INVERSION FUNCTION OF MDS FOR SENTENCES ANALYSIS
Erqing Xu
2010
Abstract
Traditional sentence analysis refers to finding the sentence structure for a given sentence. A question different from this is: given a sentence Curry-Horwad isomorphic with a type, can we establish the proof tree representing the sentence? Therefore, this paper combines the extensional Kripke interpretation and MDS (Minimalist Deductive System); derives the Kripke model of MDS; provides the applicable inversion function such that we are able to obtain the proof tree of typed -terms which represents sentence structure; and demonstrates that the product-free proof trees obtained with inversion function of MDS enjoy the property of Church-Rosser equality. Application examples demonstrate that our work is valid. The main difference between our work and traditional sentence analysis approach is that the objects of analysis are different. The object of our work is: Kripke model of MDS and type of sentence satisfied by assignment. But the object of traditional sentence analysis approach is sentence. This paper enlarges the range of application of sentence analysis, improves sentence analysis approach, enhances natural language understanding, and thus is meaningful. Our work has not been seen in literature.
References
- Hindley, J. R., Seldin, J. P., 1986. Introduction to combinators and ?-calculus, Cambridge University Press. Cambridge.
- Jiang, Y., Pan, H. H., 1998. An introduction to formal semantics, Chinese Social Science Press. Beijing.
- Retore, C., 2005. The logic of categorical grammars. In Rapport de recherche, No. 5703. INRIA.
- Lecomte, A., 2004. Rebuilding MP on a logical ground. In Research on language and computation. Vol 2, pp. 27-55.
- Morrill, G. V., 1994. Type logical grammar-categorical logic of signs, Kluwer Academic Publishers.
- Qu, Y. W., 1998. Fundamentals and formal descriptions of formal semantics, Science Press. Beijing.
- Ranta, A., 1994. Type-theoretical grammar, Oxford University Press. Oxford.
- Simpson, A. K., 1992. Kripke semantics for a logical framework. In Paper presented at Workshop on Types for Proofs and Programs. pp. 313-340, Baastad, Sweden.
- Wang, H. P., 1997. Mathematical Logic, Peking University Press. Beijing.
- Coquand, C., 2002. A formalized proof of soundness and completeness of a simply typed Lambda-calculus with explicit substitutions. In High-order and Symbolic Computation. Vol 15, pp. 57-90.
Paper Citation
in Harvard Style
Xu E. (2010). INVERSION FUNCTION OF MDS FOR SENTENCES ANALYSIS . In Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-674-021-4, pages 151-156. DOI: 10.5220/0002590401510156
in Bibtex Style
@conference{icaart10,
author={Erqing Xu},
title={INVERSION FUNCTION OF MDS FOR SENTENCES ANALYSIS },
booktitle={Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2010},
pages={151-156},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002590401510156},
isbn={978-989-674-021-4},
}
in EndNote Style
TY - CONF
JO - Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - INVERSION FUNCTION OF MDS FOR SENTENCES ANALYSIS
SN - 978-989-674-021-4
AU - Xu E.
PY - 2010
SP - 151
EP - 156
DO - 10.5220/0002590401510156