=Paper=
{{Paper
|id=Vol-292/paper-7
|storemode=property
|title=Ontology Revision as Non-Prioritized Belief Revision
|pdfUrl=https://ceur-ws.org/Vol-292/paper7.pdf
|volume=Vol-292
|authors=Mauro Mazzieri and Aldo Franco Dragoni,pages 58-69
|dblpUrl=https://dblp.org/rec/conf/semweb/MazzieriD07
}}
==Ontology Revision as Non-Prioritized Belief Revision==
https://ceur-ws.org/Vol-292/paper7.pdf
Ontology Revision as Non-Prioritized Belief
Revision
Mauro Mazzieri and Aldo Franco Dragoni
Department of Electronics, Artificial Intelligence and Telecommunications,
Università Politecnica delle Marche, Ancona, Italy
{m.mazzieri,a.f.dragoni}@univpm.it
Abstract. Ontology revision is the process of managing an ontology
when a new axiom or fact would render it inconsistent. So far, the AGM
approach to belief revision has been adapted to work with ontologies.
However, when multiple sources are contributing uncertain knowledge
about a static domain, an approach that doesn’t give priority to incoming
information and allows to recover previously discarded axioms is more
suited.
We describe an ontology revision framework that links symbolic and
numerical techniques to allow the consistent evolution of an ontology
from the contributions of multiple potentially unreliable sources.
Key words: Ontology revision, belief revision, OWL.
1 Introduction
An explicit specification of a conceptualization for a shared domain of discourse
is called an ontology[1]. Hence, changes in ontologies are caused by changes either
in the domain, or in the conceptualization, or in the defined specification[2].
Ontology evolution[3] is the process of modifying an ontology in response to
a change in the domain (first kind of change) or its conceptualization (second
kind). The case of change in the domain is analogous to belief updating, thus it
can be defined as ontology updating (more on this on §3). This work deals with
changes in the shared conceptualization: a problem analogous to belief revision,
thus the name ontology revision. The third kind of change refers to a change in
the way the conceptualization is formally recorded; this type of change is dealt
with in the field of ontology translation[4].
Current work on ontology evolution is based on the idea of bringing the
AGM belief change theory[5, 6] to work within ontology evolution; Flouris’ PhD
thesis[3] contains both novel contributions and a survey of the field; [7] depicts
the state of the art in AGM-based ontology revision.
However, AGM belief revision is not apt to all kind of ontology changes. One
of its principles states that incoming information has a priority: it must belong
to the new set of beliefs. This principle works well when the new information
represent a certain fact: either a realization of the new contingent state of the
world, or a correction of a previous error in conceptualization, or a required
58 International Workshop on Emergent Semantics and Ontology Evolution
2 Mauro Mazzieri and Aldo Franco Dragoni
property of the formalization. The principle can not be accepted when the new
information represents a new evidence about the world, supposed to be a fixed
static entity, while its description is only partial and uncertain. In particular,
it can not be accepted in a distributed environment, where multiple potentially
unreliable information sources are present. Not only an information from an
external source can not be unconditionally accepted (can you trust everything
you hear?); also, there is not always a relation between the arrival order of
information and their acceptability.
There are many different possibility to discard the principle of priority to
incoming information. Hansson[8] makes a survey of different varieties of non-
prioritized belief revision, i.e. belief revision in which the new information has
no special priority due to its novelty. The problem is when and how to choose if
the new information must be accepted. We will follow an integrated approach,
already successfully applied to a juridical domain[9], which deals with old and
new information as they were come at the same time. This approach relies both
on symbolic and numerical techniques and make use of a new principle, called
principle of recoverability[10] 1 :
Any previously held piece of knowledge should belong to the current
knowledge space if consistent with it.
To circumscribe the work, we will refer to a specific use case. A team of
loosely-coordinated domain experts has the duty to build an ontology for their
domain. Each team member contributes to the activity building his conceptual-
ization with an editor. The domain is assumed as a fixed static entity, while the
conceptualization is constantly changing during the building and refinement pro-
cess. The work of each member is shared with the other experts in a peer-to-peer
way: each member receives the contribution of the other experts. A supporting
software must be able to use an ontology revision mechanism to maintain a con-
sistent local ontology to be visualized and used as the basis for further editing.
