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

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... ...between these... ...and these? 7

Oops! 8

“LOGICAL” errors! 9

“LOGICAL” solution! 10

“LOGICAL” solution! Formal Verification! 11

Use logic to...  Describe  Specify  Reason  Assist 12

Web Services 13

Web Services 14

Web Services 15

Web Service Description: Inputs Outputs Preconditions Effects Service 16

Web Service Description: IOPEs Service Input Output 17

Web Service Description: IOPEs Service Preconditions Effects 18

Web Service Description: More? Cost! Quality! Service Location! Certification! 19

Web Services Description Language 20

Business Process Execution Language 21

Semantic Web Services: OWL-S 22

Example domain 23

USD to NOK Cm Select to Ski Inch Buyer Select Select Length Model 24

Example domain 25

House Alert Home Settlement Directory Home Criminal Insurance Service Buyer Title Search Estate Agent Contract Mortgage Service Service 26

Web Services Composition User Input Estate Settlement Agent House Alert Buyer Home Contract Directory Service Criminal Service Title Settlement Search or Home Exception Mortgage Insurance Service 27

Requirements  Compose correctly  Handle exceptions  Provide trust 28

We are also...  Offline  Quality-driven  Formal 29

The approach Classical π - Linear calculus Logic Proofs as processes 30

The approach HOL Light Classical π - Theorem Prover Linear calculus Logic Proofs as processes 31

The theory: π -calculus P ::= | 0 null process | x(y).P input | x<y>.P output |( ν x) P local variable | P || P parallel processes | P + P choice 32

The theory: Classical Linear Logic  FOL  CLL ⟦ p ; q ⟧ ⇒ p ⟦ p ; q ⟧ ⇒ p 33

The theory: Classical Linear Logic Disjunction Conjunction ⅋ ⊗ Multiplicative ⊕ & Additive . ⊥ Negation Red: input Blue: output 34

∧ The theory: Classical Linear Logic ∨ Disjunction Conjunction ⅋ ⊗ Multiplicative ⊕ & Additive . ⊥ Negation ¬ Red: input Blue: output 35

The theory: Classical Linear Logic ⊢ A ⊥ , B 36

The theory: Classical Linear Logic ⊢ A ⊥ , B ⊢ B ⊥ , C 37

The theory: Classical Linear Logic ⊢ A ⊥ , B ⊢ B ⊥ , C ⊢ A ⊥ , C 38

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

The theory: Classical Linear Logic ⊢ Height_cm ⊥ , Weight_kg ⊥ , Length_cm ⊢ Length_cm ⊥ , Length_inch ⊢ Height_cm ⊥ , Weight_kg ⊥ , Length_inch Select Cm to Length Inch 40

The theory: Classical Linear Logic 41

The theory: Proofs-as-processes Γ ⇒ π 42

Example: Tensor ( ⊗ ) rule 43

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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 45

WS Composition using proofs-as-processes Prove Extract Realisation Translate π -calculus Requested to CLL ... Service term 46

WS Composition using proofs-as-processes Prove Extract Realisation Translate π -calculus Requested to CLL ... Service term 47

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

Real Estate Example specified in CLL HomeDir : ⊢ HOME_CRITERIA ⊥ , HOME_LISTING 1. CriminalService : ⊢ REGION ⊥ , CRIMINAL_ACT 2. HouseAlert : ⊢ HOME_LISTING ⊥ , CRIMINAL_ACT ⊥ , 3. DESIRED_LEVEL ⊥ , HOME_TITLE_ID ⊗ HOME_AGENT_ID ⊗ HOME_DESC Buyer : ⊢ HOME_DESC ⊥ , HOME_OFFER 4. EstateAgentSeller : ⊢ HOME_AGENT_ID ⊥ , HOME_OFFER ⊥ , 5. ACCEPTED_OFFER ⊕ REJECTED_OFFER MortgageService : ⊢ CLIENT_INFO ⊥ , PREAPPROVAL ⊕ EXM 6. ContractService : ⊢ PREAPPROVAL ⊥ , ACCEPTED_OFFER ⊥ , 7. CONTRACT TitleSearch : ⊢ HOME_TITLE_ID ⊥ , TITLE ⊗ 8. (HOME_INSURANCE ⊕ HOME_INS_ID) HomeInsurance : ⊢ HOME_INS_ID ⊥ , HOME_INS 9. Settlement : ⊢ TITLE ⊥ , CONTRACT ⊥ , HOME_INS ⊥ , 10. SETTLEMENT 49

Ski Request in CLL ⊢ PRICE_LIMIT ⊥ , SKILL_LEVEL ⊥ , HEIGHT_CM ⊥ , WEIGHT_KG ⊥ , PRICE_NOK ⊕ ?EXCEPTION 50

Ski Request in CLL ⊢ PRICE_LIMIT ⊥ , SKILL_LEVEL ⊥ , HEIGHT_CM ⊥ , WEIGHT_KG ⊥ , PRICE_NOK ⊕ ?EXCEPTION What is the final exception?  Metavariables + unification! 51

WS Composition using proofs-as-processes Prove Extract Realisation Translate π -calculus Requested to CLL ... Service term 52

Proof for the Ski example 53

WS Composition using proofs-as-processes Prove Extract Realisation Translate π -calculus Requested to CLL ... Service term 54

Ski Result in π -calculus 55

Real Estate Result 56

WS Composition using proofs-as-processes Prove Extract Realisation Translate π -calculus Requested to CLL Execution Service term 57

Execution: PiVizTool  π -calculus is executable!  PiVizTool:  Visualisation of connections  Animation of execution  Empirical verification 58

PiVizTool 59

WS Composition using proofs-as-processes Prove Extract Realisation Translate π -calculus Requested to CLL Translation Service term Upcoming! BPEL OWL-S 60

Implementation: Details  HOL Light – flexible, programmable  Isabelle Light – procedural proofs, metavariables π -calculus CLL  Conservative  Syntax (polymorphic type)  Combined inference rules – proofs-as-processes  Substitution  A few functions 61

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

Implementation: CLL 63

Implementation: Proofs-as- processes 64

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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