semantic matchmaking and ranking: beyond deduction in retrieval scenarios

The 6th International Conference on Web Reasoning and Rule Systems

September 10, 2012, Vienna, Austria

Tommaso Di Noia SisInf Lab - Politecnico di Bari, Bari, Italy

[email protected]

http://sisinflab.poliba.it/dinoia/

Semantic Matchmaking and Ranking:Semantic Matchmaking and Ranking:Beyond Deduction in Retrieval ScenariosBeyond Deduction in Retrieval Scenarios

mailto:[email protected]

http://sisinflab.poliba.it/dinoia/

The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

Matchmaking

“Matchmaking is the process of matching two people together, usually for the purpose of marriage, but the word is also used in the context of sporting events, such as boxing, and in business.”


Matchmaking

Matchmaking is an information retrieval task whereby queries and resources are expressed using semi-structured text in the form of advertisements, and task results are ordered (ranked) lists of those resources best fulfilling the query.


Semantic Matchmaking

Semantic matchmaking is a matchmaking task whereby queries and resources advertisements are expressed with reference to a shared specification of a schema for the knowledge domain at hand, i.e. an ontology.


P2P Marketplaces

Icons by http://dryicons.com

Looking for a non smoking room with WiFi included.

Bedroom for non smokers with cable connection

a

b

c

d

Twin room with Internet connection. Smoking.

Single room. Price includes SAT TV and use of SPA

Twin room. Smoking not allowed. Price includes WiFi,

SAT TV and Breakfast


Matching and ranking


Bedroom for non smokers with cable connection

a

At least I know that I have an Internet

connection





I will ask if they have WiFi

b






I will ask if they have WiFi and if I it is a

non smoking room

c

Single room. Price includes SAT TV and use of SPA





d

Twin room. Smoking not allowed. Price includes WiFi,

SAT TV and Breakfast




a

b

c

d

Looking for a smoking room with WiFi included.




a

b

c

d


B e s t !




a

b

c

d


How to rank?



OWA

Open-World Assumption (deal with incomplete information)

– The absence of any characteristic must not be interpreted as a constraint of absence

– Any characteristic can be added during a refinement process


Non-Symmetric

Non-Symmetric Evaluation

– The process is performed matching Resource description with respect to the Query

– The matchmaking result is different if we flip over Resource/Query descriptions


What's next

• Penalty functions for ranking

• Non-standard reasoning tasks for matching

• A logic-based framework for matching and ranking


Running example and logic language

• B&B / Hotel– Semanticized Craiglist

• Description Logics– The framework can be

easily adapted to other logic languages


The Ontology OCableConnection v InternetConnection

WiFi v InternetConnection

WiFi v :CableConnection

SPA v FitnessFacilities

SAT-TV v TV v HotelFacilities

FitnessFacilities t Breakfast v HotelFacilities

Bedroom ´ Roomu 9hasBedsu 9guestsu 9price includesSingleRoom ´ Bedroomu (· 1 hasBeds) u (· 1 guests)

TwinRoom ´ Bedroomu (= 2 hasBeds) u (· 2 guests)

SmokingRoom ´ Bedroomu 8guests.SmokerNonSmokingRoom ´ Bedroomu 8guests.(:Smoker)


Deductive Inference Services in DLs

• Satisfiability: the query q is (not) compatible with resource description r

• Subsumption: the resource description completely satisfies the query

O j= r v q

a b

c

d


O j= q u r v ?

O j= q u r 6v ?


Match classes

1FULL Match: the resource description implies all the characteristics required by the query. The query is fully satisfied.

Full, match is also known as Subsumption match

O j= r v q

r 2 Fu(q;O)


Match classes

1

2

FULL Match: the resource description implies all the characteristics required by the query. The query is fully satisfied.

POTENTIAL Match: the resource description is compatible with the query. It could potentially match the query.

O 6j= r u q v ?r 2 Po(q;O)

O j= r v q

r 2 Fu(q;O)

Potential, match is also known as Intersection match


Match classes

1

2

3

FULL Match: the resource description implies all the characteristics required by the query. The query is fully satisfied.

POTENTIAL Match: the resource description is compatible with the query. It could potentially match the query.

PARTIAL Match: the resource description is not compatible with the query. There are some chacteristics in the query that overlap the ones represented in the resource description. This latter, partially matches the query.

