Matchmaking can be basically seen as the process of computing a ranked list of resources with respect to a given query. Semantic matchmaking can be hence described as the process of computing such ordered list also taking into account the semantics of resources description and of the query, provided with reference to a logic theory (an ontology, a set of rules, etc.). A matchmaking step is fundamental in a number of retrieval scenarios spanning from (Web) service discovery and composition to e-commerce transactions up to recruitment in human resource management for task assignment, just to cite a few of them. Also in interactive exploratory tasks, matchmaking and ranking play a fundamental role in the selection of relevant resources to be presented to the user and, in case, further explored. In all the above mentioned frameworks, the user query may contain only hard (strict) requirements or may represent also her preferences. In this talk we see how to use not only deductive reasoning tasks, e.g., subsumption and consistency checking, while computing the ranked list of most promising resources with respect to a query (with preferences).

1. Semantic Matchmaking and Ranking:
Beyond Deduction in Retrieval Scenarios
Tommaso Di Noia
SisInf Lab - Politecnico di Bari, Bari, Italy
t.dinoia@poliba.it
http://sisinflab.poliba.it/dinoia/
The 6th International Conference on Web Reasoning and Rule Systems
September 10, 2012, Vienna, Austria

2. 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.”
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

3. 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.
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

4. 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.
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

5. P2P Marketplaces
Looking for a non smoking room with WiFi included.
Bedroom for non smokers with cable connection
a
Twin room with Internet connection. Smoking.
b
Single room. Price includes SAT TV and use of SPA
c
Twin room. Smoking not allowed. Price includes WiFi,
d SAT TV and Breakfast
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

6. Matching and ranking
Looking for a non smoking room with WiFi included.
At least I know that I
have an Internet
connection
Bedroom for non smokers with cable connection
a
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

7. Matching and ranking
Looking for a non smoking room with WiFi included.
I will ask if they have
WiFi
Twin room with Internet connection. Smoking.
b
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

8. Matching and ranking
Looking for a non smoking room with WiFi included.
I will ask if they have
WiFi and if I it is a
non smoking room
Single room. Price includes SAT TV and use of SPA
c
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

9. Matching and ranking
Looking for a non smoking room with WiFi included.
Twin room. Smoking not allowed. Price includes WiFi,
d SAT TV and Breakfast
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

10. Matching and ranking
Looking for a smoking room with WiFi included.
a
b
c
d
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

11. Matching and ranking
Looking for a smoking room with WiFi included.
a
b
c
Best!
d
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

12. Matching and ranking
Looking for a smoking room with WiFi included.
a
b
How to rank?
c
d
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

13. 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
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

14. 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
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

15. What's next
• Penalty functions for ranking
• Non-standard reasoning tasks for matching
• A logic-based framework for matching and
ranking
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

16. Running example and
logic language
• B&B / Hotel
– Semanticized Craiglist
• Description Logics
– The framework can be
easily adapted to other
logic languages
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

17. The Ontology O
CableConnection v InternetConnection
WiFi v InternetConnection
WiFi v :CableConnection
SPA v FitnessFacilities
SAT-TV v TV v HotelFacilities
FitnessFacilities t Breakfast v HotelFacilities
Bedroom ´ Room u 9hasBeds u 9guests u 9price includes
SingleRoom ´ Bedroom u (· 1 hasBeds) u (· 1 guests)
TwinRoom ´ Bedroom u (= 2 hasBeds) u (· 2 guests)
SmokingRoom ´ Bedroom u 8guests.Smoker
NonSmokingRoom ´ Bedroom u 8guests.(:Smoker)
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

18. Deductive Inference Services in DLs
• Satisfiability: the query q is (not) compatible with
resource description r
O j= q u r v ?
a b
O j= q u r 6v ?
c
• Subsumption: the resource description completely
satisfies the query
O j= r v q d
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

19. Match classes
O j= r v q FULL Match: the resource description implies
1 all the characteristics required by the query.
r 2 F u(q; O) The query is fully satisfied.
Full, match is also known as Subsumption match
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

