1994
DOI: 10.1093/jigpal/2.1.3
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Linguistics, Logic and Finite Trees

Abstract: A modal logic is developed to deal with nite ordered binary trees as they are used in (computational) linguistics. A modal language is introduced with operators for the`mother of',` rst daughter of' and`second daughter of' relations together with their transitive re exive closures. The relevant class of tree models is de ned 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 given … Show more

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Cited by 79 publications
(62 citation statements)
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“…Parsing takes place on a left-to-right basis with a direct and dynamic mapping from linearly-ordered words to structured semantic representations on these trees. The Logic of Finite Trees (LOFT, Blackburn andMeyer-Viol 1994, Kempson et al 2001) is used to annotate tree nodes and makes it possible to explicitly state relations that hold between the tree nodes. An overview of the tree annotations employed in this paper is provided in (1) below.…”
Section: Dynamic Syntax 21 the Tools Of The Frameworkmentioning
confidence: 99%
“…Parsing takes place on a left-to-right basis with a direct and dynamic mapping from linearly-ordered words to structured semantic representations on these trees. The Logic of Finite Trees (LOFT, Blackburn andMeyer-Viol 1994, Kempson et al 2001) is used to annotate tree nodes and makes it possible to explicitly state relations that hold between the tree nodes. An overview of the tree annotations employed in this paper is provided in (1) below.…”
Section: Dynamic Syntax 21 the Tools Of The Frameworkmentioning
confidence: 99%
“…Nevertheless, there are aspects of the theory which display isolationist modelling tendencies. For instance, the semantic typing system (a modified version of Montague grammar) is defined separately from the modal logic definitions involved with the tree formalism which is a variant of the Logic of Finite Trees (Blackburn and Meyer-Viol 1994). 15 In DS, linguists are still in the business of developing minimal models and attempting to "generate" (in the sense of minimal determination) the properties or explanations thereof by offering a causal basis which ignores even potentially relevant or related material.…”
Section: Modelling Dynamicsmentioning
confidence: 99%
“…Such trees are formalised using LOFT (Blackburn and Meyer-Viol 1994), a modal logic designed to allow the processor to refer to partial, complete or required tree structure. LOFT makes available modal operators h:i,h;i defining the concepts of mother and daughter nodes and their iterated underspecified counterparts, h" Ã i;h# Ã i, 8 defining the notions be dominated by and dominate, thus allowing for partially specified trees in terms of structure.…”
Section: Content Representationsmentioning
confidence: 99%