Partial match is also known as Disjoint match

O j= r u q v ?r 2 Pa(q;O)

O 6j= r u q v ?r 2 Po(q;O)

O j= r v q

r 2 Fu(q;O)


Some issues

FULL matches represent equivalently good resources with respect to the query

POTENTIAL and PARTIAL matches are the most common cases in resource discovery scenarios.

From the user's point of view is not so useful to have a bunch of resources that match potentially/partially the query

Within a class, all the items are eqivalently good!


Problem statement

In case of Potential or Partial match, how can a semantic matchmaker help users to choose the

best or at least the most promising results?


Penalty Functions

Non-Symmetric: the penalty degree has a direction

Syntax Independent: the penalty depends only on the semantics of q and r

p(r; q;O) 6= p(q; r;O)

O j= r1 ´ r2 ¡! p(r1; q;O) = p(r2; q;O)


Potential Match

monotonic over implication

if and

then

O j= r1 v r2r1; r2 2 Po(q;O)

pPo(r1; q;O) · pPo(r2; q;O)

pPo(r; q;O)


Example

q = NoSmokingRoomu 8price includes.WiFi

r1 = NoSmokingRoomu 8price includes.(SAT-TVu InternetConnection)

r2 = Bedroomu 8price includes.(TVu InternetConnection)

WiFi v InternetConnection

: : :

SAT-TV v TV v HotelFacilities

: : :

Bedroom ´ Roomu 9hasBedsu 9guestsu 9price includesNoSmokingRoom ´ Bedroomu 8guests.(:Smoker)

O j= r1 v r2


Example




Example




r2 = Bedroomu 8price includes.(TVu InternetConnection)


Partial Matches

antimonotonic over implication

if and

then

pPa(r; q;O)

O j= r1 v r2r1; r2 2 Pa(q;O)

pPa(r1; q;O) ¸ pPa(r2; q;O)


Example

CableConnection t WiFi v InternetConnection

WiFi v :CableConnection: : :

Bedroom ´ Roomu 9hasBedsu 9guestsu 9price includesNoSmokingRoom ´ Bedroomu 8guests.(:Smoker)SmokingRoom ´ Bedroomu 8guests.Smoker


r3 = SmokingRoomu 8price includes.CableConnection

r4 = Bedroomu 8guests.Smoker

O j= r3 v r4


Example




Example




r4 = Bedroomu 8guests.Smoker


Questions

• Are match classes related with each other?• Since partial matches are not necessarily

unrecoverable matches, can they be compared with potential matches?

• What does the penalty score represent for partial matches?

• What does the penalty score represent for potential matches?

• Can we have a single ranked list of resources?• How to use descriptions of discovered resources to

help the user in refining her query?


Concept Contraction

Let L be a Description Logic, O an ontology in L and

both r and q two concepts in L satisfiable w.r.t. O such

that O ⊧ r ⊓ q ⊑ ⟂.

Find two concepts G (for Give up) and K (for Keep) in L such that

O j= GuK ´ q

O 6j= K u r v ?


Concept Contraction



that O ⊧ r ⊓ q ⊑ ⟂.

Find two concepts G (for Give up) and K (for Keep) in L such that

O j= GuK ´ q

O 6j= K u r v ?

Partial match


Concept Abduction



that O ⊭ r ⊓ q ⊑ ⟂.

Find a concept H (for Hypotheses) in L such that

O 6j= r uH v ?O j= r uH v q


Concept Abduction



that O ⊭ r ⊓ q ⊑ ⟂.

Find a concept H (for Hypothesis) in L such that

Potential match



Questions








From Partial Match to Full Match

O j= G uK ´ q

O 6j= K u r v ?

O j= q u r v ? Partial match



O j= G uK ´ q

O 6j= K u r v ?

O j= q u r v ? Partial match

Concept Contraction



O j= G uK ´ q

O 6j= K u r v ?

O j= q u r v ?

Potential match

Contracted query

Partial match



O j= G uK ´ q

O 6j= K u r v ?

O j= q u r v ?

Potential match

Partial match

O 6j= r uH v ?O j= r uH v K

Concept Adbuction



O j= G uK ´ q

O 6j= K u r v ?

O j= q u r v ?