An example of a work session will be shown in section 5.
In the following we will first summarize in an informal way the syntax and
semantic of the OWL ontology language (§2). Then, after an introdution to the
problem of ontology revision (§3), we will show the proposed revision procedure
(§4), both in its symbolical (§4.1) and numerical (§4.2) steps. Finally in §6 we
sketch the future research perspectives.
2 Ontology
The OWL web ontology language[12] is the language used for publishing and
sharing ontologies on the World Wide Web. OWL is developed as an extension
of the RDF[13] knowledge representation language. The language has two specific
subsets: OWL DL and OWL Lite. The complete language is called OWL Full
1
Introduced as the store and recover principle[11] and also known as the principle of
persistence[9].
ESOE, Busan - Korea, November 2007 59
Ontology Revision as Non-Prioritized Belief Revision 3
to distinguish it from the subsets. The DL in OWL DL stands for “Description
Logic”[14], a decidable subset of first order logic used for expressing structured
knowledge. OWL DL and OWL Lite are both based on description logic; the
former is more expressive, while the latter has better computational properties.
In order to introduce the problem of ontology revision and to make the work
self-contained, we will give here an informal definition of an ontology language
syntax and semantics, roughly correspondant to OWL Lite. The full formal se-
mantics and syntact can be found in [15].
2.1 Syntax
The basic building blocks of an ontology are classes, individuals and properties.
A class is related to a set of individuals, called class extension. Properties can be
either data-valued, relating individuals to values, or individual-valued, relating
individuals to other individuals.
An ontology is a set of class axioms, property axioms and facts.
There are two kinds of class axioms. A class can be defined as either exactly
equivalent to the conjunction of a set of superclasses, or as a subclass of the
conjunction of a set of superclasses. A superclass can be either another class, or
an anonymous class specified giving constraints on properties.
The allowed restrictions on property values are:
– all the values must be instances of a class (or from a datatype, in the case
of data-valued properties);
– some of the values must be instances of a class (or from a datatype, in the
case of data-valued properties);
– the cardinality must be at least (or at most, or equal to) either 0 or 1.
Property axioms are used to define properties. A property can be given a
super-property, allowing the construction of a property hierarchy. Properties
can also be given domains and ranges.
Data-valued properties can be specified as partial functional, i.e. with at most
a value. Individual-valued properties can be specified to be functional, inverse-
functional, symmetric, transitive, or the inverse of another property.
Finally, a fact states that an individual belongs to a class or that an individ-
ual’s property has a certain value.
2.2 Semantics
An OWL interpretations defines:
– a class as a collection of individuals,
– a datatype as a set of literal values,
– a data-valued property as a relation from individuals to literal values,
– an individual-valued property as a relation from individuals to other indi-
viduals.
60 International Workshop on Emergent Semantics and Ontology Evolution
4 Mauro Mazzieri and Aldo Franco Dragoni
An interpretation I satisfies an ontology O if it obeys to all restrictions given
by O’s axioms and facts.
An ontology O is consistent if there is at least an interpretation I which
satisfies the ontology.
An ontology O entails an ontology O if each interpretation I which satisfies
O also satisfies O .
3 Ontology Revision
3.1 Belief Revision
Ontology revision has many similarities with belief revision.
Belief revision is the process of rearranging a knowledge base to preserve
global consistency while accommodating incoming information. In the AGM
theory[5, 6], the belief is formalized as a set of logical statements, (the belief
set), i.e. a logic theory K described in a formal language L. The belief set is
closed under logical consequences. A finite subset B of K such that K = Th(B)
is a knowledge base for K. The problem of revision arises when we get a new
formula p that makes the knowledge base inconsistent. Then, we have to revise
the knowledge base, retracting some of the beliefs, in order to restore consistency.
The revised theory is K ∗ p. The AGM theory gives three rationality principles
affecting K ∗ p:
Consistency The revised belief K ∗ p must be consistent.
Minimal change The revision process should alter as little as possible the
current belief set.
