"Heath","year":"2011"},{"key":"2026032700502790000_ref12","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1109\/TNNLS.2021.3070843","article-title":"A survey on knowledge graphs: representation, acquisition, and applications","volume":"33","author":"Ji","year":"2022","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"2026032700502790000_ref13","first-page":"64","article-title":"Developing the Semantic Web via the resolution of meaning ambiguities","volume-title":"Software Engineering and Formal Methods","author":"Pinna","year":"2022"},{"key":"2026032700502790000_ref14","doi-asserted-by":"crossref","first-page":"20","DOI":"10.2307\/2181906","article-title":"Two dogmas of empiricism","volume":"60","author":"Quine","year":"1951","journal-title":"The Philosophical Review"},{"key":"2026032700502790000_ref15","first-page":"20","article-title":"Preprogramming for mechanical translation. Mechanical","volume":"3","author":"Richens","year":"1956","journal-title":"Translation"},{"key":"2026032700502790000_ref16","article-title":"Introducing the knowledge graph: things, not strings","author":"Singhal","year":"2012"},{"key":"2026032700502790000_ref17","first-page":"1493","article-title":"Semantic networks","volume-title":"Encyclopedia of Artificial Intelligence,","author":"Sowa","year":"1992"},{"key":"2026032700502790000_ref18","volume-title":"Philosophical Investigations,","author":"Wittgenstein","year":"2009"},{"key":"2026032700502790000_ref19","article-title":"RDF semantics","author":"W3C","year":"2004","journal-title":"W3C Recommendation"},{"key":"2026032700502790000_ref20","article-title":"Defining n-ary relations on the semantic web","author":"W3C","year":"2006","journal-title":"W3C Working Group Note,"},{"key":"2026032700502790000_ref21","volume-title":"OWL 2 Web Ontology Language Document Overview","author":"W3C","year":"2012"},{"key":"2026032700502790000_ref22","volume-title":"RDF Schema 1.1. 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These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.<\/jats:p>","DOI":"10.1093\/jigpal\/jzaa060","type":"journal-article","created":{"date-parts":[[2020,10,29]],"date-time":"2020-10-29T20:11:48Z","timestamp":1604002308000},"page":"263-276","source":"Crossref","is-referenced-by-count":6,"title":["Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder"],"prefix":"10.1093","volume":"30","author":[{"given":"Christian","family":"Amor","sequence":"first","affiliation":[{"name":"School of Aerospace Engineering, Universidad Polit\u00e9cnica de Madrid, 28040, Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 M","family":"P\u00e9rez","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering, Universidad Polit\u00e9cnica de Madrid, 28040, Madrid, 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A natural question is, can we find a minimal theory for which $\\textsf{G1}$ holds? We examine the Turing degree structure of recursively enumerable (RE) theories for which $\\textsf{G1}$ holds and the interpretation degree structure of RE theories weaker than the theory $\\textbf{R}$ with respect to interpretation for which $\\textsf{G1}$ holds. We answer all questions that we posed in [2], and prove more results about them. It is known that there are no minimal essentially undecidable theories with respect to interpretation. We generalize this result and give some general characterizations, which tell us under what conditions there are no minimal RE theories having some property with respect to interpretation.<\/jats:p>","DOI":"10.1093\/jigpal\/jzaf012","type":"journal-article","created":{"date-parts":[[2025,4,23]],"date-time":"2025-04-23T06:49:12Z","timestamp":1745390952000},"source":"Crossref","is-referenced-by-count":0,"title":["The limitless first incompleteness theorem"],"prefix":"10.1093","volume":"33","author":[{"given":"Yong","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Philosophy, Wuhan University , Wuhan 430072 Hubei, People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,4,22]]},"reference":[{"key":"2025052605515203200_ref1","doi-asserted-by":"publisher","first-page":"503","DOI":"10.2307\/2272251","article-title":"G\u00f6del\u2019s second incompleteness theorem for 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In particular, we prove that the category of dually hemimorphic semi-Heyting algebras is equivalent to the category of dually hemimorphic centered semi-Nelson algebras. We also study the lattice of congruences of a dually hemimorphic semi-Nelson algebra through some of its deductive systems.<\/jats:p>","DOI":"10.1093\/jigpal\/jzz030","type":"journal-article","created":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T11:24:59Z","timestamp":1563967499000},"page":"316-340","source":"Crossref","is-referenced-by-count":3,"title":["Dually hemimorphic semi-Nelson algebras"],"prefix":"10.1093","volume":"28","author":[{"given":"Juan Manuel","family":"Cornejo","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidad Nacional del Sur and Instituto de Matem\u00e1tica de Bah\u00eda Blanca (INMABB) - Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas, Av. Leandro N. 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