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2018 | OriginalPaper | Buchkapitel

4. Formalism for Description of Decision Rules

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Abstract

In this chapter we discuss the eXtended Tabular Trees knowledge representation method for rules. It uses strict formalization of rule syntax and improves design and verification of RBS. It is the core of the Semantic Knowledge Engineering approach. This chapter discusses the core features of XTT. We begin with the formalization of single rules with the ALSV(FD) logic. Inference with ALSV(FD) is discussed next. Based on this, the formalization of rule bases with the XTT method is discussed. Then rule base modularization is described. Such rule bases need custom inference algorithms considered next. Finally, the formalization allows for the XTT rule bases to be verified.

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Fußnoten
1
This assumption has an engineering motivation. In most of the practical applications, the domains of attributes can be defined in a satisfactory way as finite. This is due to a number of physical limitations of the modeled systems.
 
2
The examples of books given here are as follows: It by Stephen King (considered to be a horror book), Logical Foundations for RBS by Antoni Ligęza (a science book), and The Call of Cthulhu by Howard P. Lovecraft (a fantasy book), where Cthulhu is the name of an extraterrestrial entity.
 
3
An example of this kind of architecture for the SKE approach will be given later on in Sect. 9.​3.
 
4
For example, \(A_{i} = V_{i}\) can be defined as \(A_{i} \subseteq V_{i}\wedge A_{i} \supseteq V_{i}\), but it is much more concise and natural to use just “=” directly.
 
5
This is a simplified case, where these formulae are the only conditions. Moreover, the decisions of both rules must be the same. For a detailed discussion refer to section “Subsumption of a Pair of Rules”.
 
6
Here only the assignment operator is used. In fact some RBS provide more robust operators, such as restrict in Kheops [10]. It allows the set of values of a given attribute to be narrowed. While such an operator is useful in certain applications (e.g. in diagnostic systems, where the set of potential diagnoses can be incrementally narrowed), it poses practical verification problems. Therefore, it is not used in ALSV(FD).
 
7
The LHS/RHS convention is common among a number of classic RBS, e.g. see [11].
 
8
In fact, it can also be a generalization of structures describing other inference processes such as business processes described using BPMN (Business Process Model and Notation) [12], or selected UML diagrams.
 
