Luís Moniz Pereira Centro de Inteligência Artificial - CENTRIA

1. User preference information in query answering Pierangelo Dell’Acqua Aida Vitória Dept. of Science and Technology - ITN Linköping University, Sweden Luís Moniz Pereira Centro de Inteligência Artificial - CENTRIA Universidade Nova de Lisboa, Portugal

2. Motivation • Query answering systems are often difficult to use because they do not attempt to cooperate with their users. • We discuss the use of additional information about the user to enhance cooperative behaviour from query answering systems.

3. Idea • Consider a system whose knowledge is defined as: (P, R) P is a set of rules and R expresses preference information over the rules in P. When the rules in P conflict, then some rules are preferred over others according to R. P is used to derive conclusions and the preferences in R to derive the preferred conclusions.

4. Idea • Extra level of flexibility - if the user can provide preference information at query time: ?- (G,Pref ) Given (P,R), the system has to derive G from P by taking into account the preferences in R which are updated by the preferences in Pref.

5. Idea • Finally, it is desirable to make the background knowledge (P,R) of the system updatable in a way that it can be modified to reflect changes in the world (including preferences).

6. Update reasoning • Updates model dynamically evolving worlds. • Knowledge, whether complete or incomplete, can be updated to reflect world change. • New knowledge may contradict and override older one. • Updates differ from revisions which are about an incomplete static world model.

7. Preference reasoning • Preferences are employed with incomplete knowledge when several models are possible. • Preferences act by choosing some of the possible models. • They do this via a partial order among rules. Rules will only fire if they are not defeated by more preferred rules.

8. Preference and updates combined • Despite their differences preferences and updates display similarities. • Both can be seen as wiping out rules: • in preferences the less preferred rules, so as toremove models which are undesired. • in updates the older rules, inclusively for obtaining models in otherwise inconsistent theories. • This view helps put them together into a single uniform framework. • In this framework, preferences can be updated.

9. LP framework Atomic formulae: Aatom not Adefault atom Formulae: L0¬ L1 ,... , Ln generalized rule every Li is an atom or a default atom

10. LP framework Let N={ n1,…, nk } be a set of constants containing a unique name for each generalized rule. priority rule Zis a literal nr<nu or not nr<nu Z ¬ L1 , ... , Ln nr<nu means that rule r is preferred to rule u Def. Prioritized logic program Let P be a set of generalized rules and R a set of priority rules. Then =(P,R) is a prioritized logic program.

11. Dynamic prioritized programs Let S={1,…,s,…} be a set of states (natural numbers). Def. Dynamic prioritized program Let (Pi,Ri) be a prioritized logic program for every iS, then = {(Pi,Ri) : iS} is a dynamic prioritized program. Intuitively, the meaning of such a sequence results from updating (P1, R1) with the rules from (P2, R2), and then updating the result with … the rules from (Pn, Rn)

12. Example: dynamic prioritized program This example illustrates the use of contextual preferences to select preferred models. (1) Suppose a scenario where John wants to buy a magazine. He can buy either a sport magazine (sm), a travel magazine (tm) or a financial magazine (fm). sm ¬ not fm, not tm (r1) tm ¬ not fm, not sm (r2) fm ¬ not sm, not tm (r3) office (r4) n1<n3¬ holiday n2<n3¬ holiday n3<n1 ¬ office n3<n2 ¬ office P1 R1 When John is at the office his preferred magazine is a financial magazine.

13. Example: dynamic prioritized program (2) Next, suppose that John goes on vacation. P2 not office (r5) holiday (r6) R2 Now, John has two alternative magazines equally preferable: sport and travel magazine.

14. Queries with preferences • The ability to take into account the user information makes the system able to target its answers to the user’s goal and interests. Def. Queries with preferences Let G be a goal,  a prioritized logic program and ={(Pi,Ri) : iS} a dynamic prioritized program. Then ?- (G,) is a query wrt. 

