13 found
  1.  65
    Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
    Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic (...)
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  2.  64
    Propositions as Games as Types.Aarne Ranta - 1988 - Synthese 76 (3):377 - 395.
    Without violating the spirit of Game-Theoretical semantics, its results can be re-worked in Martin-Löf''s Constructive Type Theory by interpreting games as types of Myself''s winning strategies. The philosophical ideas behind Game-Theoretical Semantics in fact highly recommend restricting strategies to effective ones, which is the only controversial step in our interpretation. What is gained, then, is a direct connection between linguistic semantics and computer programming.
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  3. Natural Languages as Collections of Resources.Robin Cooper & Aarne Ranta - unknown
    We propose a shift in perspective from the view of natural languages as formal languages to natural languages as a collection of resources for constructing local languages for use in particular situations. This is suggested by our experience constructing natural language grammars for particular applications using the Grammatical Framework. It points to a research programme investigating how such resources play a role in linguistic innovation by agents constructing situation-specific local languages and how they can be made dynamic, modified by the (...)
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  4.  84
    Type Theory and Universal Grammar.Aarne Ranta - 2009 - Philosophia Scientiae:115-131.
    The paper takes a look at the history of the idea of universal grammar and compares it with multilingual grammars, as formalized in the Grammatical Framework, GF. The constructivist idea of formalizing math- ematics piece by piece, in a weak logical framework, rather than trying to reduce everything to one single strong theory, is the model that guides the development of grammars in GF.
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  5.  31
    Intuitionistic Categorial Grammar.Aarne Ranta - 1991 - Linguistics and Philosophy 14 (2):203 - 239.
  6.  62
    Constructing Possible Worlds.Aarne Ranta - 1991 - Theoria 57 (1-2):77-99.
  7.  12
    Type Theory and Universal Grammar.Aarne Ranta - 2006 - Philosophia Scientae:115-131.
  8.  28
    Dialogue Systems as Proof Editors.Aarne Ranta & Robin Cooper - 2004 - Journal of Logic, Language and Information 13 (2):225-240.
    This paper shows how a dialogue system for information-seekingdialogues can be implemented in a type-theory-based syntax editor,originally developed for editing mathematical proofs.The implementation gives a simple logical metatheory tosuch dialogue systems and also suggests new functions forthem, e.g., a local undo operation. The method developed provides alogically based declarative way of implementing simple dialoguesystems that is easy to port to new domains.
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  9.  34
    Pgf: A Portable Run-Time Format for Type-Theoretical Grammars. [REVIEW]Krasimir Angelov, Björn Bringert & Aarne Ranta - 2010 - Journal of Logic, Language and Information 19 (2):201-228.
    Portable Grammar Format (PGF) is a core language for type-theoretical grammars. It is the target language to which grammars written in the high-level formalism Grammatical Framework (GF) are compiled. Low-level and simple, PGF is easy to reason about, so that its language-theoretic properties can be established. It is also easy to write interpreters that perform parsing and generation with PGF grammars, and compilers converting PGF to other formats. This paper gives a concise description of PGF, covering syntax, semantics, and parser (...)
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  10. Implementing Urdu Grammar as Open Source Software.Muhammad Humayoun, Harald Hammarström & Aarne Ranta - unknown
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  11.  37
    Syntactic Calculus with Dependent Types.Aarne Ranta - 1998 - Journal of Logic, Language and Information 7 (4):413-431.
    The aim of this study is to look at the the syntactic calculus of Bar-Hillel and Lambek, including semantic interpretation, from the point of view of constructive type theory. The syntactic calculus is given a formalization that makes it possible to implement it in a type-theoretical proof editor. Such an implementation combines formal syntax and formal semantics, and makes the type-theoretical tools of automatic and interactive reasoning available in grammar.In the formalization, the use of the dependent types of constructive type (...)
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  12. Type-Theoretical Grammar.Aarne Ranta - 1994
  13.  29
    Type-Theoretical Interpretation and Generalization of Phrase Structure Grammar.Aarne Ranta - 1995 - Logic Journal of the IGPL 3 (2-3):319-342.
    In this paper, we shall present a generalization of phrase structure grammar, in which all functional categories have type restrictions, that is, their argument types are specific domains. In ordinary phrase structure grammar, there is just one universal domain of individuals. The grammar does not make a distinction between verbs and adjectives in terms of domains of applicability. Consequently, it fails to distinguish between sentences like every line intersects every line, which is well typed, and every line intersects every point, (...)
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