1. A Distributed Tabling Algorithm for Rule Based Policy Systems
Miguel Alves, Carlos Damasio, Wolfgang Nejdl, Daniel Olmedilla
IEEE Policy, June 4-6, 2006

2. Motivation Scenario Online Sharing Pictures
Bob:
Is Tom a friend of Bob?
Bob:
Is Tom a friend of Alice?
Bob:
Check local friend list
Bob:
Is Tom a friend of Frank?
Alice:
Is Tom a friend of Alice?
Frank:
Is Tom a friend of Frank?
Alice:
Is Tom a friend of Bob?
Alice:
Is Tom a friend of Frank?
Frank:
Is Tom a friend of Alice?
Frank:
Is Tom a friend of Bob?
Alice:
Check local friend list
Frank:
Check local friend list
Policy 2006
22/04/2019

3. Problem Statement CIA Agents
I show you my CIA badge
If you show me yours first
I show you my CIA badge
If you show me yours first
[ Li, Du,BonehWinsborough, Seamons, Jones. Oblivious Signature-Based Envelope DARPA ACM Symposium on Principles of Distributed Computing, 2003]
Policy 2006
22/04/2019

4. Problem Statement Loop Detection
From a declarative specification point of view
Loops may easily occur
Policies are complex and large in number
Typically, they are not under the control of a single person
Loops are not errors
However, if not handled correctly
They may end up in non-terminating evaluation
Policy 2006
22/04/2019

5. Problem Statement Existing Validation & Verification Techniques
Locally (on own policies)
Policy specification
Static checking
Tabling
Model checking
Etc.
They do not apply in a distributed setting because
Too large number of potential policies
Policies at other entities may be private
Policies are dynamic
Applicable policies are known only at runtime
Policy 2006
22/04/2019

6. SLD Resolution Definition
Goal G = ( L1, … , Lk , … , Lm )
Clause C = ( A :- M1 , … , Mn )
Resolvent G’ = ( L1, … , Lk-1 , M1 , … , Mn , Lk-1 , … , Lm ) θ
θ = mgu (Lk , A)
Policy 2006
22/04/2019

7. Each new sub-goal is tabled, and its answers stored in that table
Tabling Definition
Technique for goal-oriented evaluation of logic programs by storing computed answers in tables (a.k.a. tabulation)
Each new sub-goal is tabled, and its answers stored in that table
Resolution returns the answers of the table
Repeated answers are not propagated
Policy 2006
22/04/2019

8. friendOf(alice,alice)
Tabling Example
friendOf(X,alice)
friendOf(X,bob). friendOf (X,Y) :- friendOf (Y,X). friendOf (X,alice). □
friendOf(alice,X)
{bob/X}
{alice/X} □ □
friendOf(X,alice)
Subgoals
Answers □
friendOf(X,alice)
friendOf(X,alice)
friendOf(alice,X)
friendOf(alice,bob)
Reuse answer
Reuse answer
friendOf(alice,alice)
Policy 2006
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9. Distributed Tabling Elements
Peer Prover
Perform the logical operations on goals
Send a request to peer client for each new sub-goal selected and wait for the answers
Able to produce the proof of an answer
Peer Client
Keep the tables and answers for goal calls
Goal Manager
Interfaces a community with the outside world
One per community
Major function is to detect termination
Policy 2006
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10. Distributed Tabling Example of Running Architecture
Policy 2006
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11. Distributed Tabling Security & Privacy
Sharing dependencies during evaluation makes tabling easier
It brings privacy concerns
Sharing dependencies may discover partnerships and the policies themselves
Two kind of predicates:
Public: can be queried and included in the proof
Private: cannot be queried and must remain hidden
Two kinds of calls:
Authorization call (call for evaluation)
Proof (explanation of the evaluation)
Policy 2006
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12. Distributed Tabling Messages Interaction
Policy 2006
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13. Distributed Tabling Example
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14. Distributed Tabling Termination Detection
Crucial to detect
In order to inform the requester there are no more answers (or request failed)
Needed for Negation as Failure
Allow to free resources used during evaluation
Global Termination
Detect when all goals are finished
No need to share dependencies among peers
Local Termination
Detect when each goal is finished
Need to share dependencies
Privacy problems
It allows to have NAF
Policy 2006
22/04/2019

15. Conclusions & Further Work
A distributed tabling algorithm is presented
Detects loops
Without increasing the complexity of the system (PTIME)
Handles public and private policies and proof generation
Implemented and tested
Further work
Reduce communication among peers
Better management of information
Reduce risk of information leakage
Research on local termination algorithms
Taking privacy into account
In order to allow NAF
Policy 2006
22/04/2019