Potential match

Partial match

O 6j= r uH v ?O j= r uH v K Full match


Back to the initial example...



I will ask if they have WiFi

b




b


NoSmokingRoomu 8price includes.WiFi

O j=

u

v ?

TwinRoomu SmokingRoom u8price includes.InternetConnection



q ´ Bedroom u 8price includes.WiFi u8guests.(:Smoker)

K = Bedroom u 8price includes.WiFi

G = 8guests.(:Smoker)



r = TwinRoomu SmokingRoomu8price includes.InternetConnection

H = 8price includes.WiFi

K = Bedroom u 8price includes.WiFi


Questions








Relationship between Penalty Functions and Concept Contraction

pPa(r; q;O)incompatibility degree of r with respect to q



pPa(r; q;O)incompatibility degree of q with respect to r

O 6j= K u r v ?O j= G uK ´ q

The reason why q is not compatible with r


Intuition

O j= r1 v r2

O j= q u r1 v ?

O j= q u r2 v ?

O j= G1 uK1 ´ q

O j= K1 u r1 6v ?O j= G2 uK2 ´ q

O j= K2 u r2 6v ?


Intuition

O j= r1 v r2

O j= q u r1 v ?

O j= q u r2 v ?

We espect O j= G1 v G2

O j= G1 uK1 ´ q

O j= K1 u r1 6v ?O j= G2 uK2 ´ q

O j= K2 u r2 6v ?


Intuition

O j= G1 v G2r1 is “more incompatibile” than r2


Intuition

O j= G1 v G2

Antimonotonic property of pPa



Intuition

O j= G1 v G2

1.pPa depends on G and K



Intuition

O j= G1 v G2

1.pPa depends on G and K

2.G and K represent an explanation for pPa



Questions









how much we do not know about r with respect to q

pPo(r; q;O)



The reason why r is not subsumed by q

how much we do not know about r with respect to q

pPo(r; q;O)



Intuition

O j= r1 v r2

O 6j= q u r1 v ?

O 6j= q u r2 v ?

O j= r1 uH1 v q

O j= r2 uH2 v q


Intuition

We espect

O j= r1 v r2

O 6j= q u r1 v ?

O 6j= q u r2 v ?

O j= r1 uH1 v q

O j= r2 uH2 v q

O j= H2 v H1


Intuition

r1 is “more informative” than r2 with respect to qO j= H2 v H1


Intuition

r1 is “more informative” than r2 with respect to q

pPa(r1; q;O) · pPa(r2; q;O)

O j= H2 v H1


Intuition

Monotonic property of pPo


O j= H2 v H1


Intuition

1.pPo depends on H


O j= H2 v H1


Intuition

1.pPo depends on H

2.H represents an explanation for pPo


O j= H2 v H1


Questions








Global Penalty Function and Explanation

G, K and H represent an explanation for p

p(r; q;O) = f(pPa(r; q;O); pPo(r;K;O))


Questions








Query refinement

• We are under an Open World Assumption. • What the user does not specify in the query is

something the user – did not know– did not care– completely forgot to mention

• We can suggest the user to refine her query by using extra information found in the resources retrieved by the matchmaker


Query refinement

• Hq represents what has to be hypothesized in q in order to satisfy r

• Hq represents those characteristics described in r but not specified (yet) in q

O j= q uHq v r


Example

O j= q uHq v r

q = NoSmokingRoomu 8price includes.WiFir = NoSmokingRoomu

8price includes.(SAT-TVu InternetConnection)

8price includes.SAT-TV


Questions








So far...

• Matchmaking as discovery

• Unilateral process

• The query “represents” the user

• No interaction with the two parties


What if...

• We have information on user preferences (profile)

• Both the users involved in the process express their own preferences

• The process is bilateral


What if...

• We have information on user preferences (profile)

• Both the users involved in the process express their own preferences

• The process is bilateral

Bilateral Matchmaking = Bilateral Negotiation


Weighted formulas and User Profile

p = hP; vi



p = hP; vi

Logic Formula

Utility associated to P



p = hP; vi

U = fhP1; v1i; : : : ; hPn; vnig

For each pair

such that

then

hPi; vii; hPj ; vji 2 U

O j= Pi ´ Pj

vi = vj


Problem statement

What is the utility, for each user, associated to the final agreement?


