Combinators for Paraconsistent Attitudes

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    Abstract

    In order to analyse the semantics of natural language sentences a translation into a partial type logic using lexical and logical combinators is presented. The sentences cover a fragment of English with propositional attitudes like knowledge, belief and assertion. A combinator is a closed term of the lambda calculus possibly containing lexical and/or logical constants. Such combinators seem promising from both a cognitive and computational point of view. There is approximately one lexical combinator for each word, but just eleven logical combinators for the present fragment. The partiality is only used for embedded sentences expressing propositional attitudes, thereby allowing for inconsistency without explosion (also called paraconsistency), and is based on a few key equalities for the connectives giving four truth values (truth, falsehood, and undefinedness with negative and positive polarity; only the first truth value is designated, i.e. yields the logical truths).
    Original languageEnglish
    Title of host publicationLogical Aspects of Computational Linguistics : 4th International Conference, LACL 2001 Le Croisic, France, June 27–29, 2001, Proceedings
    EditorsPhilippe de Groote, Glyn Morrill, Christian Retoré
    PublisherSpringer
    Publication date2001
    Pages261-278
    ISBN (Print)978-3-540-42273-0
    ISBN (Electronic)978-3-540-48199-7
    DOIs
    Publication statusPublished - 2001

    Cite this

    Villadsen, J. (2001). Combinators for Paraconsistent Attitudes. In P. de Groote, G. Morrill, & C. Retoré (Eds.), Logical Aspects of Computational Linguistics: 4th International Conference, LACL 2001 Le Croisic, France, June 27–29, 2001, Proceedings (pp. 261-278). Springer. https://doi.org/10.1007/3-540-48199-0_16