15. Joinability function S+ = S  { max(S) + 1 } Def. Joinability at state s Let sS+ be a state, ={(Pi,Ri) : iS} a dynamic prioritized program and =(PX,RX) a prioritized logic program. The joinability function s at state s is: s  = {(Pi,Ri) : iS+} (Pi, Ri) if 1  i < s (Pi,Ri) = (PX, RX) if i = s (Pi-1, Ri-1) if s < i  max(S+)

16. Example: car dealer Consider the following program that exemplifies the process of quoting prices for second-hand cars. price(Car,200) ¬ stock(Car,Col,T), not price(Car,250), not offer (r1) price(Car,250) ¬ stock(Car,Col,T), not price(Car,200), not offer (r2) prefer(orange) ¬ not prefer(black) (r3) prefer(black) ¬ not prefer(orange) (r4) stock(Car,Col,T) ¬ bought(Car,Col,Date), T=today-Date (r5)

17. Example: car dealer When the company buys a car, the information about the car must be added to the stock via an update: bought(fiat,orange,d1) When the company sells a car, the company must remove the car from the stock: not bought(volvo,black,d2)

18. Example: car dealer The selling strategy of the company can be formalized as: n2 < n1 ¬ stock(Car,Col,T), T < 10 n1 < n2 ¬ stock(Car,Col,T), T  10, not prefer(Col) n2 < n1 ¬ stock(Car,Col,T), T  10, prefer(Col) n4 < n3 price(Car,200) ¬ stock(Car,Col,T), not price(Car,250), not offer (r1) price(Car,250) ¬ stock(Car,Col,T), not price(Car,200), not offer (r2) prefer(orange) ¬ not prefer(black) (r3) prefer(black) ¬ not prefer(orange) (r4) stock(Car,Col,T) ¬ bought(Car,Col,Date), T=today-Date (r5)

19. Example: car dealer Suppose that the company adopts the policy to offer a special price for cars at a certain times of the year. price(Car,100) ¬ stock(Car,Col,T), offer (r6) not offer Suppose an orange fiat bought in date d1 is in stock and offer does not hold. Independently of the joinability function used: ?- ( price(fiat,P), ({},{}) ) P = 250 if today-d1 < 10 P = 200 if today-d1  10

20. Example: car dealer ?- ( price(fiat,P), ({},{not (n4 < n3), n3 < n4}) ) P = 250 • For this query it is relevant which joinability function is used: • if we use 1, then we do not get the intended answer since the user • preferences are overwritten by the default preferences of the company; • on the other hand, it is not so appropriate to use max(S+) since a • customer could ask: ?- ( price(fiat,P), ({offer},{}) )

21. Joinability function • In some applications the user preferences in  must have priority over the preferences in . In this case, the joinability function max(S+) must be used. Example: a web-site application of a travel agency whose database  maintains information about holiday resorts and preferences among touristy locations. When a user asks a query ?- (G, ), the system must give priority to . • Some other applications need the joinability function 1to give priority to the preferences in .

22. Conclusions • Novel logical framework: • update and preference information can be specified and used in query answering systems. • declarative semantics is stable model based. • procedural semantics based on a syntactical transformation (correct and complete).

23. Future work • A preference metalanguage that compiles the pairwise preference specification. • Detect inconsistent preference specifications. • How to incorporate abduction in our framework: abductive preferences leading to conditional answers depending on accepting a preference. • How to tackle the problem arising when several users query the system together.

24. Preferred stable models Let = {(Pi,Ri) : iS} be a dynamic prioritized program, Q = { PiRi : iS }, PR = i(PiRi) and M an interpretation of P. Def. Default and Rejected rules Default(PR,M) = {not A :  (A¬Body) in PR and M |=body} Reject(s,M,Q) = { r  PiRi : r’ PjRj, head(r)=not head(r’), i<js and M |=body(r’) }

25. Preferred stable models Def. Unsupported and Unprefered rules Unsup(PR,M) = {r  PR : M |=head(r) and M |¹body-(r)} Unpref(PR,M) is the least set including Unsup(PR, M) and every rule r such that: • r’  (PR – Unpref(PR, M)) : M |=r’ < r,M |=body+(r’) and [not head(r’)body-(r) or(not head(r)  body-(r’) and M |=body(r))]

26. Preferred stable models Def. Preferred stable models Let s be a state, ={(Pi,Ri) : iS} a dynamic prioritized program, and M a stable model of . M is a preferred stable model of  at state s iff M = least( [X - Unpref(X, M)]  Default(PR, M) ) where: PR = is(PiRi) Q = { PiRi : iS } X = PR - Reject(s,M,Q)

27. Preferred conclusions Def. Preferred conclusions Let sS+ be a state and ={(Pi,Ri) : iS} a dynamic prioritized program. The preferred conclusions of  with joinability function s are: (G,) : G is included in every preferred stable model of s  at state max(S+)