Abstract
In this paper we keep on discussing satisfiability of conditions by objects when information about the situation considered, including objects of some sort and concepts comprised of them, is incomplete. Our approach to satisfiability is that of concept modelling and we have a rough granular view on the problem. Objects considered are known partially, in terms of values of attributes of Pawlak information systems. An additional knowledge (domain knowledge) is assumed to be available. We choose descriptor languages for Pawlak information systems as specification languages in which we will express conditions about objects and concepts.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Hornby, A.S. (ed.): Oxford Advanced Learner’s Dictionary of Current English, 7th edn. with Vocabulary Trainer. Oxford University Press, Oxford (2007)
Klir, G.J., Wierman, M.J.: Uncertainty-based Information: Elements of Generalized Information Theory. Physica, Heidelberg (1998)
Keefe, R.: Theories of Vagueness. Cambridge University Press, Cambridge (2000)
Demri, S., Orłowska, E. (eds.): Incomplete Information: Structure, Inference, Complexity. Springer, Heidelberg (2002)
Kephart, J.O.: Research challenges of autonomic computing. In: Proc. 27th Int. Conf. on Software Engineering (ICSE 2005), May 2005, pp. 15–22. ACM Press, New York (2005)
Liu, J.: Autonomy-oriented computing (AOC): The nature and implications of a paradigm for self-organized computing. In: Proc. 4th Int. Conf. on Natural Computation (ICNC 2008), Jinan, China, October 2008, pp. 3–11. IEEE Computer Society Press, Los Alamitos (2008)
Liu, J., Jin, X., Tsui, K.C.: Autonomy Oriented Computing: From Problem Solving to Complex Systems Modeling. Kluwer, Dordrecht (2005)
Jankowski, A., Skowron, A.: A wistech paradigm for intelligent systems. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J.W., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 94–132. Springer, Heidelberg (2007)
Kondratoff, Y., Michalski, R.S. (eds.): Machine Learning: An Artificial Intelligence Approach, vol. 3. Morgan Kaufmann, San Mateo (1990)
Michalski, R.S., Carbonell, T.J., Mitchell, T.M. (eds.): Machine Learning: An Artificial Intelligence Approach. TIOGA Publ., Palo Alto (1983)
Michalski, R.S., Tecuci, G. (eds.): Machine Learning – A Multistrategy Approach, vol. 4. Morgan Kaufmann, San Mateo (1994)
Mitchell, T.M.: Machine Learning. McGraw-Hill, Portland (1998)
Cios, K.J., Pedrycz, W., Swiniarski, R.W., Kurgan, L.A.: Data Mining: A Knowledge Discovery Approach. Springer Science + Business Media, LLC (2007)
Kloesgen, W., Żytkow, J.: Handbook of Knowledge Discovery and Data Mining. Oxford University Press, Oxford (2002)
Maimon, O., Rokach, L. (eds.): The Data Mining and Knowledge Discovery Handbook. Springer, Heidelberg (2005)
Kahneman, D., Slovic, P., Tversky, A. (eds.): Judgment Under Uncertainty: Heuristics and Biases. Cambridge University Press, New York (1982)
Kant, I.: Critique of Judgment. Clarendon, Oxford (1988); Transl. by Meredith, J. C.
