Petros Papapanagiotou Automated Reasoning Lecture 9 What have you - - PowerPoint PPT Presentation

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Petros Papapanagiotou Automated Reasoning Lecture 9 What have you - - PowerPoint PPT Presentation

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Petros Papapanagiotou Automated Reasoning Lecture 9 What have you done so far? Done To Go 2 Learned new things!.. 3 ...and some (more) logic!.. 4 ...and practiced using Isabelle!.. 5 ...but why? 6 Where is the connection...

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SLIDE 1 Petros Papapanagiotou Automated Reasoning Lecture 9
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What have you done so far?

Done To Go 2
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Learned new things!..

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...and some (more) logic!..

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...and practiced using Isabelle!..

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...but why?

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Where is the connection...

...between these... ...and these?

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Oops!

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“LOGICAL” errors!

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“LOGICAL” solution!

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“LOGICAL” solution!

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Formal Verification!

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Use logic to...

 Describe  Specify  Reason  Assist

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Web Services

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Web Services

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Web Services

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Web Service Description:

Inputs Outputs Preconditions Effects

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Service

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Web Service Description: IOPEs

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Service

Input Output

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Web Service Description: IOPEs

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Service

Preconditions Effects

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Service

Web Service Description: More?

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Cost! Location! Quality!

Certification!

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Web Services Description Language

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Business Process Execution Language

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Semantic Web Services: OWL-S

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Example domain

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Buyer

USD to NOK Cm to Inch Select Model Select Length Select Ski

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Example domain

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Buyer

House Alert Home Directory Criminal Service Estate Agent Mortgage Service Contract Service Title Search Home Insurance Settlement
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Web Services Composition

27 Home Directory House Alert Settlement Mortgage Service Contract Service Criminal Service Estate Agent Title Search Home Insurance

Buyer

User Input Settlement
  • r
Exception
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Requirements

 Compose correctly  Handle exceptions  Provide trust

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We are also...

 Offline  Quality-driven  Formal

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The approach

Proofs as processes

Classical Linear Logic π- calculus

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HOL Light

Theorem Prover

The approach

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Proofs as processes

Classical Linear Logic π- calculus

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The theory: π-calculus

32 P ::= | 0 null process | x(y).P input | x<y>.P
  • utput
|(ν x) P local variable | P || P parallel processes | P + P choice
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The theory: Classical Linear Logic

 FOL

⟦ p ; q ⟧ ⇒ p

 CLL

⟦ p ; q ⟧ ⇒ p

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The theory: Classical Linear Logic

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Red: input Blue: output

Disjunction Conjunction Multiplicative

⅋ ⊗

Additive

⊕ &

Negation

.⊥

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The theory: Classical Linear Logic

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Red: input Blue: output

Disjunction Conjunction Multiplicative

⅋ ⊗

Additive

⊕ &

Negation

.⊥

¬ ∧ ∨

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The theory: Classical Linear Logic

⊢ A⊥, B

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The theory: Classical Linear Logic

⊢ A⊥, B ⊢ B⊥, C

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The theory: Classical Linear Logic

⊢ A⊥, B ⊢ B⊥, C ⊢ A⊥, C

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The theory: Classical Linear Logic

⊢ Height_cm ⊥, Weight_kg ⊥, Length_cm ⊢ Length_cm ⊥, Length_inch ⊢ Height_cm⊥, Weight_kg ⊥, Length_inch 39
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The theory: Classical Linear Logic

⊢ Height_cm ⊥, Weight_kg ⊥, Length_cm ⊢ Length_cm ⊥, Length_inch ⊢ Height_cm⊥, Weight_kg ⊥, Length_inch 40

Select Length Cm to Inch

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The theory: Classical Linear Logic

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The theory: Proofs-as-processes

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Γ ⇒ π

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Example: Tensor (⊗) rule

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B U F F E R

P A R A L L E L C H O I C E S E Q U E N C E

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WS Composition using proofs-as-processes

Translate to CLL Prove Requested Service Extract π-calculus term Realisation ...

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WS Composition using proofs-as-processes

Translate to CLL Prove Requested Service Extract π-calculus term Realisation ...