Literatur
1.
Zurück zum Zitat Nalepa, G.J., Ligęza, A., Kaczor, K.: Formalization and modeling of rules using the XTT2 method. Int. J. Artif. Intell. Tools 20(6), 1107–1125 (2011)CrossRef Nalepa, G.J., Ligęza, A., Kaczor, K.: Formalization and modeling of rules using the XTT2 method. Int. J. Artif. Intell. Tools 20(6), 1107–1125 (2011)CrossRef
2.
Zurück zum Zitat Nalepa, G.J.: Semantic Knowledge Engineering. A Rule-Based Approach. Wydawnictwa AGH, Kraków (2011) Nalepa, G.J.: Semantic Knowledge Engineering. A Rule-Based Approach. Wydawnictwa AGH, Kraków (2011)
3.
Zurück zum Zitat Ligęza, A., Wojnicki, I., Nalepa, G.J.: Tab-trees: a case tool for design of extended tabular systems. In: Mayr, H.C., Lazansky, J., Quirchmayr, G., Vogel, P. (eds.) Database and Expert Systems Applications. Lecture Notes in Computer Sciences, vol. 2113, pp. 422–431. Springer, Berlin (2001)CrossRef Ligęza, A., Wojnicki, I., Nalepa, G.J.: Tab-trees: a case tool for design of extended tabular systems. In: Mayr, H.C., Lazansky, J., Quirchmayr, G., Vogel, P. (eds.) Database and Expert Systems Applications. Lecture Notes in Computer Sciences, vol. 2113, pp. 422–431. Springer, Berlin (2001)CrossRef
4.
Zurück zum Zitat Nalepa, G.J.: A new approach to the rule-based systems design and implementation process. Comput. Sci. 6, 65–79 (2004) Nalepa, G.J.: A new approach to the rule-based systems design and implementation process. Comput. Sci. 6, 65–79 (2004)
5.
Zurück zum Zitat Nalepa, G.J., Ligęza, A.: A graphical tabular model for rule-based logic programming and verification. Syst. Sci. 31(2), 89–95 (2005)MATH Nalepa, G.J., Ligęza, A.: A graphical tabular model for rule-based logic programming and verification. Syst. Sci. 31(2), 89–95 (2005)MATH
6.
Zurück zum Zitat Nalepa, G.J., Ligęza, A.: XTT+ rule design using the ALSV(FD). In: Giurca, A., Analyti, A., Wagner, G. (eds.) ECAI 2008: 18th European Conference on Artificial Intelligence: 2nd East European Workshop on Rule-based applications, RuleApps2008: Patras, 22 July 2008, pp. 11–15. University of Patras, Patras (2008) Nalepa, G.J., Ligęza, A.: XTT+ rule design using the ALSV(FD). In: Giurca, A., Analyti, A., Wagner, G. (eds.) ECAI 2008: 18th European Conference on Artificial Intelligence: 2nd East European Workshop on Rule-based applications, RuleApps2008: Patras, 22 July 2008, pp. 11–15. University of Patras, Patras (2008)
7.
Zurück zum Zitat Nalepa, G.J., Ligęza, A.: On ALSV rules formulation and inference. In: Lane, H.C., Guesgen, H.W. (eds.) FLAIRS-22: Proceedings of the Twenty-Second International Florida Artificial Intelligence Research Society Conference: 19–21 May 2009, Sanibel Island, Florida, USA, Menlo Park, California, FLAIRS, pp. 396–401. AAAI Press (2009) Nalepa, G.J., Ligęza, A.: On ALSV rules formulation and inference. In: Lane, H.C., Guesgen, H.W. (eds.) FLAIRS-22: Proceedings of the Twenty-Second International Florida Artificial Intelligence Research Society Conference: 19–21 May 2009, Sanibel Island, Florida, USA, Menlo Park, California, FLAIRS, pp. 396–401. AAAI Press (2009)
8.
Zurück zum Zitat Nalepa, G.J., Ligęza, A.: HeKatE methodology, hybrid engineering of intelligent systems. Int. J. Appl. Math. Comput. Sci. 20(1), 35–53 (2010)CrossRefMATH Nalepa, G.J., Ligęza, A.: HeKatE methodology, hybrid engineering of intelligent systems. Int. J. Appl. Math. Comput. Sci. 20(1), 35–53 (2010)CrossRefMATH
9.
Zurück zum Zitat Ligęza, A.: Logical Foundations for Rule-Based Systems. Springer, Berlin (2006)MATH Ligęza, A.: Logical Foundations for Rule-Based Systems. Springer, Berlin (2006)MATH
10.
Zurück zum Zitat Gouyon, J.P.: Kheops users’s guide. Technical Report 92503, Report of Laboratoire d’Automatique et d’Analyse des Systemes, Toulouse, France (1994) Gouyon, J.P.: Kheops users’s guide. Technical Report 92503, Report of Laboratoire d’Automatique et d’Analyse des Systemes, Toulouse, France (1994)
11.
Zurück zum Zitat Giarratano, J., Riley, G.: Expert Systems. Principles and Programming, 4th edn. Thomson Course Technology, Boston (2005). ISBN 0-534-38447-1 Giarratano, J., Riley, G.: Expert Systems. Principles and Programming, 4th edn. Thomson Course Technology, Boston (2005). ISBN 0-534-38447-1
12.
Zurück zum Zitat OMG: Business Process Model and Notation (BPMN): Version 2.0 specification. Technical report formal/2011-01-03, Object Management Group (January 2011) OMG: Business Process Model and Notation (BPMN): Version 2.0 specification. Technical report formal/2011-01-03, Object Management Group (January 2011)
13.
Zurück zum Zitat Nalepa, G., Bobek, S., Ligęza, A., Kaczor, K.: Algorithms for rule inference in modularized rule bases. In: Bassiliades, N., Governatori, G., Paschke, A. (eds.) Rule-Based Reasoning, Programming, and Applications. Lecture Notes in Computer Science, vol. 6826, pp. 305–312. Springer, Berlin (2011)CrossRef Nalepa, G., Bobek, S., Ligęza, A., Kaczor, K.: Algorithms for rule inference in modularized rule bases. In: Bassiliades, N., Governatori, G., Paschke, A. (eds.) Rule-Based Reasoning, Programming, and Applications. Lecture Notes in Computer Science, vol. 6826, pp. 305–312. Springer, Berlin (2011)CrossRef
Metadaten
Titel
Formalism for Description of Decision Rules
verfasst von
Grzegorz J. Nalepa
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-66655-6_4