20. Match classes
O j= r v q FULL Match: the resource description implies
1 all the characteristics required by the query.
r 2 F u(q; O) The query is fully satisfied.
O 6j= r u q v ? POTENTIAL Match: the resource description is
2 compatible with the query. It could potentially
r 2 P o(q; O) match the query.
Potential, match is also known as Intersection match
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

21. Match classes
O j= r v q FULL Match: the resource description implies
1 all the characteristics required by the query.
r 2 F u(q; O) The query is fully satisfied.
O 6j= r u q v ? POTENTIAL Match: the resource description is
2 compatible with the query. It could potentially
r 2 P o(q; O) match the query.
PARTIAL Match: the resource description is
O j= r u q v ? not compatible with the query. There are some
3 chacteristics in the query that overlap the ones
r 2 P a(q; O) represented in the resource description. This
latter, partially matches the query.
Partial match is also known as Disjoint match
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

22. Some issues
Within a class, all the items are eqivalently good!
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
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

23. 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?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

24. Penalty Functions
Non-Symmetric: the penalty degree has a direction
p(r; q; O) 6= p(q; r; O)
Syntax Independent: the penalty depends only on
the semantics of q and r
O j= r1 ´ r2 ¡! p(r1 ; q; O) = p(r2 ; q; O)
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

25. Potential Match
pP o (r; q; O)
monotonic over implication
if r1 ; r2 2 P o(q; O) and O j= r1 v r2
then pP o (r1 ; q; O) · pP o (r2 ; q; O)
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

26. Example
WiFi v InternetConnection
:::
SAT-TV v TV v HotelFacilities
:::
Bedroom ´ Room u 9hasBeds u 9guests u 9price includes
NoSmokingRoom ´ Bedroom u 8guests.(:Smoker)
q = NoSmokingRoomu 8price includes.WiFi
r1 = NoSmokingRoomu 8price includes.(SAT-TV u InternetConnection)
r2 = Bedroom u 8price includes. u InternetConnection)
(TV
O j= r1 v r2
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

27. Example
q = NoSmokingRoomu 8price includes.WiFi
r1 = NoSmokingRoomu 8price includes.(SAT-TV u InternetConnection)
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

28. Example
q = NoSmokingRoomu 8price includes.WiFi
r1 = NoSmokingRoomu 8price includes.(SAT-TV u InternetConnection)
q = NoSmokingRoomu 8price includes.WiFi
r2 = Bedroom u 8price includes. u InternetConnection)
(TV
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

29. Partial Matches
pP a (r; q; O)
antimonotonic over implication
if r1 ; r2 2 P a(q; O) and O j= r1 v r2
then pP a (r1 ; q; O) ¸ pP a (r2 ; q; O)
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

30. Example
CableConnection t WiFi v InternetConnection
WiFi v :CableConnection
:::
Bedroom ´ Room u 9hasBeds u 9guests u 9price includes
NoSmokingRoom ´ Bedroom u 8guests.(:Smoker)
SmokingRoom ´ Bedroom u 8guests.Smoker
q = NoSmokingRoom u 8price includes.WiFi
r3 = SmokingRoom u 8price includes.CableConnection
r4 = Bedroom u 8guests.Smoker
O j= r3 v r4
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

31. Example
q = NoSmokingRoom u 8price includes.WiFi
r3 = SmokingRoom u 8price includes.CableConnection
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

32. Example
q = NoSmokingRoom u 8price includes.WiFi
r3 = SmokingRoom u 8price includes.CableConnection
q = NoSmokingRoomu 8price includes.WiFi
r4 = Bedroom u 8guests.Smoker
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

33. 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?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

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

35. 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 ⊑ ⟂. Partial match
Find two concepts G (for Give up) and K (for Keep) in
L such that
O j= GuK ´ q
O 6j= K ur v ?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

36. Concept Abduction
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 a concept H (for Hypotheses) in L such that
O 6j= ruH v ?
O j= ruH v q
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

37. Concept Abduction
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 ⊑ ⟂. Potential match
Find a concept H (for Hypothesis) in L such that
O 6j= ruH v ?
O j= ruH v q
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

38. 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?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

