EL description logic modeling querying web and
      learning imperfect user preferences

                                     Peter Vojtáš

           Dpt. Software Eng., Fac. Math. Phys., Charles University Prague
                    Inst. Computer Sci., Czech Acad. Sci, Prague


        Abstract. In this position paper we share ideas on modeling querying
        web resources by (imperfect) combination of particular user preferences
        based on description logic. Our basic assumption is, that web resources
        are modeled crisp. Imperfection (uncertainty, vagueness,...) comes from
        user context and preferences. We offer a model based on connection be-
        tween three EL-description logic systems: classical, annotated(fuzzy) and
        a new variant of Bayesian description logic. The Bayesian part enables
        learning each single user’s combination function and concepts.


    In [2] R. Fagin et al. propose heuristics for a middleware for finding best
(top-k) answer when the data that we wish to access and combine may reside in
a variety of web repositories. We can look to the Fagin’s model as working with
fuzzy RDF data (ordered by user preference of particular attribute) and using a
combination function providing global score for ordering of resources. Our main
goal is to provide description logic counterpart for Fagin’s model.
    Typical example is a user looking for a hotel for vacation which is cheap
and close to a beach. Particular user preferences (wrt a fixed ordinal preference
scale T ) need to be combined to get an overall ordering of results. Our model
should be also able, for another user, to deliver e.g. hotels with medium price
and distance.
    In [9] we have proposed f-EL@ description logic allowing existential restric-
tions, crisp roles, T -fuzzy concepts and T -fuzzy aggregation functions. Our sys-
tem is less expressive than fuzzy description logic of U. Straccia [7] but more
effective and embeddable into RDF (and OWL) without reification.
    The user’s aggregation function is learned from his/her global preferences
by an Inductive logic programming system ([3]), combining T -degree of being
cheap and close to a global T -degree of being good for vacation). In practical
situations a problem can occur: when user evaluates a sample of resources by
a global preference, few inconsistencies in evaluation can lead to a constant
aggregation function as an only possible, strictly logical, solution. To overcome
this, we need to extend our model with a Bayesian part.
    For this, we can transform our previous work on imperfection in logic pro-
gramming [8] to description logic framework . In [8] we have shown that gener-
alized annotated programs (GAP) of M. Kifer and V.S. Subrahmanian [5] are
1
    Email: peter.vojtas@mff.cuni.cz , supported by Czech IT project 1ET100300517,
    1ET100300419 and MSM–0021620838
equivalent with an extension of classical logic programs with monotonicity ax-
ioms added, and these are (weakly) embeddable into Bayesian logic program of
K. Kersting and L. De Raedt [4]. Experiments where provided with Bayesian
networks BN (cheap, close and vacation are random variables over T ).
    In this position paper we share ideas on using connections between classical
EL description logic, f-EL@ description logic and a new variant of Bayesian
description logic B-EL for modeling user preference querying web resources.
    Several models of Bayesian description logic were described already in [1]. In
[6] Bayesian description logic programs are described. All mentioned systems use
a random distribution on the domain ∆I , or a measure on the power set of ∆I
and provide a challenge of inducing probability distribution over web resources,
properties and values.
    Our system does not model randomness over web data. Uncertainty and
vagueness comes with user and his/her context, interpretation of web data and
preferences. Resource data (roles price, distance) remain crisp, randomness is
touching only user query concepts (like a hotel for vacation) and user preference
concepts (like cheap, close) which are random variable over the ordinal prefer-
ence scale T . A cpd can describe user preference depending on distribution of
∃price.cheap and ∃distance.close.
    We did not provide any experiments with this model. Our experiments in
the logic programming framework give a well supported expectation that this
could be a technically sound candidate for a simple, sufficiently expressive model
for description of user preference querying of web resources. This leads to a
layered model - web resources are crisp and each single user specific part with
imperfection and learning ability.


References
  1. F. Baader, R. Kuesters, F. Wolter. Extensions to Description Logic, Handbook
     DL, 2003, 219-261
  2. R. Fagin, A. Lotem and M. Naor. Optimal aggregation algorithms for middleware,
     J. Computer and System Sciences 66 (2003), pp. 614–656
  3. T. Horváth, P. Vojtáš. Ordinal Classification with Monotonicity Constraints, In
     Proc. ICDM2006, LNAI 4065, Springer-Verlag 2006, 217 - 225
  4. K. Kersting, L. De Raedt. Bayesian Logic Programs, Technical Report 151, Uni-
     versity of Freiburg, 52 pages
  5. M. Kifer, V. S. Subrahmanian. ”Theory of generalized annotated logic program-
     ming and its applications”, J. Logic Programming, 12 (1992) pp 335–367
  6. L. Predoiu, Information Integration with Bayesian Description Logic Programs,
     WWW2006, May 2326, 2006, Edinburgh, UK
  7. U. Straccia. A fuzzy description logic for the Semantic web, In FLSW, Elsevier
     (2006) 73–90
  8. P. Vojtáš, M. Vomlelová. ”On models of comparison of multiple monotone clas-
     sifications”, In Proc. IPMU’2006, Éditions EDK, Paris, pp. 1236-1243
  9. P. Vojtáš. A description logic with combination of user preference concepts, crisp
     roles and existential restrictions, In EJC 2006, pp. 176-183, 2006