Plous, S.: The Psychology of Judgement and Decision Making. McGraw-Hill, New York (1993)
Thiele, L.P.: The Heart of Judgment: Practical Wisdom, Neuroscience, and Narrative. Cambridge University Press, New York (2006)
Tarski, A.: The semantical concept of truth and the foundations of semantics. Philosophy and Phenomenological Research 4, 341–375 (1944)
Banerjee, M., Chakraborty, M.K.: Rough consequence and rough algebra. In: Ziarko, W. (ed.) Proc. 2nd Int. Workshop on Rough Sets and Knowledge Discovery (RSKD 1993), Banff, Canada, October 1993, pp. 196–207. Springer/British Computer Society, Berlin/London (1994)
Barwise, J., Seligman, J.: Information Flow: The Logic of Distributed Systems. Cambridge University Press, Cambridge (1997)
Belnap, N.D.: A useful four-valued logic. In: Dunn, J.M., Epstein, G. (eds.) Modern Uses of Multiple-valued Logic, pp. 8–37. Reidel, Dordrecht (1977)
Bolc, L., Borowik, P.: Many-valued Logics, vol. 1. Springer, Berlin (1992)
Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980); Reprinted with corrections in 1988
Emerson, E.A.: Temporal and modal logic. In: Leeuwen, J.v. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 995–1072. Elsevier/The MIT Press (1990)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. The MIT Press, Cambridge (1995)
Kleene, S.C.: Introduction to Metamathematics. North-Holland, Amsterdam (1952)
Kripke, S.A.: Semantical analysis of modal logic I: Normal propositional calculi. Zeit. Math. Logik. Grund. 9, 67–96 (1963)
Kripke, S.A.: Semantical analysis of modal logic II: Non-normal propositional calculi. In: Addison, J.W., et al. (eds.) The Theory of Models, pp. 206–220. North-Holland, Amsterdam (1965)
Łukasiewicz, J.: On three-valued logic (in Polish). Ruch Filozoficzny 5, 170–171 (1920); English transl. in [132], pp. 87–88
Łukasiewicz, J.: Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls. C. R. Soc. Sci. Lettr. Varsovie 23, 51–77 (1930); English transl. in [132], pp. 153–178
Pavelka, J.: On fuzzy logic I. Zeit. Math. Logic Grund. Math. 25, 45–52 (1979); See also parts II and III in the same volume, pp. 119–134, 447–464
Pawlak, Z.: Rough logic. Bull. Polish Acad. Sci. Tech. 35, 253–258 (1987)
Pogorzelski, W.A.: Notions and Theorems of Elementary Formal Logic. Białystok Division of Warsaw University, Białystok (1994)
Rescher, N.: Many-valued Logic. McGraw-Hill, New York (1969)
Rosser, J.B., Turquette, A.R.: Many-valued Logics. North Holland, Amsterdam (1958)
Segerberg, K.: An Essay in Classical Modal Logic, vol. 1-3. Uppsala Universitet (1971)
Zadeh, L.A.: Fuzzy logic and approximate reasoning. Synthese 30, 407–428 (1975)
Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)
Cook, S.A.: The complexity of theorem proving procedure. In: Proc. 3rd Annual ACM Symp. on Theory of Computing, pp. 151–158 (1971)
Penczek, W., Szreter, M.: SAT-based unbounded model checking of timed automata. Fundamenta Informaticae 85, 425–440 (2008)
Penczek, W., Woźna, B., Zbrzezny, A.: Bounded model checking for the universal fragment of CTL. Fundamenta Informaticae 51, 135–156 (2002)
Woźna, B., Zbrzezny, A., Penczek, W.: Checking reachability properties for timed automata via SAT. Fundamenta Informaticae 55, 223–241 (2003)
Pawlak, Z.: Information systems – theoretical foundations. Information Systems 6, 205–218 (1981)
Pawlak, Z.: Information Systems: Theoretical Foundations (in Polish). Wydawnictwo Naukowo-Techniczne, Warsaw (1983)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer, Dordrecht (1991)
Pawlak, Z.: Rough set elements. In: [103], vol. 1, pp. 10–30 (1998)
Bazan, J.G.: Hierarchical classifiers for complex spatio-temporal concepts. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 474–750. Springer, Heidelberg (2008)
Fensel, D.: Ontologies: A Silver Bullet for Knowledge Management and Electronic Commerce. Springer, Berlin (2003)
Nguyen, S.H., Nguyen, H.S.: Improving rough classifiers using concept ontology. In: Ho, T.-B., Cheung, D., Liu, H. (eds.) PAKDD 2005. LNCS (LNAI), vol. 3518, pp. 312–322. Springer, Heidelberg (2005)
