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31Ecidence Logic: A New Look at Neighborhood StructuresIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 97-118. 1998.
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28Evidence Logic: A New Look at Neighborhood StructuresIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 97-118. 1998.
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11Non-finite Axiomatizability of Dynamic Topological LogicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 200-216. 1998.
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9Absolute Completeness of S4u for Its Measure-Theoretic SemanticsIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 100-119. 1998.
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6Kripke Models of Transfinite Provability LogicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 185-199. 1998.
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6Absolute Completeness of S4u for Its Measure-Theoretic SemanticsIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 100-119. 1998.
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3Non-finite Axiomatizability of Dynamic Topological LogicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 200-216. 1998.
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6Kripke Models of Transfinite Provability LogicIn Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 185-199. 1998.
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Retiology as Ideological Determinism in the Media: A Political Economy PerspectiveIn José Luís Garcia (ed.), Pierre Musso and the Network Society: From Saint-Simonianism to the Internet, Springer Verlag. 2016.
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14Use case cards: a use case reporting framework inspired by the European AI ActEthics and Information Technology 26 (2): 1-23. 2024.Despite recent efforts by the Artificial Intelligence (AI) community to move towards standardised procedures for documenting models, methods, systems or datasets, there is currently no methodology focused on use cases aligned with the risk-based approach of the European AI Act (AI Act). In this paper, we propose a new framework for the documentation of use cases that we call use case cards, based on the use case modelling included in the Unified Markup Language (UML) standard. Unlike other docum…Read more
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8The Baire Closure and its LogicJournal of Symbolic Logic 89 (1): 27-49. 2024.The Baire algebra of a topological space X is the quotient of the algebra of all subsets of X modulo the meager sets. We show that this Boolean algebra can be endowed with a natural closure operator, resulting in a closure algebra which we denote $\mathbf {Baire}(X)$. We identify the modal logic of such algebras to be the well-known system $\mathsf {S5}$, and prove soundness and strong completeness for the cases where X is crowded and either completely metrizable and continuum-sized or locally c…Read more
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15Tableaux for structural abductionLogic Journal of the IGPL 20 (2): 388-399. 2012.In this work, we shall study structural abduction and how ways of searching for solutions to the corresponding abductive problems could be modeled. Specifically, we shall define modal semantic tableaux for normal modal systems and study its applications to structural abduction. This method even makes structural abduction clearer and, as it shall be seen, when a radical change of logic is epistemologically required, the corresponding tableau will have pertinent information to suggest it
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20Well-orders in the transfinite Japaridze algebraLogic Journal of the IGPL 22 (6): 933-963. 2014.
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5What Academic Factors Influence Satisfaction With Clinical Practice in Nursing Students? Regressions vs. fsQCAFrontiers in Psychology 11. 2020.Clinical practices are considered one of the cornerstones in nurses' education. This study provides a framework to determine how factors in the academic environment, influence nursing student's satisfaction with their practices. A cross-sectional analytical study was conducted in a convenience sample of 574 nursing students at a private university in Valencia, during the 2016/2017 academic year, 79% were women. Two statistical methodologies were used for data analysis: hierarchical regression mo…Read more
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23The polytopologies of transfinite provability logicArchive for Mathematical Logic 53 (3-4): 385-431. 2014.Provability logics are modal or polymodal systems designed for modeling the behavior of Gödel’s provability predicate and its natural extensions. If Λ is any ordinal, the Gödel-Löb calculus GLPΛ contains one modality [λ] for each λ < Λ, representing provability predicates of increasing strength. GLPω has no non-trivial Kripke frames, but it is sound and complete for its topological semantics, as was shown by Icard for the variable-free fragment and more recently by Beklemishev and Gabelaia for t…Read more
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39The omega-rule interpretation of transfinite provability logicAnnals of Pure and Applied Logic 169 (4): 333-371. 2018.
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37Tangled modal logic for topological dynamicsAnnals of Pure and Applied Logic 163 (4): 467-481. 2012.
