Using SOIQ(D) to Formalize Semantics within one Semantic Decision Table
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Transcript of Using SOIQ(D) to Formalize Semantics within one Semantic Decision Table
Using to Formalize Semantics
within a Semantic Decision Table
Yan Tang Demey and Trung-Kien Tran
21/09/2012 | pag. 1
Outlines
• Background
• Related Work
• Our approach: use domain semantics to
validate decision tables
• Discussion and Conclusion
21/09/2012 | pag. 2
What is a decision table?
• CSA, (1970): Z243.1-1970 for Decision Tables, Canadian Standards
Association
21/09/2012 | pag. 3
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 *
Reject * * * *
Condition
stub
Condition
entry
Action stub
Action
entry
Decision
rule
Decision tables in IS and
business
• Easily learned, understandable and
readable
• Concise and precise
• Clear relations of decisional alternatives
• Decision rule set
– Completeness
– Correctness
– Exclusivity
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The Group Decision Modelling
Environment
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McGrath, J. E. (1984): Groups: Integration and Performance, Prentice-Hall, Englewood Cliffs, ISBN 0-13-365700-0
Validation and Verification
• In order to make a “good” decision table, it
needs to be validated and verified
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consistent
correct
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
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Instantiations of concepts
Constraints
Grouping contexts
Articulation (mapping to glossary)
Concepts alignment across contexts
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
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 minimized
21/09/2012 | pag. 9
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
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)
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– 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 types
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• Expressive enough for SDT
• Good balance between expressiveness
and computational complexity
• OWL2 recommended by W3C is based on
. , which includes
21/09/2012 | pag. 13
21/09/2012 | pag. 14
Basic Structure of a
Decision Table
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A Decision Rule (Column)
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Ontological Commitments in
an SDT
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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 * * * *
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Choose a random value
within the range
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
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. 20
Interpret condition
entries “Yes”, “No” into
true or false in DL
axioms
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
3. Mandatory
• A special case of role cardinality
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𝑅𝑜𝑜𝑚 ⊑≥ 1 ℎ𝑎𝑠. 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟
Or, 𝑅𝑜𝑜𝑚 ⊑ ∃ℎ𝑎𝑠. 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟
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 ⊑ ∃ℎ𝑎𝑠. 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊓ ¬∀ℎ𝑎𝑠𝐶𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝐸𝑛𝑡𝑟𝑦 𝑓𝑎𝑙𝑠𝑒
3. Mandatory
21/09/2012 | pag. 23
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 * * * * *
3. Mandatory
• An example of N/A
21/09/2012 | pag. 24
Condition 1 2 3
X-Box Humidity
Sensor
{X-Box557, X-Box120} {X-Box557, MS Xbox360} N/A
Action
Actuator x * *
𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟I= 𝑥𝐵𝑜𝑥557, 𝑥𝐵𝑜𝑥120, 𝑚𝑆𝑋𝑏𝑜𝑥360
𝑛/𝑎 ⊑ ¬𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟
𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 𝑛/𝑎
A mapping is needed
4. Uniqueness
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𝑅𝑜𝑜𝑚 ⊑≤ 1 ℎ𝑎𝑠. 𝑋𝐵𝑜𝑥𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊓ ∃ℎ𝑎𝑠𝐶𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝐸𝑛𝑡𝑟𝑦 𝑡𝑟𝑢𝑒
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 * * * * *
4. Uniqueness
21/09/2012 | pag. 26
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 ⊔ 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟
4. Uniqueness
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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 *
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𝑅𝑜𝑜𝑚 ⊑ ¬ ∃ℎ𝑎𝑠. 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊓ ∃ℎ𝑎𝑠. 𝐿𝑖𝑔ℎ𝑡𝑆𝑒𝑛𝑠𝑜𝑟
𝑅𝑜𝑜𝑚 ⊑ ∃ℎ𝑎𝑠. 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊔ 𝐿𝑖𝑔ℎ𝑡𝑆𝑒𝑛𝑠𝑜𝑟
𝑅𝑜𝑜𝑚 ⊑ ∃𝑎𝑐𝑡𝑖𝑣𝑎𝑡𝑒. 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟𝑥 ⊔ 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟𝑦
𝑅𝑜𝑜𝑚 ⊑ ¬ ∃𝑎𝑐𝑡𝑖𝑣𝑎𝑡𝑒. 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟𝑥 ⊓ ∃𝑎𝑐𝑡𝑖𝑣𝑖𝑎𝑡𝑒. 𝐴𝑐𝑡𝑢𝑎𝑡𝑜𝑟𝑦
6. Subtyping
Condition 1 2 3 4
Humidity
Sensor
Yes Yes No No
Sensor Yes No Yes No
Action
Actuator x * * *
21/09/2012 | pag. 30
𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟 ⊑ 𝑆𝑒𝑛𝑠𝑜𝑟
𝑅𝑜𝑜𝑚 ⊑ ∃ℎ𝑎𝑠. 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑆𝑒𝑛𝑠𝑜𝑟
𝑅𝑜𝑜𝑚 ⊑ ∀ℎ𝑎𝑠. ¬𝑆𝑒𝑛𝑠𝑜𝑟
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 tables
21/09/2012 | pag. 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_SOIQ
21/09/2012 | pag. 32
Thanks!
21/09/2012 | pag. 33