39. From Partial Match to Full Match
O j= q u r v ? Partial match
O j= GuK ´q
O 6j= K ur v ?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

40. From Partial Match to Full Match
O j= q u r v ? Partial match
O j= GuK ´q
O 6j= K ur v ?
Concept Contraction
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

41. From Partial Match to Full Match
O j= q u r v ? Partial match
O j= GuK ´q
O 6j= K ur v ? Potential match
Contracted query
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

42. From Partial Match to Full Match
O j= q u r v ? Partial match
O j= GuK ´q
O 6j= K ur v ? Potential match
O 6j= ruH v?
Concept Adbuction
O j= ruH vK
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

43. From Partial Match to Full Match
O j= q u r v ? Partial match
O j= GuK ´q
O 6j= K ur v ? Potential match
O 6j= ruH v?
O j= ruH vK Full match
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

44. Back to the initial example...
Looking for a non smoking room with WiFi included.
I will ask if they have
WiFi
Twin room with Internet connection. Smoking.
b
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

45. Back to the initial example...
O j=
NoSmokingRoomu 8price includes.WiFi
u
TwinRoom u SmokingRoom u
b 8price includes.InternetConnection
v?
Icons by http://dryicons.com
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

46. Back to the initial example...
q ´ Bedroom u 8price includes.WiFi u
8guests.(:Smoker)
K = Bedroom u 8price includes.WiFi
G = 8guests.(:Smoker)
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

47. Back to the initial example...
K = Bedroom u 8price includes.WiFi
r = TwinRoom u SmokingRoomu
8price includes.InternetConnection
H = 8price includes.WiFi
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

48. 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?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

49. Relationship between Penalty Functions
and Concept Contraction
incompatibility degree
pP a (r; q; O) of r with respect to q
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

50. Relationship between Penalty Functions
and Concept Contraction
incompatibility degree
pP a (r; q; O) of q with respect to r
O 6j= K ur v ?
O j= GuK ´ q
The reason why q is not
compatible with r
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

51. Intuition
O j= r1 v r2
O j= G1 u K1 ´ q
O j= q u r1 v ?
O j= K1 u r1 6v ?
O j= G2 u K2 ´ q
O j= q u r2 v ?
O j= K2 u r2 6v ?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

52. Intuition
O j= r1 v r2
O j= G1 u K1 ´ q
O j= q u r1 v ?
O j= K1 u r1 6v ?
O j= G2 u K2 ´ q
O j= q u r2 v ?
O j= K2 u r2 6v ?
We espect O j= G1 v G2
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

53. Intuition
r1 is “more incompatibile”
O j= G1 v G2 than r2
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

54. Intuition
r1 is “more incompatibile”
O j= G1 v G2 than r2
pP a (r1 ; q; O) ¸ pP a (r2 ; q; O)
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

55. Intuition
O j= G1 v G2
pP a (r1 ; q; O) ¸ pP a (r2 ; q; O)
Antimonotonic property of pPa
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

56. Intuition
O j= G1 v G2
pP a (r1 ; q; O) ¸ pP a (r2 ; q; O)
1.pPa depends on G and K
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

57. Intuition
O j= G1 v G2
pP a (r1 ; q; O) ¸ pP a (r2 ; q; O)
1.pPa depends on G and K
2.G and K represent an explanation for pPa
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

58. 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?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

59. Relationship between Penalty Functions
and Concept Contraction
pP o (r; q; O) how much we do not know
about r with respect to q
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

60. Relationship between Penalty Functions
and Concept Contraction
pP o (r; q; O) how much we do not know
about r with respect to q
O 6j= ruH v ?
O j= ruH v q
The reason why r is not
subsumed by q
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

61. Intuition
O j= r1 v r2
O 6j= q u r1 v ? O j= r1 u H1 v q
O 6j= q u r2 v ? O j= r2 u H2 v q
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

62. Intuition
O j= r1 v r2
O 6j= q u r1 v ? O j= r1 u H1 v q
O 6j= q u r2 v ? O j= r2 u H2 v q
We espect O j= H2 v H1
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

