Transformation of TCP-Net Queries into Preference Database Queries

Transcription

1 Transformation of TCP-Net Queries into Preference Database Queries Markus Endres and W. Kießling University of Augsburg Institute for Computer Science ECAI Advances in Preference Handling Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

2 Outline 1.Preferences Representation Representation 2.Database Systems Bridge Bridge 4.Ceteris Paribus Embedding 3.Artificial Intelligence 5.Summary and Outlook Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

3 1. Preferences are ubiquitous in all our daily lives Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

4 Representation of preferences (for product configuration) Database Community Artificial Intelligence Preference Algebra PSQL, PXPATH [J. Chomicki, W. Kießling] TCP-Nets [R. Brafman, C. Domshlak] Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

5 Representation of preferences (for product configuration) Database Community Artificial Intelligence Preference Algebra PSQL, PXPATH [J. Chomicki, W. Kießling] TCP-Nets [R. Brafman, C. Domshlak] Determine the best feasible outcome SELECT * FROM dinner PREFERRING maindish IN (meat) ELSE (fish) AND sidedish IN (rice) Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

6 Representation of preferences (for product configuration) Database Community Artificial Intelligence Preference Algebra PSQL, PXPATH [J. Chomicki, W. Kießling] TCP-Nets [R. Brafman, C. Domshlak] Determine the best feasible outcome SELECT * FROM dinner PREFERRING maindish IN (meat) ELSE (fish) AND sidedish IN (rice) Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

7 2. Database Community Preference Algebra Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

8 Preference Algebra Representation Preference is a strict partial order P = (A, < P ), where < P dom(a) dom(a). x < P y means I like y better than x better-than graph (BTG) Preference Constructors POS, NEG, POS/POS, POS/NEG, Prioritized, Pareto, LOWEST, HIGHEST, AROUND, BETWEEN, EXPLICIT,... Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

9 Preference Algebra POS-preference POS-preference a < P b a / POSset b POSset Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

10 Preference Algebra POS-preference POS-preference a < P b a / POSset b POSset Dinner example Dinner with dom(md) = {Meat, Fish, Pizza} Meat preferred to Fish or Pizza POS(MD, {Meat}) Preference term: a < P b (a = Fish a = Pizza) b = Meat Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

11 Preference Algebra Prioritized preference Prioritized preference P 1 = (A, < P1 ), P 2 = (B, < P2 ) base preferences P 1 is more important than P 2 : P 1 & P 2 Dinner example - continued Main dish more important than side dish: P 1 & P 2 dom(md) = {Meat, Fish, Pizza} dom(sd) = {Rice, Chips, Salad} Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

12 3. Artificial Intelligence TCP-nets Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

13 TCP-Nets Representation A schematic example of a tradeoff-enhanced CP-net a ā a : b b ā : b b b : c c b : c c A cp-arc i-arc B E B,E C D ci-arc e ē b : d d b : d d be : C D be : D C bē : D C Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

14 TCP-Nets Representation A schematic example of a tradeoff-enhanced CP-net a ā a : b b ā : b b b : c c b : c c A cp-arc i-arc B E B,E C D ci-arc be : C D be : D C bē : D C e ē b : d d b : d d Semantics Ceteris Paribus i.e. all else equal tradeoff, i.e. compromises Example preference ordering abcde ābcde ā b cde ā bcde Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

15 Dinner Configuration TCP and BTG S f S v Soup S f : W w W r S v : W r W Wine w Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

16 Dinner Configuration TCP and BTG S f S v Soup (S f, W w ) (S f, W r ) S f : W w W r S v : W r W Wine w (S v, W r ) (S v, W w ) Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

17 The Target Building a bridge Missing Condition in DB I prefer a red wine with a vegetable soup, and a white wine with a fish soup. Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

18 Given 4. Ceteris Paribus Embedding A new preference constructor a strict partial order preference P = (A, < P ) a set of attributes B with dom(a) dom(b) = tuples (a 1, b 1 ), (a 2, b 2 ) dom(a) dom(b) Then we define the ceteris paribus embedding P of P into B as: P = (A B, < P ) where (a 1, b 1 ) < P (a 2, b 2 ) a 1 < P a 2 b 1 = b 2 Notation: P := cp(p, B) P := cp(p, {b 1,..., b n }), b i dom(b) Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

