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An Object-Oriented Approach to Counter-Model Constructions in A Fragment of Natural Language

Year 2015, , 0 - 0, 22.12.2015
https://doi.org/10.17798/beufen.98426

Abstract

This article presents a technical construction of reasonings and counter-models for some sen-tenteces called fragments as in [10] in English. We bring speaking English and logical inferences together in computer based approach to natural language. We give not only the infrences in the language [7] but also counter-model constructions in case of no inference from input sentences. Approach of this construction considers usage of minimal set elements.

References

  • Andrade, E. J. and Becerra, E., 2007, Corcoran's Aristotelian syllogistic as a subsystem of first-order logic, Revista Colombiana de Matematicas, 41(1): pp. 67-80.
  • Aristotle, Categories, 1984, The complete works of Aristotle, Princeton University Press, (In J. Barnes (Ed.), vol. 1, 1256 p.
  • Bird, S., 2006, NLTK: the natural language toolkit. In Proceedings of the COLING/ACL on Interactive presentation sessions, Association for Computational Linguistics, pp. 69-72.
  • Hopcroft, J. E., Motwani, R. and Ullman, J. D., 2001, Introduction to Automata Theory, Languages and Computation. ACM SIGACT News, 32(1), pp. 60-65.
  • J. Corcoran, 1972, Completeness of an ancient logic, Journal of Symbolic Logic 37, 696-702
  • Lukasiewicz, J., 1951, Aristotle's syllogistic from the standpoint of modern formal logic, Clarendon Press, Oxford.
  • Moss, L. S., 2008, Completeness theorems for syllogistic fragments, eds. Logics for linguistic structures. Vol. 201. Walter de Gruyter, pp. 143-175.
  • Moss, L. S., 2011 Syllogistic logic with complements, Games, Norms and Reasons. Springer Netherlands, pp. 179-197.
  • Pratt-Hartmann, I., 2004, Fragments of language, Journal of Logic, Language and Information, 13.2: 207-223.
  • Pratt-Hartmann, I. , 2004, Fragments of language, Journal of Logic, Language and Information, 13.2, 207-223.
  • Pratt-Hartmann, I. and Moss, L. S., 2009, Logics for the Relational Syllogistic, The Review of Symbolic Logic, 2.04: pp. 647-683.
  • Python Software Foundation, Python Language Reference, version 2.7. Available at http://www.python.org.
  • R. Smith, Categories, 1989, Aristotle's Prior Analytics, Hackett Publishing Company, 320p.
  • Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, 1989, Introduction to Algorithms, The MIT Press and McGraw-Hill Book Company, 597p.
  • W. A. Stein et al., 2015, Sage Mathematics Software, The Sage Development Team, http://www.sagemath.org
Year 2015, , 0 - 0, 22.12.2015
https://doi.org/10.17798/beufen.98426

Abstract

References

  • Andrade, E. J. and Becerra, E., 2007, Corcoran's Aristotelian syllogistic as a subsystem of first-order logic, Revista Colombiana de Matematicas, 41(1): pp. 67-80.
  • Aristotle, Categories, 1984, The complete works of Aristotle, Princeton University Press, (In J. Barnes (Ed.), vol. 1, 1256 p.
  • Bird, S., 2006, NLTK: the natural language toolkit. In Proceedings of the COLING/ACL on Interactive presentation sessions, Association for Computational Linguistics, pp. 69-72.
  • Hopcroft, J. E., Motwani, R. and Ullman, J. D., 2001, Introduction to Automata Theory, Languages and Computation. ACM SIGACT News, 32(1), pp. 60-65.
  • J. Corcoran, 1972, Completeness of an ancient logic, Journal of Symbolic Logic 37, 696-702
  • Lukasiewicz, J., 1951, Aristotle's syllogistic from the standpoint of modern formal logic, Clarendon Press, Oxford.
  • Moss, L. S., 2008, Completeness theorems for syllogistic fragments, eds. Logics for linguistic structures. Vol. 201. Walter de Gruyter, pp. 143-175.
  • Moss, L. S., 2011 Syllogistic logic with complements, Games, Norms and Reasons. Springer Netherlands, pp. 179-197.
  • Pratt-Hartmann, I., 2004, Fragments of language, Journal of Logic, Language and Information, 13.2: 207-223.
  • Pratt-Hartmann, I. , 2004, Fragments of language, Journal of Logic, Language and Information, 13.2, 207-223.
  • Pratt-Hartmann, I. and Moss, L. S., 2009, Logics for the Relational Syllogistic, The Review of Symbolic Logic, 2.04: pp. 647-683.
  • Python Software Foundation, Python Language Reference, version 2.7. Available at http://www.python.org.
  • R. Smith, Categories, 1989, Aristotle's Prior Analytics, Hackett Publishing Company, 320p.
  • Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, 1989, Introduction to Algorithms, The MIT Press and McGraw-Hill Book Company, 597p.
  • W. A. Stein et al., 2015, Sage Mathematics Software, The Sage Development Team, http://www.sagemath.org
There are 15 citations in total.

Details

Journal Section Articles
Authors

Selçuk Topal

Publication Date December 22, 2015
Submission Date April 20, 2015
Published in Issue Year 2015

Cite

IEEE S. Topal, “An Object-Oriented Approach to Counter-Model Constructions in A Fragment of Natural Language”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 4, no. 2, 2015, doi: 10.17798/beufen.98426.



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