Weighted propositional formulas

The final agreement is a propositional model

u(m) =X

fv j hP; vi 2 U and m j= Pg


Example

p1 = htwin-room_ double-room; 0:3ip2 = hcable-connection^ :twin-room; 0:4ip3 = hdouble-room! king-size; 0:3i

m = ftwin-room= true;double-room= false;

cable-connection= true;king-size= trueg

m j= twin-room_ double-room

m 6j= cable-connection^ :twin-roomm j= double-room! king-size

u(m) = 0:3 + 0:3


Weighted DLs formulas

Infinite set of models

Possible solution: Subsumption (implication-based)

The final agreement is a satisfiable DL formula

uv(A) =X

fv j hP; vi 2 P and O j= A v Pg


Issue

uv(A) = v3

p1 = h9price includes.FitnessFacilities; v1ip2 = h9price includes.Breakfast; v2ip3 = hNoSmokingRoom; v3i

A = (9price includes.FitnessFacilitiest9price includes.Breakfast)uNoSmokingRoom

O 6j= A v 9price includes.FitnessFacilitiesO 6j= A v 9price includes.BreakfastO j= A v NoSmokingRoom


Issue

O 6j= A v ?AI 6= ;

(NoSmokingRoom)I 6= ;

(9price includes.FitnessFacilities)I [(9price includes.Breakfast)I 6= ;


Issue

O 6j= A v ?AI 6= ;



At least one of these two sets must be non empty


Issue

O 6j= A v ?AI 6= ;



u(A) = minfv1 + v3; v2 + v3g


Interpretations

AI 6= ; ) I j= A


Interpretations

AI 6= ; ) I j= A

I1 j= 9price includes.FitnessFacilitiesu9price includes.BreakfastuNoSmokingRoom

I2 j= :9price includes.FitnessFacilitiesu9price includes.BreakfastuNoSmokingRoom

I3 j= 9price includes.FitnessFacilitiesu:9price includes.BreakfastuNoSmokingRoom


Interpretations

AI 6= ; ) I j= A

I1 j= 9price includes.FitnessFacilitiesu9price includes.BreakfastuNoSmokingRoom

I2 j= :9price includes.FitnessFacilitiesu9price includes.BreakfastuNoSmokingRoom

I3 j= 9price includes.FitnessFacilitiesu:9price includes.BreakfastuNoSmokingRoom

What if we also have an

ontology?


Minimal models and minimal utility value

I j= fAg [ Ou(A) =

Xfv j hP; vi 2 U and I j= Pg is minimal

Minimal utility value

Minimal model


Ontological constraints

U = fhP1; v1i; : : : ; hPn; vnig

² O j= A v Pi

² O j= A v Pi t :Pj t : : :

² O j= A u Pi u :Pj u : : : v ?

² O j= A u Pi u :Pj u : : : v Pk u :Ph u : : :


Ontological closure

O j= A v :Pi t Pj t : : : t :Pk


Ontological closure

Á

minimalO j= A v :Pi t Pj t : : : t :Pk

CL(A;O;U) = fÁ1; : : : ; Áhg


From Ontological closure to minimal utility value

Revert to ILP

{0,1}-variable

CL(A;O;U) = fÁ1; : : : ; Áhg

Ái 2 CL(A;O;U) )X

f(1 ¡ p) j :P 2 Áig +X

fp j P 2 Áig ¸ 1


From Ontological closure to minimal utility value

Revert to ILP

u(A;O) = minX

fv ¢ p j hP; vi 2 Ug

CL(A;O;U) = fÁ1; : : : ; Áhg

Ái 2 CL(A;O;U) )X

f(1 ¡ p) j :P 2 Áig +X

fp j P 2 Áig ¸ 1


Example

A = Bedroomu (8guests.Smokert 8guests.:Smoker) u8price includes.WiFi

p1 = hNoSmokingRoom; 0:5ip2 = hSmokingRoom; 0:1ip3 = h8price includes.InternetConnection; 0:4i


Example

A = Bedroomu (8guests.Smokert 8guests.:Smoker) u8price includes.WiFi

p1 = hNoSmokingRoom; 0:5ip2 = hSmokingRoom; 0:1ip3 = h8price includes.InternetConnection; 0:4i

