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Using           to Formalize Semantics                 within a Semantic Decision Table                      Yan Tang Deme...
Outlines       • Background       • Related Work       • Our approach: use domain semantics to         validate decision t...
What is a decision table?       • CSA, (1970): Z243.1-1970 for Decision Tables, Canadian Standards         Association    ...
Decision tables in IS and                        business       • Easily learned, understandable and         readable     ...
The Group Decision Modelling                                      Environment21/09/2012 | pag. 5                      McGr...
Validation and Verification       • In order to make a “good” decision table, it         needs to be validated and verifie...
Semantic Decision Tables       • Allows rule modellers to analyse decision         tables using domain semantics          ...
Related Work       • V&V approaches to decision tables              – Combining columns to reduce columns                 ...
Compared to their work       • We focus on using ontological axioms to         validate a decision table              – Sh...
What has been done       • How ontological constraints can be directly         applied to decision tables              –  ...
Motivation and Contribution       • Formalization and semantics for         computational properties for validating a     ...
– A dialect of Description Logics              – DL: decidable fragments of FOL              – An extension to      (most ...
• Expressive enough for SDT       • Good balance between expressiveness         and computational complexity       • OWL2 ...
21/09/2012 | pag. 14
Basic Structure of a                       Decision Table21/09/2012 | pag. 15
A Decision Rule (Column)21/09/2012 | pag. 16
Ontological Commitments in                       an SDT21/09/2012 | pag. 17
1. Value Constraint        Condition            1         2         3         4          …   n              …        Age  ...
1. Value Constraint        Condition            1         2         3         4          …   n              …        Age  ...
2. Cardinality and                             Occurrence Frequency       Condition       1     2     3     4     5     6 ...
2. Cardinality and                             Occurrence Frequency       Condition       1     2     3     4     5     6 ...
3. Mandatory       • A special case of role cardinality                             𝑅𝑜𝑜𝑚 ⊑≥ 1 ℎ𝑎𝑠. 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟     ...
3. Mandatory        Condition      1     2     3     4     5     6     7     8        X-Box 557      Yes   Yes   Yes   Yes...
3. Mandatory       • An example of N/A            Condition               1                      2                        ...
4. Uniqueness          Condition         1      2     3      4     5      6      7     8          X-Box 557         Yes   ...
4. Uniqueness          Condition             1                 2               3          Humidity Sensor       {X-Box557}...
4. Uniqueness21/09/2012 | pag. 27
5. Exclusive-Or        Condition         1            2                3        4        Humidity Sensor   Yes          Ye...
6. Subtyping         Condition      1               2     3     4         Humidity       Yes             Yes   No    No   ...
Discussion       • Business value: to support a decision group to draw decisions       • Advantages:              – Semant...
Conclusion       • Using domain semantics to validate decision tables         (within one table)       • Directly applied ...
Thanks!21/09/2012 | pag. 33
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Using SOIQ(D) to Formalize Semantics within one Semantic Decision Table

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Using SOIQ(D) to Formalize Semantics within one Semantic Decision Table

  1. 1. Using to Formalize Semantics within a Semantic Decision Table Yan Tang Demey and Trung-Kien Tran21/09/2012 | pag. 1
  2. 2. Outlines • Background • Related Work • Our approach: use domain semantics to validate decision tables • Discussion and Conclusion21/09/2012 | pag. 2
