1. 1 Features as Constraints Rafael AccorsiUniv. Freiburg Carlos ArecesUniv. Amsterdam Wiet BoumaKPN Research Maarten de RijkeUniv. Amsterdam

2. 2 Overview of talk  Background & motivation  Non-monotonicity & constraint programming  Stable model semantics, Smodels  Using Smodels  Evaluation  Discussion

3. 3 Background & motivation  Wanted: ­User-oriented view of FI: encoding of behavior graphs ­Systematic approach to non-monotonicity  Try to avoid complications with model-oriented approaches like modelling IN-CS n in LOTOS, SDL or Process Algebra  Co-operation with UvA since 1999  Description Logic and Constraint Programming  Work on DL appeared independently in: Proceedings MASCOTS’99, October 1999, IEEE Computer Society ISBN 0-7695-0381-0

4. 4 Non-monotonicity & constraint programming  Idea: use constraints as a natural way to model non- monotonicity, or: give semantics to a system by the set of its possible models  Add features by constraining it further. Prune some models, generate new ones  non-monotonic additions  Model construction as well as querying can be implemented efficiently  Chose Smodels because of efficient implementation, and its facilities for querying

5. 5 Stable model semantics, Smodels  Standard logic programming semantics: where are atomic properties (predicates)  Clean semantics, but … no negation possible  Stable model semantics elegant way to model negation: if are in the model, and are not, then A should be included. Such models should be minimal (as in the classic case)

6. 6 Stable model semantics, Smodels -2-  A program can have 0, 1 or many stable models  Provided we ­don’t use functions, ­and look only at domain-restricted programs, there are efficient procedures for finding stable models of a logic program  Smodels is an implementation of these procedures with attractive extra features  Connection to non-monotonic reasoning is obvious  The compute statement enables to search for a specified number of models that include/exclude specified atomic predicates

7. 7 Stable model semantics, Smodels -3-  Model behavior graphs (Transition Systems) in such a way that the stable models correspond to the valid runs of the system is modeled as: S S2S2 S1S1 A1A1 A2A2

8. 8 Using Smodels  Need some refinements to encode subscribers, cycles and runs  Need new atoms to record state changes for other users  Use constraints on the dial action to prune unwanted behavior, like ­A subscriber can only establish one call in a given cycle

9. 9 Using Smodels -2-  Testing the BCS: 1.Generate all models, i.e. all valid runs for all subscribers. Current limit is 4 subscribers, 3 cycles (not included). Example: 3 subscribers, 3 runs gives ~18M models, and takes plm. 14hrs, 45 minutes 2.Ask queries by looking for (a number of) models with specific properties. Examples:  Two independent calls can be set up in a given cycle. compute 1 {path(s1, t1, s2,t1), path(s3,t1,s4,t1)} Plm. 15 minutes execution time  In 3 cycles, a user can establish 3 different calls. compute 1 {path(s1,1,_,_), path(s1,2,_,_),path(s3,3,_,_)} Plm. 11 minutes execution time

10. 10 Using Smodels -3-  Add features by adding constraints that prune the set of models, and enlarge it by adding new atoms  Simple methodology for adding features: 1.Define behavior 2.Identify how the feature explicitly modifies the behavior of BCS 3.Check properties on the featured system

11. 11 Using Smodels -4-  TCS  CFU + axioms that refine BCS. Needed because a naive implementation loses models that one wants to keep.

12. 12 Evaluation  Features can be added without changing code for BCS or other features  Checking properties on the featured BCS discovers interaction, because no valid runs are left for a specific configuration (modeled by a compute statement)  This way we show the existence of suspected interactions  So, have to write a sufficient set of properties in advance for each feature, or discover suspeced interactions by aqnother technique, e.g. model checking

13. 13 Discussion  Main aim: use stable model semantics as a means to model non-monotonicity. Proof of concept has been delivered  Advantage: used standard notions, methods and tools form the field of computational logic. So, a connection between Knowledge Engineering and FI has been made  Other implementations of stable model semantics like DeRes or XSB should be tested  A LOT more work has to be done