•  49
    Hybrid Logics: Characterization, Interpolation and Complexity
    with Carlos Areces and Maarten Marx
    Journal of Symbolic Logic 66 (3): 977-1010. 2001.
    Hybrid languages are expansions of propositional modal languages which can refer to worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work has focussed on a more constrained system called $\mathscr{H}$. We show in detail that $\mathscr{H}$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations and a syntactic characterization. The key result to emerge is that $\mathscr{H}$ corresponds to the fragment of first-o…Read more
  •  17
    Remarks on Gregory's “Actually” Operator
    with Marx Maarten
    Journal of Philosophical Logic 31 (3): 281-288. 2002.
    In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing “actually” operators, Journal of Philosophical Logic 30(1): 57–78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an “actually” o…Read more
  •  17
    Instructions for authors
    Journal of Logic, Language and Information 14 (1): 491-496. 2005.
  •  15
    Modal logic and model-theoretic syntax
    In Maarten de Rijke (ed.), Advances in Intensional Logic, Kluwer Academic Publishers. pp. 29--60. 1997.
  •  21
    Hybrid languages and temporal logic
    with M. Tzakova
    Logic Journal of the IGPL 7 (1): 27-54. 1999.
    Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages. Although developed in interesting ways by Robert Bull, and by the Sofia school , the method remains little known. In our view this has deprived temporal logic of a valuable tool.The aim of the paper is to explain why hybridization is useful in temporal logic. We make two major points, the first technical, the second conceptual. First, we show that hybridization gives rise to well-behaved log…Read more
  •  34
    Nominal tense logic
    Notre Dame Journal of Formal Logic 34 (1): 56-83. 1992.
  •  231
    Computational semantics
    with Johan Bos
    Theoria 18 (1): 27-45. 2003.
    In this article we discuss what constitutes a good choice of semantic representation, compare different approaches of constructing semantic representations for fragments of natural language, and give an overview of recent methods for employing inference engines for natural language understanding tasks
  •  68
    Arthur Prior and ‘Now’
    with Klaus Frovin Jørgensen
    Synthese 193 (11). 2016.
    On the 4th of December 1967, Hans Kamp sent his UCLA seminar notes on the logic of ‘now’ to Arthur N. Prior. Kamp’s two-dimensional analysis stimulated Prior to an intense burst of creativity in which he sought to integrate Kamp’s work into tense logic using a one-dimensional approach. Prior’s search led him through the work of Castañeda, and back to his own work on hybrid logic: the first made temporal reference philosophically respectable, the second made it technically feasible in a modal fra…Read more
  •  30
    How can computers distinguish the coherent from the unintelligible, recognize new information in a sentence, or draw inferences from a natural language passage? Computational semantics is an exciting new field that seeks answers to these questions, and this volume is the first textbook wholly devoted to this growing subdiscipline. The book explains the underlying theoretical issues and fundamental techniques for computing semantic representations for fragments of natural language. This volume wi…Read more
  •  26
    Rijke. PDL for ordered trees
    with Loredana Afanasiev, Ioanna Dimitriou, Gaiffe Evan, Goris Maarten, and Marx Maarten
    Journal of Applied Non-Classical Logics. forthcoming.
  •  60
    Modal logic
    Cambridge University Press. 2001.
    This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.
  •  2
    Editorial
    Journal of Logic, Language and Information 11 (1): 1-1. 2002.
  •  2
    Book Review (review)
    Journal of Logic, Language and Information 6 (3): 353-355. 1997.
  •  64
    Reichenbach, Prior and hybrid tense logic
    with Klaus Frovin Jørgensen
    Synthese 193 (11): 3677-3689. 2016.
    In this paper we argue that Prior and Reichenbach are best viewed as allies, not antagonists. We do so by combining the central insights of Prior and Reichenbach in the framework of hybrid tense logic. This overcomes a well-known defect of Reichenbach’s tense schema, namely that it gives multiple representations to sentences in the future perfect and the future-in-the-past. It also makes it easy to define an iterative schema for tense that allows for multiple points of reference, a possibility n…Read more
  •  15
    Special Issue on Hybrid Logics
    with Carlos Areces
    Journal of Applied Logic 8 (4): 303-304. 2010.
  •  65
    Modal Logic As Dialogical Logic
    Synthese 127 (1-2): 57-93. 2001.
    The title reflects my conviction that, viewed semantically,modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy. Nonetheless, by making use of ideas which trace back to Arthur Prior (notably the use of nominals, special proposition symbols which ‘name’ worlds) I will show how to lift the dia…Read more
  •  62
    Inference and computational semantics
    with Michael Kohlhase
    Journal of Logic, Language and Information 13 (2): 117-120. 2004.
  •  51
    Computational Semantics
    with Johan Bos
    Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 18 (1): 27-45. 2010.
    ...
  •  13
    Upcoming Themes
    Journal of Logic, Language and Information 8 (2): 263-263. 1999.
  •  67
    Arthur Prior and Hybrid Logic
    Synthese 150 (3): 329-372. 2006.
    Contemporary hybrid logic is based on the idea of using formulas as terms, an idea invented and explored by Arthur Prior in the mid-1960s. But Prior’s own work on hybrid logic remains largely undiscussed. This is unfortunate, since hybridisation played a role that was both central to and problematic for his philosophical views on tense. In this paper I introduce hybrid logic from a contemporary perspective, and then examine the role it played in Prior’s work.
  • REVIEWS-Modal logic
    with M. De Rijke, Y. Venema, and Marcus Kracht
    Bulletin of Symbolic Logic 8 (2): 299-300. 2002.
  •  124
    Completeness in Hybrid Type Theory
    with Carlos Areces, Antonia Huertas, and María Manzano
    Journal of Philosophical Logic (2-3): 1-30. 2013.
    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 rigid…Read more
  •  176
    Modal Logic: Graph. Darst
    with Maarten de Rijke and Yde Venema
    Cambridge University Press. 2001.
    This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.
  •  18
    Hybrid completeness
    with M. Tzakova
    Logic Journal of the IGPL 6 (4): 625-650. 1998.
    In this paper we discuss two hybrid languages, ℒ and ℒ, and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to 'label' states by using A and ↓ to bind special state variables.This paper explores the consequences of hybridization for completeness. As we shall show, the challenge is to blend the modal idea …Read more
  •  29
    Linguistics, Logic and Finite Trees
    Logic Journal of the IGPL 2 (1): 3-29. 1994.
    A modal logic is developed to deal with finite ordered binary trees a they are used in linguistics. A modal language is introduced with operators for the ‘mother of’, ‘first daughter of’ and ‘second daughter of’ relations together with their transitive reflexive closures. The relevant class of tree models is defined and three linguistic applications of this language are discussed: context free grammars, command relations, and trees decorated with feature structures. An axiomatic proof system is …Read more
  • Characterization, Interpolation and Complexity, by Carlos Areces, Patrick Blackburn and Maarten Marx
    with Maarten Marx Hybrid Logic
    Journal of Symbolic Logic 66 (3): 977-1010. 2001.
  •  26
    Zooming in, zooming out
    with Maarten De Rijke
    Journal of Logic, Language and Information 6 (1): 5-31. 1997.
    This is an exploratory paper about combining logics, combining theories and combining structures. Typically when one applies logic to such areas as computer science, artificial intelligence or linguistics, one encounters hybrid ontologies. The aim of this paper is to identify plausible strategies for coping with ontological richness.