Papers by Ricardo Oscar Rodriguez
International Journal of Approximate Reasoning
This paper investigates the definition of belief revision operators that correspond to the incons... more This paper investigates the definition of belief revision operators that correspond to the inconsistency tolerant semantics in the Ontology Based Data Access (OBDA) setting. By doing this, we aim at providing a more general characterisation, as well as the construction, of the above mentioned semantics. In fact, the main result of this paper is the idea of using kernel consolidation in Datalog to achieve a new semantic for inconsistent tolerant ontology query
Lecture Notes in Computer Science, 2014
This paper investigates the definition of belief revision operators that correspond to the IAR an... more This paper investigates the definition of belief revision operators that correspond to the IAR and ICR inconsistency tolerant semantics in the Ontology Based Data Access (OBDA) setting. By doing this equivalence our long term goal is to provide an axiomatic characterisation of the above mentioned semantics.
Journal of Computer and System Sciences, 2017
We consider two kinds of logics for approximate reasoning: one is weaker than classical logic and... more We consider two kinds of logics for approximate reasoning: one is weaker than classical logic and the other is stronger. In the first case, we are led by the principle that from given premises we can jump to conclusions which are only approximately (or possibly) correct. In the second case, which was not considered so far, in contrast, we follow the principle that conclusions must remain (necessarily) correct even if the premises are slightly changed. In this paper we recall the definitions and characterizations of the first logic, and we investigate the basic properties of the second logic, as well as its soundness and completeness with respect to Ruspini's semantics based on fuzzy similarity relations.
arXiv (Cornell University), Apr 28, 2018
Fuzzy Epistemic Logic is an important formalism for approximate reasoning. It extends the well kn... more Fuzzy Epistemic Logic is an important formalism for approximate reasoning. It extends the well known basic propositional logic BL, introduced by Hájek, by offering the ability to reason about possibility and necessity of fuzzy propositions. We consider an algebraic approach to study this logic, introducing Epistemic BL-algebras. These algebras turn to be a generalization of both, Pseudomonadic Algebras introduced by [Bezhanishvili(2002)] and serial, euclidean and transitive Bi-modal Gödel Algebras proposed by [Caicedo and Rodriguez(2015)]. We present the connection between this class of algebras and fuzzy possibilistic frames, as a first step to solve an open problem proposed by Hájek [Hájek(1998), chap. 8].
Information and Computation, 2021
Abstract A correspondence is established between one-variable fragments of (first-order) intermed... more Abstract A correspondence is established between one-variable fragments of (first-order) intermediate logics defined over a fixed countable linear frame and Godel modal logics defined over many-valued equivalence relations with values in a closed subset of the real unit interval. It is also shown that each of these logics can be interpreted in the one-variable fragment of the corresponding constant domain intermediate logic, which is equivalent to a Godel modal logic defined over (crisp) equivalence relations. Although the latter modal logics in general lack the finite model property with respect to their frame semantics, an alternative semantics is defined that has this property and used to establish co-NP-completeness results for the one-variable fragments of the corresponding intermediate logics both with and without constant domains.
Fuzzy Logic and Soft Computing, 1999
In this paper we are concerned with the formalization of a similarity-based type of reasoning dea... more In this paper we are concerned with the formalization of a similarity-based type of reasoning dealing with expressions of the form approximately ϕ, where ϕ is a fuzzy proposition. From a technical point of view we need a fuzzy logic as base logic to deal with the fuzziness of propositions and also we need a modality to account for the notion of approximation or closeness. Therefore we propose a modal fuzzy logic with semantics based on Kripke structures where the accesibility relations are fuzzy similarity relations measuring how similar are the possible worlds. We provide completeness results.
Proceedings of the Twentieth International Conference on Principles of Knowledge Representation and Reasoning
In this article, we provide the weak version of ensconcement which characterizes an interesting f... more In this article, we provide the weak version of ensconcement which characterizes an interesting family of Shielded base contractions. In turn, this characterization induces a class of AGM contractions satisfying certain postulates that we reveal here. Finally, we show a connection among the class of contractions given by our weak ensconcement and other kinds of base contraction operators. In doing so, we also point out a flaw in the original theorems that link the epistemic entrenchment with ensconcement (which are well established in the literature), and then we provide two possible solutions.
Communications in computer and information science, 2016
In this work we lay a theoretical framework for developing dynamic epistemic logics in a many-val... more In this work we lay a theoretical framework for developing dynamic epistemic logics in a many-valued setting. We consider in particular the logic of Public Announcements, which is one of the simplest and best-known dynamic epistemic systems in the literature. We show how to develop a Public Announcement Logic based on finite-valued Łukasiewicz modal logic. We define our logic through a relational semantics based on many-valued Kripke models, and also introduce an alternative but equivalent algebra-based semantics using MV-algebras endowed with modal operators. We provide a Hilbert-style calculus for our logic and prove completeness with respect to both semantics.
Logic, Language, Information, and Computation, 2019
The one-variable fragment of the first-order logic of linear intuitionistic Kripke models, referr... more The one-variable fragment of the first-order logic of linear intuitionistic Kripke models, referred to here as Corsi logic, is shown to have as its modal counterpart the many-valued modal logic S5(G). It is also shown that S5(G) can be interpreted in the crisp many-valued modal logic S5(G) C , the modal counterpart of the one-variable fragment of first-order Gödel logic. Finally, an algebraic finite model property is proved for S5(G) C and used to establish co-NP-completeness for validity in the aforementioned modal logics and one-variable fragments.
Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2020
In his 1991 seminal paper, Enrique H. Ruspini proposed a similarity-based semantics for fuzzy set... more In his 1991 seminal paper, Enrique H. Ruspini proposed a similarity-based semantics for fuzzy sets and approximate reasoning which has been extensively used by many other authors in various contexts. This brief note, which is our humble contribution to honor Ruspini's great legacy, describes some of the main developments in the field of logic that essentially rely on his ideas.
Logic, Language, Information, and Computation, 2019
In this paper we introduce and study finite Gödel algebras with operators (GAOs for short) and th... more In this paper we introduce and study finite Gödel algebras with operators (GAOs for short) and their dual frames. Taking into account that the category of finite Gödel algebras with homomorphisms is dually equivalent to the category of finite forests with order-preserving open maps, the dual relational frames of GAOs are forest frames: finite forests endowed with two binary (crisp) relations satisfying suitable properties. Our main result is a Jónsson-Tarski like representation theorem for these structures. In particular we show that every finite Gödel algebra with operators determines a unique forest frame whose set of subforests, endowed with suitably defined algebraic and modal operators, is a GAO isomorphic to the original one.
Studia Logica
In this paper we provide a simplified, possibilistic semantics for the logics K45(G), i.e. a many... more In this paper we provide a simplified, possibilistic semantics for the logics K45(G), i.e. a many-valued counterpart of the classical modal logic K45 over the [0, 1]-valued Gödel fuzzy logic $$\mathbf{G}$$ G . More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Gödel frames $$\langle W, \pi \rangle $$ ⟨ W , π ⟩ , where W is a non-empty set of worlds and $$\pi : W \mathop {\rightarrow }[0,1]$$ π : W → [ 0 , 1 ] is a possibility distribution on W. We provide decidability results as well. Moreover, we show that all the results also apply to the extension of K45(G) with the axiom (D), provided that we restrict ourselves to normalised Gödel Kripke frames, i.e. frames $$\langle W, \pi \rangle $$ ⟨ W , π ⟩ where $$\pi $$ π satisfies the normalisation condition $$\sup _{w \in W} \pi (w) = 1$$ sup w ∈ W π ( w ) = 1 .
Soft Computing, 2019
This special issue is dedicated to Lluís Godo in the occasion of his 60th anniversary. Lluís is a... more This special issue is dedicated to Lluís Godo in the occasion of his 60th anniversary. Lluís is a man with solid academic foundations. He studied Mathematics at the University of Barcelona and Industrial Engineering at the Technical University of Catalonia, and throughout his academic life, he has been loyal to both traditions: the purely scientific and the applied. Even though he has published numerous theoretical works, he never shied away from finding how to model and solve a practical problem. Lluís enjoys a privileged intelligence, primed with a knack for recognizing significant ideas that he shares generously with his numerous PhD students, with everyone that collaborates with him and with anyone that attends one of his lectures. Lluís is an achiever: "he is always on", quipped someone who knows him well. And this is something that-B Carles Noguera
Neuroinformatics
Researchers in neuroscience have a growing number of datasets available to study the brain, which... more Researchers in neuroscience have a growing number of datasets available to study the brain, which is made possible by recent technological advances. Given the extent to which the brain has been studied, there is also available ontological knowledge encoding the current state of the art regarding its different areas, activation patterns, key words associated with studies, etc. Furthermore, there is an inherent uncertainty associated with brain scans arising from the mapping between voxels-3D pixels-and actual points in different individual brains.
La teoría de cambio de creencias irrumpe en la lógica filosófica y la inteligencia artificial en ... more La teoría de cambio de creencias irrumpe en la lógica filosófica y la inteligencia artificial en la última década. El paso inicial fue provisto por Levi [Lev80] y Alchourrón, Gardenfors y Makinson en [AGM85] (comúnmente llamado el modelo AGM). Posteriormente, Levi propone un modelo de creencias que difiere en importantes aspectos del modelo AGM [Lev91]. En [H095], Hansson y Olsson muestran una comparación entre ambos modelos, y crean una caracterización axiomática de las funciones Levi-contraction. En dicho artículo muestran que toda contracción AGM es una Levi-contractions y ambas posturas están confrontadas por el polémico postulado de Recovery. A medio camino entre ambas, en [Fer95] Fermé define las funciones semi-contraction, donde si bien no se satisface el postulado de Recovery, se preserva la idea de mínima pérdida. En este artículo proveeremos un método para construir funciones semi-contraction (basado en las construcciones ''meet'' de AGM y los conjuntos saturables de Levi) y su caracterización axiomática. 678 3er. Worlcshop sobre Aspectos Teórico~ t:fe la Inteligencia Artificial
The aim of this contribution is to present our representation for finite Gödel algebras with oper... more The aim of this contribution is to present our representation for finite Gödel algebras with operators and to present further research lines in this direction. In particular, we first discuss on a possible way to extend of the same to the whole family of Gödel algebras with operators (the so defined variety will be denoted by GAO) and secondly we present a logic, denoted by GK¿,¿¿ being its syntactic counterpart
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Papers by Ricardo Oscar Rodriguez