Nguyen, S.H., Nguyen, T.T., Nguyen, H.S.: Ontology driven concept approximation. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 547–556. Springer, Heidelberg (2006)
Skowron, A., Stepaniuk, J.: Ontological framework for approximation. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 718–727. Springer, Heidelberg (2005)
Staab, S., Studer, R. (eds.): Handbook on Ontologies. Springer, Heidelberg (2004)
Gomolińska, A.: Variable-precision compatibility spaces. Electronical Notices in Theoretical Computer Science 82, 1–12 (2003), http://www.elsevier.nl/locate/entcs/volume82.html
Gomolińska, A.: Approximation spaces based on relations of similarity and dissimilarity of objects. Fundamenta Informaticae 79, 319–333 (2007)
Pawlak, Z.: A treatise on rough sets. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets IV. LNCS, vol. 3700, pp. 1–17. Springer, Heidelberg (2005)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)
Słowiński, R., Greco, S., Matarazzo, B.: Dominance-based rough set approach to reasoning about ordinal data. In: Kryszkiewicz, M., Peters, J.F., Rybiński, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 5–11. Springer, Heidelberg (2007)
Słowiński, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: Wang, P.P. (ed.) Advances in Machine Intelligence and Soft Computing, vol. 4, pp. 17–33. Duke University Press (1997)
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. Int. J. of Man–Machine Studies 37, 793–809 (1992)
Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A review of rough set models. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis of Imprecise Data, pp. 47–75. Kluwer, Dordrecht (1997)
Ziarko, W.: Variable precision rough set model. J. Computer and System Sciences 46, 39–59 (1993)
Ziarko, W.: Probabilistic rough sets. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 283–293. Springer, Heidelberg (2005)
Zadeh, L.A.: Outline of a new approach to the analysis of complex system and decision processes. IEEE Trans. on Systems, Man, and Cybernetics 3, 28–44 (1973)
Zadeh, L.A.: Fuzzy sets and information granularity. In: Gupta, M., Ragade, R., Yager, R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 3–18. North-Holland, Amsterdam (1979)
Gomolińska, A.: Judgement of satisfiability under incomplete information. In: Czaja, L., Szczuka, M. (eds.) Proc. 18th Workshop on Concurrency, Specification and Programming (CS& P 2009), Kraków Przegorzały, September 2009, vol. 1. Warsaw University, Warsaw, pp. 164–175 (2009)
Gomolińska, A.: A graded meaning of formulas in approximation spaces. Fundamenta Informaticae 60, 159–172 (2004)
Gomolińska, A.: On rough judgment making by socio-cognitive agents. In: Skowron, A., et al. (eds.) Proc. 2005 IEEE/WIC/ACM Int. Conf. on Intelligent Agent Technology (IAT 2005), Compiègne, France, September 2005, pp. 421–427. IEEE Computer Society Press, Los Alamitos (2005)
Gomolińska, A.: Satisfiability and meaning of formulas and sets of formulas in approximation spaces. Fundamenta Informaticae 67, 77–92 (2005)
Gomolińska, A.: Satisfiability of formulas from the standpoint of object classification: The RST approach. Fundamenta Informaticae 85, 139–153 (2008)
Greco, S., Matarazzo, B., Słowiński, R.: Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 146–157. Springer, Heidelberg (1999)
Grzymała-Busse, J.W.: Characteristic relations for incomplete data: A generalization of the indiscernibility relation. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets IV. LNCS, vol. 3700, pp. 58–68. Springer, Heidelberg (2005)
Kryszkiewicz, M.: Rough set approach to incomplete information system. Information Sciences 112, 39–49 (1998)
Lipski, W.: Informational systems with incomplete information. In: Proc. 3rd Int. Symp. on Automata, Languages and Programming, pp. 120–130. Edinburgh University Press, Edinburgh (1976)
Stefanowski, J., Tsoukiàs, A.: Incomplete information tables and rough classification. Computational Intelligence 17, 545–566 (2001)
Rissanen, J.: Modeling by shortest data description. Automatica 14, 465–471 (1978); See also An introduction to the MDL Principle, http://www.mdl-research.org/jorma.rissanen
Gomolińska, A.: Construction of rough information granules. In: [82], pp. 449–470 (2008)