A v NoSmokingRoomt SmokingRoom

A u NoSmokingRoomv :SmokingRoomA v 8price includes.InternetConnection

Ontology


Example

min(0:5 ¢ s+ 0:1 ¢ ns + 0:4 ¢ i)

ns+ s ¸ 1

(1 ¡ ns) + (1 ¡ s) ¸ 1

i ¸ 1

CL(A;O;U) = fNoSmokingRoomt SmokingRoom ;

:NoSmokingRoomt :SmokingRoom ;8price includes.InternetConnectiong


Bilateral matchmaking

Two user profilesU1 = fhP 11 ; v11i; : : : ; hP 1n ; v1nigU2 = fhP 21 ; v21i; : : : ; hP 2m; v2mig


Bilateral matchmaking

Two user profilesU1 = fhP 11 ; v11i; : : : ; hP 1n ; v1nigU2 = fhP 21 ; v21i; : : : ; hP 2m; v2mig

Utility user1

Utility user2

Pareto frontier


Pareto efficiency

Utility user2

Utility user1

• Nash solution: maximize• Welfare: maximize

u1 ¢ u2u1 + u2


Conclusion

• Semantic resource retrieval needs frameworks and tools that go beyond pure deductive procedures

• Non-standard reasoning as a powerful tool for matchmaking as discovery

• Utility theory for bilateral matchmaking as negotiation


Acknowledgments

In alphabetical order:

Simona Colucci, Eugenio Di Sciascio, Francesco M. Donini, Agnese Pinto, Azzurra Ragone, Michele Ruta, Eufemia Tinelli

and all the other guys at SisInf Lab


Some references [1/3]

• T. Di Noia, E. Di Sciascio, and F.M. Donini. Extending Semantic-Based Matchmaking via Concept Abduction and Contraction. In EKAW ’04, pp. 307–320, 2004.

• T. Di Noia, E. Di Sciascio, and F.M. Donini. Semantic Matchmaking as Non-Monotonic Reasoning: A Description Logic Approach. JAIR, 29:269–307, 2007.

• T. Di Noia, E. Di Sciascio, and F.M. Donini. Semantic matchmaking via non-monotonic reasoning: the MaMas-tng matchmaking engine. Communications of SIWN, 5:67–72, 2008.

• T. Di Noia, E. Di Sciascio, F.M. Donini, and M. Mongiello. A system for principled Matchmaking in an electronic marketplace. IJEC, 8(4):9–37, 2004.

• T. Di Noia, E. Di Sciascio, and F. M. Donini. Computing information minimal match explanations for logic-based matchmaking. In WI/IAT ’09, pp. 411–418, 2009.



• S. Colucci, T. Di Noia, E. Di Sciascio, F.M. Donini, and M. Mongiello. A Uniform Tableaux-Based Method for Concept Abduction and Contraction in Description Logics. In ECAI ’04, pp. 975–976, 2004.

• S. Colucci, T. Di Noia, E. Di Sciascio, F. M. Donini, and A. Ragone. A unified framework for non-standard reasoning services in description logics. In ECAI ’10, pp. 479–484, 2010.

• S. Colucci, T. Di Noia, A. Pinto, A. Ragone, M. Ruta, and E. Tinelli. A non-monotonic approach to semantic matchmaking and request refinement in e-marketplaces. IJEC, 12(2):127–154, 2007.

• A. Ragone, T. Di Noia, E. Di Sciascio, and F.M. Donini. Logic-based automated multi-issue bilateral negotiation in peer-to-peer e-marketplaces. J.AAMAS, 16(3):249–270, 2008.



• A. Ragone, U. Straccia, T. Di Noia, E. Di Sciascio, and F.M. Donini. Fuzzy matchmaking in e-marketplaces of peer entities using Datalog. FSS, 10(2):251–268, 2009.

• A. Ragone, T. Di Noia, E. Di Sciascio, F. M. Donini, and Michael Wellman. Computing utility from weighted description logic preference formulas. In DALT ’09, pp. 158–173, 2009.

• A. Ragone, T. Di Noia, F. M. Donini, E. Di Sciascio, and Michael Wellman. Weighted description logics preference formulas for multiattribute negotiation. In SUM ’09, pp. 193–205, 2009.


Thank You

semantic matchmaking and ranking: beyond deduction in retrieval scenarios

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