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Ski example specified in CLL

SelectModel:

⊢ PRICE_LIMIT⊥, SKILL_LEVEL⊥, BRAND ⊗ MODEL

SelectLength:

⊢ HEIGHT_CM⊥, WEIGHT_KG⊥, LENGTH_CM

Cm2Inch:

⊢ LENGTH_CM⊥, LENGTH_IN

Usd2Nok:

⊢ PRICE_USD⊥, PRICE_NOK

SelectSki:

⊢ LENGTH_IN⊥, BRAND⊥, MODEL⊥, PRICE_USD ⊕ EXCEPTION 48
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Real Estate Example specified in CLL

1. HomeDir: ⊢ HOME_CRITERIA⊥, HOME_LISTING 2. CriminalService: ⊢ REGION⊥, CRIMINAL_ACT 3. HouseAlert: ⊢ HOME_LISTING⊥, CRIMINAL_ACT⊥,

DESIRED_LEVEL⊥, HOME_TITLE_ID ⊗ HOME_AGENT_ID ⊗ HOME_DESC

4. Buyer: ⊢ HOME_DESC⊥, HOME_OFFER 5. EstateAgentSeller: ⊢ HOME_AGENT_ID⊥, HOME_OFFER⊥,

ACCEPTED_OFFER ⊕ REJECTED_OFFER

6. MortgageService: ⊢ CLIENT_INFO⊥, PREAPPROVAL ⊕ EXM 7. ContractService: ⊢ PREAPPROVAL⊥, ACCEPTED_OFFER⊥,

CONTRACT

8. TitleSearch: ⊢ HOME_TITLE_ID⊥, TITLE ⊗

(HOME_INSURANCE ⊕ HOME_INS_ID)

9. HomeInsurance: ⊢ HOME_INS_ID⊥, HOME_INS 10. Settlement: ⊢ TITLE⊥, CONTRACT⊥, HOME_INS⊥,

SETTLEMENT

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Ski Request in CLL

⊢ PRICE_LIMIT⊥, SKILL_LEVEL⊥, HEIGHT_CM⊥, WEIGHT_KG⊥, PRICE_NOK ⊕ ?EXCEPTION

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Ski Request in CLL

⊢ PRICE_LIMIT⊥, SKILL_LEVEL⊥, HEIGHT_CM⊥, WEIGHT_KG⊥, PRICE_NOK ⊕ ?EXCEPTION

51 What is the final exception?

 Metavariables + unification!

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WS Composition using proofs-as-processes

Translate to CLL Prove Requested Service Extract π-calculus term Realisation ...

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Proof for the Ski example

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WS Composition using proofs-as-processes

Translate to CLL Prove Requested Service Extract π-calculus term Realisation ...

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Ski Result in π-calculus

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Real Estate Result

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WS Composition using proofs-as-processes

Translate to CLL Prove Requested Service Extract π-calculus term Realisation Execution

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Execution: PiVizTool

 π-calculus is executable!  PiVizTool:

 Visualisation of connections  Animation of execution  Empirical verification

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PiVizTool

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WS Composition using proofs-as-processes

Translate to CLL Prove Requested Service Extract π-calculus term Realisation Translation

Upcoming! BPEL OWL-S 60
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Implementation: Details

 HOL Light – flexible, programmable  Isabelle Light – procedural proofs, metavariables

CLL

 Conservative  Combined inference rules

– proofs-as-processes π-calculus

 Syntax (polymorphic

type)

 Substitution  A few functions 61
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Implementation: π-calculus

P ::= define_type (A) Agent = | 0 Zero | x(y).P | In A (A list) Agent | x<y>.P | Out A (A list) Agent | (ν x) P | Res (A list) Agent | P || P | Comp Agent Agent | P + P | Plus Agent Agent 62
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Implementation: CLL

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Implementation: Proofs-as- processes

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References

 P. Papapanagiotou and J. Fleuriot (2011).

Formal verification of Web Services composition using Linear Logic and the pi- calculus, In Proceedings of 9th IEEE European

Conference on Web Services (ECOWS 2011), pages 31-38, September 14-16, 2011, Lugano, Switzerland. IEEE Computer Society.

 P. Papapanagiotou and J. Fleuriot (2011).

A theorem proving framework for the formal verification of Web Services Composition,

In Proceedings WWV 2011, EPTCS 61, pp. 1-16, doi: 10.4204/EPTCS.61.1 65
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Prospect for

MSc Pr MSc Project

  • ject

and beyond!

Contact us!

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