Inuiguchi, M., Hirano, S., Tsumoto, S. (eds.): Rough Set Theory and Granular Computing. Springer, Heidelberg (2003)
Nguyen, H.S., Skowron, A., Stepaniuk, J.: Granular computing: A rough set approach. Computational Intelligence 17, 514–544 (2001)
Pedrycz, W. (ed.): Granular Computing: An Emerging Paradigm. Physica, Heidelberg (2001)
Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. John Wiley & Sons, Chichester (2008)
Skowron, A., Stepaniuk, J.: Towards discovery of information granules. In: Żytkow, J.M., Rauch, J. (eds.) PKDD 1999. LNCS (LNAI), vol. 1704, pp. 542–547. Springer, Heidelberg (1999)
Skowron, A., Swiniarski, R., Synak, P.: Approximation spaces and information granulation. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 175–189. Springer, Heidelberg (2005)
Gomolińska, A.: Possible rough ingredients of concepts in approximation spaces. Fundamenta Informaticae 72, 139–154 (2006)
Polkowski, L., Skowron, A.: Rough mereology in information systems. A case study: Qualitative spatial reasoning. In: [104], pp. 89–135 (2001)
Stepaniuk, J.: Knowledge discovery by application of rough set models. In: [104], pp. 137–233 (2001)
Leśniewski, S.: Foundations of the General Set Theory 1 (in Polish), Moscow. Works of the Polish Scientific Circle, vol. 2 (1916); Also in [89], pp 128–173
Surma, S.J., Srzednicki, J.T., Barnett, J.D. (eds.): Stanisław Leśniewski Collected Works. Kluwer/Polish Scientific Publ., Dordrecht/Warsaw (1992)
Polkowski, L., Skowron, A.: Rough mereology. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1994. LNCS (LNAI), vol. 869, pp. 85–94. Springer, Heidelberg (1994)
Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning. Int. J. Approximated Reasoning 15, 333–365 (1996)
Polkowski, L., Skowron, A.: Towards adaptive calculus of granules. In: [133], vol. 1, pp. 201–228 (1999)
Drwal, G., Mrózek, A.: System RClass – software implementation of a rough classifier. In: Kłopotek, M.A., Michalewicz, M., Raś, Z.W. (eds.) Proc. 7th Int. Symp. Intelligent Information Systems (IIS 1998), Malbork, Poland, Warsaw, PAS Institute of Computer Science, June 1998, pp. 392–395 (1998)
Gomolińska, A.: On certain rough inclusion functions. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 35–55. Springer, Heidelberg (2008)
Gomolińska, A.: Rough approximation based on weak q-RIFs. In: Peters, J.F., et al. (eds.) Transactions on Rough Sets X. LNCS, vol. 5656, pp. 117–135. Springer, Heidelberg (2009)
Polkowski, L.: A note on 3-valued rough logic accepting decision rules. Fundamenta Informaticae 61, 37–45 (2004)
Polkowski, L.: Rough mereology in analysis of vagueness. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 197–205. Springer, Heidelberg (2008)
Xu, Z.B., Liang, J.Y., Dang, C.Y., Chin, K.S.: Inclusion degree: A perspective on measures for rough set data analysis. Information Sciences 141, 227–236 (2002)
Łukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung. In: [132], pp. 16–63 (1970); First published Kraków (1913)
Zadeh, L.A.: Fuzzy logic = computing with words. IEEE Trans. on Fuzzy Systems 4, 103–111 (1996)
Zhao, Y., Yao, Y.Y., Luo, F.: Data analysis based on discernibility and indiscernibility. Information Sciences 177, 4959–4976 (2007)
Bazan, J.G., Skowron, A., Swiniarski, R.: Rough sets and vague concept approximation: From sample approximation to adaptive learning. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 39–62. Springer, Heidelberg (2006)
Polkowski, L., Skowron, A. (eds.): Rough Sets in Knowledge Discovery, vol. 1-2. Physica, Heidelberg (1998)
Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.): Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems. Physica, Heidelberg (2001)
Stepaniuk, J.: Approximation spaces in multi-relational knowledge discovery. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J.W., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 351–365. Springer, Heidelberg (2007)
Bazan, J.G., Nguyen, S.H., Nguyen, H.S., Skowron, A.: Rough set methods in approximation of hierarchical concepts. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 346–355. Springer, Heidelberg (2004)
