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

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Outlines

• Background

• Related Work

• Our approach: use domain semantics to

validate decision tables

• Discussion and Conclusion

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What is a decision table?

• CSA, (1970): Z243.1-1970 for Decision Tables, Canadian Standards

Association

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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)

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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

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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))

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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

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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 * * * *

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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 * * * * *

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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 * * * * *

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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

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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

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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

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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 * * *

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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

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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

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Thanks!

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