19 Transformation into Preference Algebra - 1. Step Soup S f S v P 1 := POS(S, {S f }) = (S W, < ) := cp(p 1, W ) Wine Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

20 Transformation into Preference Algebra - 1. Step Soup S f S v P 1 := POS(S, {S f }) = (S W, < ) := cp(p 1, W ) BTG of Wine (S f, W w ) (S f, W r ) (S v, W w ) (S v, W r ) Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

21 Transformation into Preference Algebra - 2. Step Soup Situation 1: S f : W w W r P 2,1 := POS(W, {W w }) P 2,1 = (W {S f }, < P 2,1 ) := cp(p 2,1, {S f }) Wine Situation 2: S v : W r W f P 2,2 := POS(W, {W r }) P 2,2 = (W {S v }, < P 2,2 ) := cp(p 2,2, {S v }) Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

22 Transformation into Preference Algebra - 2. Step Soup Conditional situations combined dom(s) = {S f } {S v } P 2 = (S W ), < P 2 ) := P 2,1 P 2,2 BTG of P 2 Wine (S f, W w ) P 2 (S f, W r ) (S v, W w ) (S v, W r ) P2 Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

23 Transformation into Preference Algebra - 3. Step 1. Step (S f, W w ) (S f, W r ) (S v, W w ) (S v, W r ) 2. Step (S f, W w ) P 2 (S f, W r ) (S v, W w ) (S v, W r ) P2 Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

24 Transformation into Preference Algebra - 3. Step 1. Step (S f, W w ) (S f, W r ) (S v, W w ) (S v, W r ) 3. Step: P := P 2 (S f, W w ) P 2 (S f, W r ) 2. Step (S f, W w ) P 2 (S f, W r ) (S v, W w ) (S v, W r ) P 2 (S v, W w ) (S v, W r ) P2 Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

25 Not transitive! (S v, W r ) < (S f, W w )? Transitive Closure Necessary! (S f, W w ) P 2 (S f, W r ) (S v, W w ) (S v, W r ) P 2 Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

26 Not transitive! (S v, W r ) < (S f, W w )? Transitive Closure Necessary! (S f, W w ) P 2 (S f, W r ) (S v, W w ) (S v, W r ) P 2 TC( P 2 ) P 2 (S f, W w ) (S f, W r ) P1 TC TC P1 (S v, W w ) (S v, W r ) P2 Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

27 Not transitive! (S v, W r ) < (S f, W w )? (S f, W w ) P 2 Transitive Closure Necessary! (S f, W r ) The BTG (S f, W w ) (S v, W w ) (S v, W r ) P 2 (S f, W r ) TC( P 2 ) P 2 (S f, W w ) (S f, W r ) P1 TC TC P1 (S v, W w ) (S v, W r ) P2 (S v, W r ) (S v, W w ) Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

28 TC( P 2 ) is a preference Properties of P1 and P2 is irreflexive P 1 Unidirectional edges in the BTG x 1, x 2 dom(s), y, z dom(w ) : ((x 1, y) < P 1 P2 (x 2, y) (x 2, z) < P 1 P2 (x 1, z)) (S f, W w ) P 2 (S f, W r ) (S v, W w ) (S v, W r ) P 2 Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

29 5. Summary and Outlook BMO and Search-TCP Queries Determine a feasible outcome that is preferentially optimal Retrieve best matches only Search-TCP and BMO Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

30 5. Summary and Outlook Extending TCP-nets Missing numerical constructors in TCP-Nets Infinite domains POS/POS(M, {BMW},{VW}) M BMW: BETWEEN(C, [2500,4500]) VW: AROUND(C, 1800) C P LOWEST(Price) Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

31 5. Summary and Outlook Extending TCP-nets Missing numerical constructors in TCP-Nets Infinite domains POS/POS(M, {BMW},{VW}) M BMW: BETWEEN(C, [2500,4500]) VW: AROUND(C, 1800) C P LOWEST(Price) Outlook Optimizations of TCP-Net queries in Preference Algebra PSQL and PXPATH Implementation Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22

32 Questions and Comments Transformation of TCP-Net Queries into Preference Database Queries Markus Endres Preference Algebra & TCP-Nets Workshop on Advances in Preference Handling ECAI / 22