24 found
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  1.  13
    On Provability Logics with Linearly Ordered Modalities.Lev D. Beklemishev, David Fernández-Duque & Joost J. Joosten - 2014 - Studia Logica 102 (3):541-566.
    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 fragment (...)
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  2.  29
    Evidence and Plausibility in Neighborhood Structures.Johan van Benthem, David Fernández-Duque & Eric Pacuit - 2014 - Annals of Pure and Applied Logic 165 (1):106-133.
    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 (...)
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  3.  20
    The Omega-Rule Interpretation of Transfinite Provability Logic.David Fernández-Duque & Joost J. Joosten - 2018 - Annals of Pure and Applied Logic 169 (4):333-371.
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  4.  3
    Models of Transfinite Provability Logic.David Fernández-Duque & Joost J. Joosten - 2013 - Journal of Symbolic Logic 78 (2):543-561.
    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 related to Ignatiev's. In this paper we show how to extend these constructions for arbitrary $\Lambda$. (...)
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  5.  22
    Hyperations, Veblen Progressions and Transfinite Iteration of Ordinal Functions.David Fernández-Duque & Joost J. Joosten - 2013 - Annals of Pure and Applied Logic 164 (7-8):785-801.
    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.Hyperations are a refinement of the Veblen hierarchy (...)
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  6.  8
    Ecidence Logic: A New Look at Neighborhood Structures.Johan van Benthem, David Fernández-Duque & Eric Pacuit - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Justin Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 97-118.
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  7.  20
    Tangled Modal Logic for Topological Dynamics.David Fernández-Duque - 2012 - Annals of Pure and Applied Logic 163 (4):467-481.
  8.  11
    The Polytopologies of Transfinite Provability Logic.David Fernández-Duque - 2014 - Archive for Mathematical Logic 53 (3-4):385-431.
    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 the full logic. In (...)
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  9.  10
    Predicativity Through Transfinite Reflection.Andrés Cordón-Franco, David Fernández-Duque, Joost J. Joosten & Francisco Félix Lara-martín - 2017 - Journal of Symbolic Logic 82 (3):787-808.
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  10. Absolute Completeness of S4u for Its Measure-Theoretic Semantics.David Fernández-Duque - 2010 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 100-119.
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  11.  27
    Dynamic Topological Logic Interpreted Over Minimal Systems.David Fernández-Duque - 2011 - Journal of Philosophical Logic 40 (6):767-804.
    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 (...)
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  12.  6
    A Sound and Complete Axiomatization for Dynamic Topological Logic.David Fernández-Duque - 2012 - Journal of Symbolic Logic 77 (3):947-969.
    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 (...)
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  13.  1
    Kripke Models of Transfinite Provability Logic.David Fernández-Duque & Joost J. Joosten - 2012 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 185-199.
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  14.  6
    Tableaux for Structural Abduction.Ángel Nepomuceno-fernández, Francisco Salguero-Lamillar & David Fernández-Duque - 2012 - Logic Journal of the IGPL 20 (2):388-399.
    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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  15. Ecidence Logic: A New Look at Neighborhood Structures.Johan van Benthem, David Fernández-Duque & Eric Pacuit - 2012 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 97-118.
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  16.  11
    The Dynamics of Epistemic Attitudes in Resource-Bounded Agents.Philippe Balbiani, David Fernández-Duque & Emiliano Lorini - 2019 - Studia Logica 107 (3):457-488.
    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 in the logic highlighting the relationship between the two concepts. Mental (...)
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  17.  11
    Strong Completeness of Provability Logic for Ordinal Spaces.Juan P. Aguilera & David Fernández-Duque - 2017 - Journal of Symbolic Logic 82 (2):608-628.
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  18.  31
    Dynamic Topological Logic of Metric Spaces.David Fernández-Duque - 2012 - Journal of Symbolic Logic 77 (1):308-328.
    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 (...)
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  19.  6
    Verification Logic: An Arithmetical Interpretation for Negative Introspection.Juan Pablo Aguilera & David Fernández-Duque - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 1-20.
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  20.  6
    Axiomatizing the Lexicographic Products of Modal Logics with Linear Temporal Logics.Philippe Balbiani & David Fernández-Duque - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 78-96.
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  21.  3
    Kripke Models of Transfinite Provability Logic.David Fernández-Duque & Joost J. Joosten - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 185-199.
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  22.  3
    Non-Finite Axiomatizability of Dynamic Topological Logic.David Fernández-Duque - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 200-216.
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  23.  2
    Absolute Completeness of S4u for Its Measure-Theoretic Semantics.David Fernández-Duque - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 100-119.
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  24. Non-Finite Axiomatizability of Dynamic Topological Logic.David Fernández-Duque - 2012 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 200-216.
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