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18Models of transfinite provability logicJournal of Symbolic Logic 78 (2): 543-561. 2013.For any ordinal $\Lambda$, we can define a polymodal logic $\mathsf{GLP}_\Lambda$, with a modality $[\xi]$ for each $\xi < \Lambda$. These represent provability predicates of increasing strength. Although $\mathsf{GLP}_\Lambda$ has no Kripke models, Ignatiev showed that indeed one can construct a Kripke model of the variable-free fragment with natural number modalities, denoted $\mathsf{GLP}^0_\omega$. Later, Icard defined a topological model for $\mathsf{GLP}^0_\omega$ which is very closely rel…Read more
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43Hyperations, Veblen progressions and transfinite iteration of ordinal functionsAnnals of Pure and Applied Logic 164 (7-8): 785-801. 2013.Ordinal functions may be iterated transfinitely in a natural way by taking pointwise limits at limit stages. However, this has disadvantages, especially when working in the class of normal functions, as pointwise limits do not preserve normality. To this end we present an alternative method to assign to each normal function f a family of normal functions Hyp[f]=〈fξ〉ξ∈OnHyp[f]=〈fξ〉ξ∈On, called its hyperation, in such a way that f0=idf0=id, f1=ff1=f and fα+β=fα∘fβfα+β=fα∘fβ for all α, β.Hyperation…Read more
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50Dynamic topological logic of metric spacesJournal of Symbolic Logic 77 (1): 308-328. 2012.Dynamic Topological Logic ( $\mathcal{DTL}$ ) is a modal framework for reasoning about dynamical systems, that is, pairs 〈X, f〉 where X is a topological space and f: X → X a continuous function. In this paper we consider the case where X is a metric space. We first show that any formula which can be satisfied on an arbitrary dynamic topological system can be satisfied on one based on a metric space; in fact, this space can be taken to be countable and have no isolated points. Since any metric sp…Read more
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37Dynamic Topological Logic Interpreted over Minimal SystemsJournal of Philosophical Logic 40 (6): 767-804. 2011.Dynamic Topological Logic ( ) is a modal logic which combines spatial and temporal modalities for reasoning about dynamic topological systems , which are pairs consisting of a topological space X and a continuous function f : X → X . The function f is seen as a change in one unit of time; within one can model the long-term behavior of such systems as f is iterated. One class of dynamic topological systems where the long-term behavior of f is particularly interesting is that of minimal systems ; …Read more
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20A sound and complete axiomatization for Dynamic Topological LogicJournal of Symbolic Logic 77 (3): 947-969. 2012.Dynamic Topological Logic (DFH) is a multimodal system for reasoning about dynamical systems. It is defined semantically and, as such, most of the work done in the field has been model-theoretic. In particular, the problem of finding a complete axiomatization for the full language of DFH over the class of all dynamical systems has proven to be quite elusive. Here we propose to enrich the language to include a polyadic topological modality, originally introduced by Dawar and Otto in a different c…Read more
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20Predicativity through transfinite reflectionJournal of Symbolic Logic 82 (3): 787-808. 2017.Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use $[\lambda |X]_T^{\rm{\Lambda }}\varphi$ as a formalization of “φ is provable from T and an oracle for the set X, using ω-rules of nesting depth at most λ”.For a set of formulas Γ, define predicative oracle reflection for T over Γ ) to be the schema that asserts that, if X ⊆ ℕ, Λ is a well-order and φ ∈ Γ, then$$\forall \,\lambda < {\rm{\Lambda }}\,.$$In particular, define predicative oracle consistency ) as Pred…Read more
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42On Provability Logics with Linearly Ordered ModalitiesStudia Logica 102 (3): 541-566. 2014.We introduce the logics GLP Λ, a generalization of Japaridze’s polymodal provability logic GLP ω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP ω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP Λ and the decidability of GLP Λ for recursive orderings Λ. Further, we give a restricted axiomatization of the variable-free frag…Read more
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22The Dynamics of Epistemic Attitudes in Resource-Bounded AgentsStudia Logica 107 (3): 457-488. 2019.The paper presents a new logic for reasoning about the formation of beliefs through perception or through inference in non-omniscient resource-bounded agents. The logic distinguishes the concept of explicit belief from the concept of background knowledge. This distinction is reflected in its formal semantics and axiomatics: we use a non-standard semantics putting together a neighborhood semantics for explicit beliefs and relational semantics for background knowledge, and we have specific axioms …Read more
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16Strong completeness of provability logic for ordinal spacesJournal of Symbolic Logic 82 (2): 608-628. 2017.
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51Evidence and plausibility in neighborhood structuresAnnals of Pure and Applied Logic 165 (1): 106-133. 2014.The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an evidence logic for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a neighborhood semantics, where a neighborhood N indicates that the agent has reason to believe that the true state of the world lies in N. Further notions of relative plausibility between worlds and beliefs based on the latter ordering are then defined in terms of this …Read more