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Features as Constraints

Features as Constraints. Rafael Accorsi Univ. Freiburg Carlos Areces Univ. Amsterdam Wiet Bouma KPN Research Maarten de Rijke Univ. Amsterdam. Overview of talk. Background & motivation Non-monotonicity & constraint programming Stable model semantics, Smodels Using Smodels Evaluation

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Features as Constraints

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  1. Features as Constraints Rafael Accorsi Univ. Freiburg Carlos Areces Univ. Amsterdam Wiet Bouma KPN Research Maarten de Rijke Univ. Amsterdam

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

  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-CSn 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. 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. 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. 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. S1 A1 S A2 S2 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:

  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 actionto prune unwanted behavior, like • A subscriber can only establish one call in a given cycle

  9. Using Smodels -2- • Testing the BCS: • 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 • 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. 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: • Define behavior • Identify how the feature explicitly modifies the behavior of BCS • Check properties on the featured system

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

  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. 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

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