  3. 3. What is a decision table? • CSA, (1970): Z243.1-1970 for Decision Tables, Canadian Standards Association Condition entry Condition stub Condition 1 2 3 4 5 6 Age <18 >=18,<40 >=40 <18 >=18,<40 >=40 Speak required language (s) Yes Yes Yes No No No Action Hire * Train * Action Reject * * entry * * Action stub Decision rule21/09/2012 | pag. 3
  4. 4. Decision tables in IS and business • Easily learned, understandable and readable • Concise and precise • Clear relations of decisional alternatives • Decision rule set – Completeness – Correctness – Exclusivity21/09/2012 | pag. 4
  5. 5. The Group Decision Modelling Environment21/09/2012 | pag. 5 McGrath, J. E. (1984): Groups: Integration and Performance, Prentice-Hall, Englewood Cliffs, ISBN 0-13-365700-0
  6. 6. Validation and Verification • In order to make a “good” decision table, it needs to be validated and verified consistent correct21/09/2012 | pag. 6
  7. 7. Semantic Decision Tables • Allows rule modellers to analyse decision tables using domain semantics – Hidden decision rules and meta-rules are specified in ontologies – In the activities of grounding ontological commitments Instantiations of concepts Constraints Grouping contexts Articulation (mapping to glossary) Concepts alignment across contexts21/09/2012 | pag. 7
  8. 8. Related Work • V&V approaches to decision tables – Combining columns to reduce columns (Shwayder, 1975) – Conversion and decomposition (Pooch, 1974) – PROLOGA (discovering intra-inter tabular anomalies) (Vanthienen et al., 1998) – Approximate reduction (Qian et al., 2010) – Others (Hewette et al., 2003; Ibramsha and Rajaraman, 1978; Lew, 1978)21/09/2012 | pag. 8
  9. 9. Compared to their work • We focus on using ontological axioms to validate a decision table – Sharable and community based (and even standardized) – Support group decision making in a nature way – Misunderstanding is minimized21/09/2012 | pag. 9
  10. 10. What has been done • How ontological constraints can be directly applied to decision tables – (Tang, Y.: Directly Applied ORM Constraints for Validating and Verifying Semantic Decision Tables. In: Meersman, R., Dillon, T., Herrero, P. (eds.) OTM-WS 2011. LNCS, vol. 7046, pp. 350–359. Springer, Heidelberg (2011)) • What is the mapping between SDRule-ML and OWL/RDF(s). – (Tang, Y., Meersman, R.: Towards Directly Applied Ontological Constraints in a Semantic Decision Table. In: Palmirani, M. (ed.) RuleML - America 2011. LNCS, vol. 7018, pp. 193– 207. Springer, Heidelberg (2011))21/09/2012 | pag. 10
  11. 11. Motivation and Contribution • Formalization and semantics for computational properties for validating a decision table • More Focus: – Validation (not verification) – Within one table (not across table)21/09/2012 | pag. 11
  12. 12. – A dialect of Description Logics – DL: decidable fragments of FOL – An extension to (most basic DL language of interest) by adding syntactic constructors • Transitivity • Nominal • Inverse roles • Qualified number restriction • Data types21/09/2012 | pag. 12
  13. 13. • Expressive enough for SDT • Good balance between expressiveness and computational complexity • OWL2 recommended by W3C is based on . , which includes21/09/2012 | pag. 13
  14. 14. 21/09/2012 | pag. 14
  15. 15. Basic Structure of a Decision Table21/09/2012 | pag. 15
  16. 16. A Decision Rule (Column)21/09/2012 | pag. 16
  17. 17. Ontological Commitments in an SDT21/09/2012 | pag. 17
  18. 18. 1. Value Constraint Condition 1 2 3 4 … n … Age >=18 >=18 >=18 >=18 … >=100, <=350 Temperature Sensor >=0,<30 >=0,<30 >=0,<30 >=-10,<0 … >=0,<30 Login State Yes No Maybe Yes … Yes … Action Accept * * * * Choose a random value within the range21/09/2012 | pag. 18
  19. 19. 1. Value Constraint Condition 1 2 3 4 … n … Age >=18 >=18 >=18 >=18 … >=100, <=350 Temperature Sensor >=0,<30 >=0,<30 >=0,<30 >=-10,<0 … >=0,<30 Login State Yes No Maybe Yes … Yes … Action Accept * * * *21/09/2012 | pag. 19
