Warianty tytułu
Języki publikacji
Abstrakty
The authors investigate the properties of first-order logic having its semantics based on a generalized (partial) approximation of sets. The goal of the investigation in this article is to compare the classical first-order semantics with a partial and lower approximation-based one. The idea is that lower approximation represents the reliable knowledge, so the reasoning used by the lower approximation may be valid or may be valid with some limitations. First, the authors show an experimental result which confute the previous supposition and the result of an algorithm which generates refutations for some well-known valid arguments: the 12 syllogisms of Aristotle. We think that these syllogisms represent the most common usage of categorical statements. A language with single-level quantification is constructed, as syllogisms can be formalized using this language. Based on the experimental results, the authors suggest some modifications of the semantics if the goal is to approximate the classical case.(original abstract)
Rocznik
Tom
Strony
35--40
Opis fizyczny
Twórcy
autor
- University of Debrecen, Hungary
autor
- University of Debrecen, Hungary
Bibliografia
- Chakraborty, M.K., Banerjee, M., "Rough logic with rough quantifiers," Bull. Polish Acad. Sc. (Math.), 41, 4, pp. 305-315, 1993
- Banerjee, M., Chakraborty, M.K.: "Rough logics: a survey with further directions," in: Incomplete Information: Rough Set Analysis, Or¸sowska, E. (ed.), Physica, Springer-Verlag, Heidelberg, pp. 579-600, 1998
- Yao, Y.Y.: "On generalizing rough set theory," Proceedings of the 9th International Conference Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2003). LNAI 2639, Springer-Verlag, pp. 44-51, 2003
- Yao, Y.Y.: "Information granulation and rough set approximation," International Journal of Intelligent Systems 16 (1), pp. 87-104, 2001
- Kádek, T., Mihálydeák, T.: "Some Fundamental Laws of Partial First- Order Logic Based on Set Approximations," in Rough Sets and Current Trends in Computing, Lecture Notes in Computer Science Volume 8536, Cornelis, C., Kryszkiewicz, M., Slezak, D., Menasalvas Ruiz, E., Bello, R., Shang, L. (eds.) 9th International Conference, RSCTC 2014, Granada and Madrid, Spain, pp. 47-58, 2014
- van Rooij, R.: "The propositional and relational syllogistic," Logique et Analyse, 55, pp. 85-108, 2012
- Düntsch, I., Gediga, G.: "Approximation operators in qualitative data analysis," in Theory and Applications of Relational Structures as Knowledge Instruments. Volume 2929 of Lecture Notes in Computer Science, de Swart, H.C.M., Orlowska, E., Schmidt, G., Roubens, M., (eds.) Springer, pp. 214-230, 2003
- Csajbók, Z., Mihálydeák, T.: "Fuzziness in Partial Approximation Framework," in Annals of Computer Science and Information Systems, Maria Ganzha, Leszek Maciaszek, Marcin Paprzycki (eds.) Volume 1: Proceedings of the 2013 Federated Conference on Computer Science and Information Systems (FedCSIS). pp. 35-41, 2013
- Maienborn C., Heusinger K., Portner P. (eds.): Semantics, 3, 2012, Walter de Gruyter GmbH, Berlin/Boston, ISBN 978-3-11-025337-5
- Mihálydeák, T.: "Partial first-order logic relying on optimistic, pessimistic and average partial membership functions," in Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology Pasi, G., Montero, J., Ciucci, D. (eds.) (EUSFLAT 2013), 2013 ISBN (on-line): 978-90786-77-78-9 doi:10.2991/eusflat.2013.53
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171419062