Nguyen, S.H., Bazan, J.G., Skowron, A., Nguyen, H.S.: Layered learning for concept synthesis. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 187–208. Springer, Heidelberg (2004)
Peters, J.F.: Approximation spaces for hierarchical intelligent behavioral system models. In: Dunin-Kȩplicz, B., Jankowski, A., Skowron, A., Szczuka, M. (eds.) Monitoring, Security, and Rescue Techniques in Multiagent Systems, pp. 13–30. Springer, Heidelberg (2005)
Stone, P.: Layered Learning in Multi-agent Systems: A Winning Approach to Robotic Soccer. The MIT Press, Cambridge (2000)
Synak, P., Bazan, J.G., Skowron, A., Peters, J.F.: Spatio-temporal approximate reasoning over complex objects. Fundamenta Informaticae 67, 249–269 (2005)
Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets and rough logic: A KDD perspective. In: [104], pp. 583–646 (2001)
Aamodt, A., Plaza, E.: Case-based reasoning: Foundational issues, methodological variations, and system approaches. AI Communications 7, 39–52 (1994)
Aha, D.W., Kibler, D., Albert, M.K.: Instance-based learning algorithms. Machine Learning 6, 37–66 (1991)
Bazan, J.G.: Discovery of decision rules by matching new objects against data tables. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 521–528. Springer, Heidelberg (1998)
Cover, T.M., Hart, P.E.: Nearest neighbor pattern classification. IEEE Trans. on Information Theory 13, 21–27 (1967)
Duda, R.O., Hart, P.E., Stork, R.: Pattern Classification. John Wiley & Sons, New York (2002)
Dzeroski, S., Lavrac, N. (eds.): Relational Data Mining. Springer, Berlin (2001)
Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach to case-based reasoning. In: Torra, V., Narukawa, Y., Valls, A., Domingo-Ferrer, J. (eds.) MDAI 2006. LNCS (LNAI), vol. 3885, pp. 7–18. Springer, Heidelberg (2006)
Grzymała-Busse, J.W.: LERS – a system for learning from examples based on rough sets. In: Słowiński, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory, pp. 3–18. Kluwer, Dordrecht (1992)
Grzymała-Busse, J.W.: LERS – A data mining system. In: [15], pp. 1347–1351 (2005)
Grzymała-Busse, J.W.: Rule induction. In: [15], pp. 255–267 (2005)
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Springer Science + Business Media, LLC, New York (2009)
Michalski, R.S.: Inferential theory of learning as a conceptual basis for multistrategy learning. Machine Learning 11, 111–151 (1993)
Mitchell, M.: Analogy-making as Perception: A Computer Model. The MIT Press, Cambridge (1993)
Mitchell, M.: Analogy-making as a complex adaptive system. In: Segel, L.E., Cohen, I.R. (eds.) Design Principles for the Immune System and Other Distributed Autonomous Systems, pp. 335–360. Oxford University Press, New York (2001)
Stefanowski, J.: On rough set based approaches to induction of decision rules. In: [103], vol. 1, pp. 500–529 (1998)
Stepaniuk, J., Hońko, P.: Learning first-order rules: A rough set approach. Fundamenta Informaticae 61, 139–157 (2004)
Vapnik, V.: Statistical Learning Theory. John Wiley & Sons, New York (1998)
Wojna, A.G.: Analogy-based reasoning in classifier construction. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets IV. LNCS, vol. 3700, pp. 277–374. Springer, Heidelberg (2005)
Polkowski, L.: Rough Sets: Mathematical Foundations. Physica, Heidelberg (2002)
Torra, V., Narukawa, Y.: Modeling Decisions: Information Fusion and Aggregation Operators. Springer, Heidelberg (2007)
Borkowski, L. (ed.): Jan Łukasiewicz – Selected Works. North Holland/Polish Scientific Publ., Amsterdam/Warsaw (1970)
Zadeh, L.A., Kacprzyk, J. (eds.): Computing with Words in Information/Intelligent Systems. Physica, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gomolińska, A. (2010). Satisfiability Judgement under Incomplete Information. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets XI. Lecture Notes in Computer Science, vol 5946. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11479-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-11479-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11478-6
Online ISBN: 978-3-642-11479-3
eBook Packages: Computer ScienceComputer Science (R0)