63. Intuition
r1 is “more informative”
O j= H2 v H1 than r2 with respect to q
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

64. Intuition
r1 is “more informative”
O j= H2 v H1 than r2 with respect to q
pP a (r1 ; q; O) · pP a (r2 ; q; O)
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

65. Intuition
O j= H2 v H1
pP a (r1 ; q; O) · pP a (r2 ; q; O)
Monotonic property of pPo
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

66. Intuition
O j= H2 v H1
pP a (r1 ; q; O) · pP a (r2 ; q; O)
1.pPo depends on H
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

67. Intuition
O j= H2 v H1
pP a (r1 ; q; O) ¸ pP a (r2 ; q; O)
1.pPo depends on H
2.H represents an explanation for pPo
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

68. 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?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

69. Global Penalty Function and
Explanation
p(r; q; O) = f (pP a (r; q; O); pP o (r; K; O))
G, K and H represent an explanation for p
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

70. 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?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

71. 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
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

72. Query refinement
O j= q u Hq v r
• 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
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

73. Example
q = NoSmokingRoomu 8price includes. WiFi
r = NoSmokingRoomu
8price includes.(SAT-TV u InternetConnection)
O j= q u Hq v r
8price includes.SAT-TV
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

74. 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?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

75. So far...
• Matchmaking as discovery
• Unilateral process
• The query “represents” the user
• No interaction with the two parties
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

76. What if...
• We have information on user preferences (profile)
• Both the users involved in the process express
their own preferences
• The process is bilateral
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

77. 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
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

78. Weighted formulas and
User Profile
p = hP; vi
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

79. Weighted formulas and
User Profile
p = hP; vi Utility associated to P
Logic Formula
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

80. Weighted formulas and
User Profile
p = hP; vi
U = fhP1 ; v1 i; : : : ; hPn ; vn ig
For each pair hPi ; vi i; hPj ; vj i 2 U
such that O j= Pi ´ Pj
then vi = vj
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

81. Problem statement
What is the utility, for each user,
associated to the final agreement?
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

82. Weighted propositional
formulas
X
u(m) = fv j hP; vi 2 U and m j= P g
The final agreement is a
propositional model
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

83. Example
p1 = htwin-room _ double-room; 0:3i
p2 = hcable-connection^ :twin-room; 0:4i
p3 = hdouble-room ! king-size; 0:3i
m = ftwin-room = true; double-room = f alse;
cable-connection = true; king-size = trueg
m j= twin-room_ double-room
m 6j= cable-connection^ :twin-room u(m) = 0:3 + 0:3
m j= double-room ! king-size
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

84. Weighted DLs formulas
Infinite set of models
Possible solution: Subsumption (implication-based)
X
uv (A) = fv j hP; vi 2 P and O j= A v P g
The final agreement
is a satisfiable DL formula
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

85. Issue
p1 = h9price includes. FitnessFacilities; v1 i
p2 = h9price includes. Breakfast; v2 i
p3 = hNoSmokingRoom; v3 i
A = (9price includes.FitnessFacilitiest
9price includes.Breakfast)u
NoSmokingRoom
O 6j= A v 9price includes.FitnessFacilities
O 6j= A v 9price includes.Breakfast uv (A) = v3
O j= A v NoSmokingRoom
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

86. Issue
O 6j= Av?
AI 6= ;
(NoSmokingRoom)I 6= ;
(9price includes.FitnessFacilities)I [
(9price includes.Breakfast)I 6= ;
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

87. Issue
O 6j= Av?
AI 6= ;
(NoSmokingRoom)I 6= ;
(9price includes.FitnessFacilities)I [
(9price includes.Breakfast)I 6= ;
At least one of these two sets must be non empty
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

88. Issue
O 6j= Av?
AI 6= ;
(NoSmokingRoom)I 6= ;
(9price includes.FitnessFacilities)I [
(9price includes.Breakfast)I 6= ;
u(A) = minfv1 + v3 ; v2 + v3 g
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

