17 found
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  1.  35
    Hybrid Logics: Characterization, Interpolation and Complexity.Carlos Areces, Patrick Blackburn & Maarten Marx - 2001 - Journal of Symbolic Logic 66 (3):977-1010.
    Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called $\mathscr{H}(\downarrow, @)$ . We show in detail that $\mathscr{H}(\downarrow, @)$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of Ehrenfeucht-Fraisse game, and an enriched notion of (...)
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  2.  8
    Repairing the Interpolation Theorem in Quantified Modal Logic.Carlos Areces, Patrick Blackburn & Maarten Marx - 2003 - Annals of Pure and Applied Logic 124 (1-3):287-299.
    Quantified hybrid logic is quantified modal logic extended with apparatus for naming states and asserting that a formula is true at a named state. While interpolation and Beth's definability theorem fail in a number of well-known quantified modal logics , their counterparts in quantified hybrid logic have these properties. These are special cases of the main result of the paper: the quantified hybrid logic of any class of frames definable in the bounded fragment of first-order logic has the interpolation property, (...)
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  3.  62
    Completeness in Hybrid Type Theory.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2013 - Journal of Philosophical Logic (2-3):1-30.
    We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret $@_i$ in propositional and first-order hybrid logic. This means: interpret $@_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of type $a$ that (...)
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  4.  8
    The Expressive Power of Memory Logics.Carlos Areces, Diego Figueira, Santiago Figueira & Sergio Mera - 2011 - Review of Symbolic Logic 4 (2):290-318.
    We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic (↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain.
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  5. Coinductive Models and Normal Forms for Modal Logics.Carlos Areces & Daniel Gorín - 2010 - Journal of Applied Logic 8 (4):305-318.
  6.  65
    Analyzing the Core of Categorial Grammar.Carlos Areces & Raffaella Bernardi - 2004 - Journal of Logic, Language and Information 13 (2):121-137.
    Even though residuation is at the core of Categorial Grammar (Lambek, 1958), it is not always immediate to realize how standard logical systems like Multi-modal Categorial Type Logics (MCTL) (Moortgat, 1997) actually embody this property. In this paper, we focus on the basic system NL (Lambek, 1961) and its extension with unary modalities NL() (Moortgat, 1996), and we spell things out by means of Display Calculi (DC) (Belnap, 1982; Goré, 1998). The use of structural operators in DC permits a sharp (...)
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  7.  12
    Hybrid Type Theory: A Quartet in Four Movements.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2012 - Principia 15 (2):225.
    Este artigo canta uma canção — uma canção criada ao unir o trabalho de quatro grandes nomes na história da lógica: Hans Reichenbach, Arthur Prior, Richard Montague, e Leon Henkin. Embora a obra dos primeiros três desses autores tenha sido previamente combinada, acrescentar as ideias de Leon Henkin é o acréscimo requerido para fazer com que essa combinação funcione no nível lógico. Mas o presente trabalho não se concentra nas tecnicalidades subjacentes (que podem ser encontradas em Areces, Blackburn, Huertas, e (...)
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  8.  10
    Failure of Interpolation in Combined Modal Logics.Maarten Marx & Carlos Areces - 1998 - Notre Dame Journal of Formal Logic 39 (2):253-273.
    We investigate transfer of interpolation in such combinations of modal logic which lead to interaction of the modalities. Combining logics by taking products often blocks transfer of interpolation. The same holds for combinations by taking unions, a generalization of Humberstone's inaccessibility logic. Viewing first-order logic as a product of modal logics, we derive a strong counterexample for failure of interpolation in the finite variable fragments of first-order logic. We provide a simple condition stated only in terms of frames and bisimulations (...)
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  9.  23
    Completeness Results for Memory Logics.Carlos Areces, Santiago Figueira & Sergio Mera - 2012 - Annals of Pure and Applied Logic 163 (7):961-972.
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  10.  4
    Relation-Changing Modal Operators: Fig. 1.Carlos Areces, Raul Fervari & Guillaume Hoffmann - 2015 - Logic Journal of the IGPL 23 (4):601-627.
  11.  3
    Petrópolis, Rio de Janeiro, Brazil May 9–13, 2011.Carlos Areces, Carlos Caleiro & Gregory Chaitin - 2012 - Bulletin of Symbolic Logic 18 (1).
  12.  1
    Methods for Modalities 3.Carlos Areces - 2006 - Journal of Applied Logic 4 (3):215-217.
  13.  1
    Special Issue on Hybrid Logics.Carlos Areces & Patrick Blackburn - 2010 - Journal of Applied Logic 8 (4):303-304.
  14.  1
    19th Workshop on Logic, Language, Information and Computation (Wollic 2012).Luke Ong, Carlos Areces, Santiago Figueira & Ruy de Queiroz - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    Luke Ong, Carlos Areces, Santiago Figueira and Ruy de Queiroz The Bulletin of Symbolic Logic, Volume 19, Issue 3, Page 425-426, September 2013.
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  15. Completeness in Hybrid Type Theory.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2014 - Journal of Philosophical Logic 43 (2-3):209-238.
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  16. Symmetries in Modal Logics.Carlos Areces & Ezequiel Orbe - 2015 - Bulletin of Symbolic Logic 21 (4):373-401.
  17. Hybrid Type Theory: A Quartet in Four Movements DOI:10.5007/1808-1711.2011v15n2p225.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2012 - Principia: An International Journal of Epistemology 15 (2).
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