  20. 20. 2. Cardinality and Occurrence Frequency Condition 1 2 3 4 5 6 7 8 X-Box 557 Yes Yes Yes Yes No No No No X-Box 120 Yes Yes No No Yes Yes No No MS Xbox 360 Yes No Yes No Yes No Yes No Action Actuator x * * * * * Interpret condition entries “Yes”, “No” into true or false in DL axioms21/09/2012 | pag. 20
  21. 21. 2. Cardinality and Occurrence Frequency Condition 1 2 3 4 5 6 7 8 X-Box 557 Yes Yes Yes Yes No No No No X-Box 120 Yes Yes No No Yes Yes No No MS Xbox 360 Yes No Yes No Yes No Yes No Action Actuator x * * * * *21/09/2012 | pag. 21
  22. 22. 3. Mandatory • A special case of role cardinality 𝑅𝑜𝑜𝑚 ⊑≥ 1 ℎ𝑎𝑠. 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 Or, 𝑅𝑜𝑜𝑚 ⊑ ∃ℎ𝑎𝑠. 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 𝑅𝑜𝑜𝑚 ⊑ ∃ℎ𝑎𝑠. 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊓ ¬∀ℎ𝑎𝑠𝐶𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝐸𝑛𝑡𝑟𝑦 𝑓𝑎𝑙𝑠𝑒 Condition 1 2 3 4 5 6 7 8 X-Box 557 Yes Yes Yes Yes No No No No X-Box 120 Yes Yes No No Yes Yes No No MS Xbox 360 Yes No Yes No Yes No Yes No Action Actuator x * * * * *21/09/2012 | pag. 22
  23. 23. 3. Mandatory Condition 1 2 3 4 5 6 7 8 X-Box 557 Yes Yes Yes Yes No No No No X-Box 120 Yes Yes No No Yes Yes No No MS Xbox 360 Yes No Yes No Yes No Yes No Action Actuator x * * * * *21/09/2012 | pag. 23
  24. 24. 3. Mandatory • An example of N/A Condition 1 2 3 X-Box Humidity {X-Box557, X-Box120} {X-Box557, MS Xbox360} N/A Sensor Action Actuator x * * 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟I= 𝑥𝐵𝑜𝑥557, 𝑥𝐵𝑜𝑥120, 𝑚𝑆𝑋𝑏𝑜𝑥360 𝑛/𝑎 ⊑ ¬𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 𝑛/𝑎 A mapping is needed21/09/2012 | pag. 24
  25. 25. 4. Uniqueness Condition 1 2 3 4 5 6 7 8 X-Box 557 Yes Yes Yes Yes No No No No X-Box 120 Yes Yes No No Yes Yes No No MS Xbox 360 Yes No Yes No Yes No Yes No Action Actuator x * * * * * 𝑅𝑜𝑜𝑚 ⊑≤ 1 ℎ𝑎𝑠. 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊓ ∃ℎ𝑎𝑠𝐶𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝐸𝑛𝑡𝑟𝑦 𝑡𝑟𝑢𝑒21/09/2012 | pag. 25
  26. 26. 4. Uniqueness Condition 1 2 3 Humidity Sensor {X-Box557} { MS Xbox360} {X-Box557} Sensor {EZEYE 1011A} {EZEYE 1011A} {X-Box120} Action Actuator x * * Actuator y * * 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊑ 𝑥𝐵𝑜𝑥557, 𝑚𝑆𝑋𝑏𝑜𝑥360, 𝑥𝐵𝑜𝑥120 𝑅𝑜𝑜𝑚 ⊑≤ 1ℎ𝑎𝑠. 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 𝑆𝑒𝑛𝑠𝑜𝑟 ⊑ 𝑒𝑍𝐸𝑌𝐸1011𝐴 ⊔ 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟21/09/2012 | pag. 26
  27. 27. 4. Uniqueness21/09/2012 | pag. 27
  28. 28. 5. Exclusive-Or Condition 1 2 3 4 Humidity Sensor Yes Yes No No Light Sensor Yes No Yes No Action Actuator x * * Actuator y * 𝑅𝑜𝑜𝑚 ⊑ ∃ℎ𝑎𝑠. 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊔ 𝐿𝑖𝑔ℎ𝑡𝑆𝑒𝑛𝑠𝑜𝑟 𝑅𝑜𝑜𝑚 ⊑ ¬ ∃ℎ𝑎𝑠. 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊓ ∃ℎ𝑎𝑠. 𝐿𝑖𝑔ℎ𝑡𝑆𝑒𝑛𝑠𝑜𝑟 𝑅𝑜𝑜𝑚 ⊑ ∃𝑎𝑐𝑡𝑖𝑣𝑎𝑡𝑒. 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟𝑥 ⊔ 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟𝑦 𝑅𝑜𝑜𝑚 ⊑ ¬ ∃𝑎𝑐𝑡𝑖𝑣𝑎𝑡𝑒. 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟𝑥 ⊓ ∃𝑎𝑐𝑡𝑖𝑣𝑖𝑎𝑡𝑒. 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟𝑦21/09/2012 | pag. 28
  29. 29. 6. Subtyping Condition 1 2 3 4 Humidity Yes Yes No No Sensor Sensor Yes No Yes No Action Actuator x * * * 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊑ 𝑆𝑒𝑛𝑠𝑜𝑟 𝑅𝑜𝑜𝑚 ⊑ ∃ℎ𝑎𝑠. 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 𝑅𝑜𝑜𝑚 ⊑ ∀ℎ𝑎𝑠. ¬𝑆𝑒𝑛𝑠𝑜𝑟21/09/2012 | pag. 30
  30. 30. Discussion • Business value: to support a decision group to draw decisions • Advantages: – Semantics is fully kept – Existing reasoners to check the consistency -> validation • Disadvantages: – The mapping is non-trivial – Reasoning cost: NEXPTIME • Future Work – A supporting tool of the mapping – Using reasoners to derive semantics within a table, e.g. subclasses between condition/action stubs – Validation across tables21/09/2012 | pag. 31
  31. 31. Conclusion • Using domain semantics to validate decision tables (within one table) • Directly applied ontological constraints – Value – Cardinality – Mandatory – Uniqueness – Exclusive-or – Subtyping • All the examples can be downloaded at http://starlab.vub.ac.be/website/SDT_SOIQ21/09/2012 | pag. 32
  32. 32. Thanks!21/09/2012 | pag. 33

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