89. Interpretations
AI 6= ; ) I j= A
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

90. Interpretations
AI 6= ; ) I j= A
I1 j= 9price includes.FitnessFacilitiesu
9price includes.Breakfast u
NoSmokingRoom
I2 j= :9price includes.FitnessFacilitiesu
9price includes.Breakfastu
NoSmokingRoom
I3 j= 9price includes.FitnessFacilitiesu
:9price includes.Breakfastu
NoSmokingRoom
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

91. Interpretations
AI 6= ; ) I j= A
I1 j= 9price includes.FitnessFacilitiesu
9price includes.Breakfast u
2
NoSmokingRoom
What if we
I j= :9price includes.FitnessFacilitiesu
9price includes. also have an
Breakfastu
NoSmokingRoom ontology?
I3 j= 9price includes.FitnessFacilitiesu
:9price includes.Breakfastu
NoSmokingRoom
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

92. Minimal models and
minimal utility value
Minimal model
I j= fAg [ O
X
u(A) = fv j hP; vi 2 U and I j= P g is minimal
Minimal utility value
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

93. Ontological constraints
U = fhP1 ; v1 i; : : : ; hPn ; vn ig
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 : : :
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

94. Ontological closure
O j= A v :Pi t Pj t : : : t :Pk
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

95. Ontological closure
O j= A v :Pi t Pj t : : : t :Pk minimal
Á
CL(A; O; U) = fÁ1 ; : : : ; Áh g
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

96. From Ontological closure to
minimal utility value
Revert to ILP
CL(A; O; U) = fÁ1 ; : : : ; Áh g
X
Ái 2 CL(A; O; U) ) f(1 ¡ p) j :P 2 Ái g +
X
fp j P 2 Ái g ¸ 1
{0,1}-variable
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

97. From Ontological closure to
minimal utility value
Revert to ILP
CL(A; O; U) = fÁ1 ; : : : ; Áh g
X
Ái 2 CL(A; O; U) ) f(1 ¡ p) j :P 2 Ái g +
X
fp j P 2 Ái g ¸ 1
X
u(A; O) = min fv ¢ p j hP; vi 2 Ug
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

98. Example
A = Bedroom u (8guests.Smoker t 8guests.:Smoker) u
8price includes.WiFi
p1 = hNoSmokingRoom; 0:5i
p2 = hSmokingRoom; 0:1i
p3 = h8price includes. InternetConnection; 0:4i
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

99. Example
A = Bedroom u (8guests.Smoker t 8guests.:Smoker) u
8price includes.WiFi
p1 = hNoSmokingRoom; 0:5i
p2 = hSmokingRoom; 0:1i
p3 = h8price includes. InternetConnection; 0:4i
A v NoSmokingRoomt SmokingRoom
A u NoSmokingRoom v :SmokingRoom Ontology
A v 8price includes.InternetConnection
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

100. Example
CL(A; O; U) = fNoSmokingRoomt SmokingRoom ;
:NoSmokingRoomt :SmokingRoom ;
8price includes.InternetConnectiong
ns + s ¸ 1
(1 ¡ ns) + (1 ¡ s) ¸ 1
i ¸ 1
min(0:5 ¢ s + 0:1 ¢ ns + 0:4 ¢ i)
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

101. Bilateral matchmaking
U1 = 1 1 1 1
fhP1 ; v1 i; : : : ; hPn ; vn ig
Two user profiles
U2 = 2 2 2 2
fhP1 ; v1 i; : : : ; hPm ; vm ig
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

102. Bilateral matchmaking
U1 = 1 1 1 1
fhP1 ; v1 i; : : : ; hPn ; vn ig
Two user profiles
U2 = 2 2 2 2
fhP1 ; v1 i; : : : ; hPm ; vm ig
Utility
Pareto frontier
user2
Utility
user1
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

103. Pareto efficiency
• Nash solution: maximize u1 ¢ u2
• Welfare: maximize u1 + u2
Utility
user2
Utility
user1
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

104. 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
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

105. 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
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

106. 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.
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

107. Some references [2/3]
• 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.
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

108. Some references [3/3]
• 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.
The 6th Int. Conf. on Web Reasoning and Rule Systems – Sep. 10, 2012, Vienna, Austria

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