Priority to incoming information The new information p must belong to
the new belief set K ∗ p.
From these principles eight postulates follow. However, neither the rationality
principles nor the postulates univocally define revision.
3.2 Definition of Ontology Revision
Ontology revision is defined as a change of components in ontology[16]. Co-
eherently with belief revision theory, we define ontology revision as the process
of rearranging an ontology to preserve consistency while accomodating changes.
Foo[17] presents a summary of issues concening ontology revision from artificial
intelligence, philosophy and recursion theory.
Our approach to ontology revision will be based on belief bases, a set of
sentences not closed under logical consequence, from which a belief set can be
derived[18]. Our belief base is an ontology, i.e. a set of axioms and facts. The
incoming information is represented as an axiom or a fact, i.e. a TBox or a ABox
statement2 . The problem of revision arises when the new axiom or fact would
render the ontology inconsistent.
2
Another approach, such the one in [19], considers only inconsistences due to objects
introduced in the ABox.
ESOE, Busan - Korea, November 2007 61
Ontology Revision as Non-Prioritized Belief Revision 5
The choice to represent changes at the level of single axioms is very fine-
grained, but it doesn’t forbid to define more complex, higher-level changes[20].
A finer-grade approach, involving the single constraints in class and property
axioms, would be problematic as not all combinations are allowed. For exam-
ple, in OWL Lite, not all properties can have cardinality restrictions placed on
them or be specified as functional or inverse-functional[15]. An example of this
approach, involving the weakening of the original ontology to accomodate the
incoming axiom, is presented in [3].
To choose an ontology revision procedure we have first to understand why
an axiom or fact, potentially incompatible with the current ontology, can arrive.
We want to point out two different scenarios, demanding a different approach:
– The ontology represents the current state of an evolving world, and the new
information reflects a change in the world. The consequent change in the
representation of the world is called updating.
– We have an incomplete, approximate or erroneous representation of a static
world. The new information represent a new evidence regarding this world.
The consequent change in the representation is properly called revision.
In our scenario, a loosely-coupled group of peers are incrementally building
an ontology for a fixed domain. Thus, the world is not supposed to change, while
the world’s description is constantly evolving as the participants add, refine or
retract classes and properties definitions. This scenario is that of a revision
process and need to be handled within a framework possessing some specific
requisites. The need for those requisites already appeared in a juridical scenario
(incremental building of a proof in court[9]) and in distributed multi-agent belief
revision[21].
Ability to reject incoming axioms. A belief revision system for a multi-
source environment should drop the rationality principle of “priority to the
incoming information”, which is not acceptable since the sources are asyn-
chronous and there is no strict correlation between the chronological se-
quence of information and their credibility or importance[11].
The ability to recover previously discarded axioms. Each domain expert
should be able to recover previously discarded pieces of the the ontology if
new axioms redeem them. This should be done not only when the new axioms
directly support previously rejected axioms, but also when they indirectly
support them by disclaiming the axioms that caused their ostracism.
For these reasons we adapt to ontology revision a belief revision framework
that replace the priority to incoming information with the principle of recover-
ability[10]. The rationale for this principle is that, if an axiom was part of the
ontology in the past, and it would be consistent with the current ontology, then
it should be part of the ontology again.
62 International Workshop on Emergent Semantics and Ontology Evolution
6 Mauro Mazzieri and Aldo Franco Dragoni
4 Revision procedure
Belief revision has been approached both as a qualitative syntactic process and
as a numerical mathematical issue. Our distributed ontology revision system
links symbolic and numerical techniques. Computationally, the ontology revi-
sion consists of two steps acting on the axioms of the ontology, and three steps
working with numerical weights.
Each peer stores his knowledge about the domain in at least two reposito-
ries[10]:
1. A background repository KB. This is the set of all axioms and facts available
to reasoning; it contains both the axioms and facts written by the contributor
and received from other contributors. It may be inconsistent.
2. A working ontology B ⊆ KB, which is the maximally consistent, currently
preferred ontology that should be used for reasoning or further editing.
Given an incoming contribution p (an axiom or a fact) from a source, the
evolution process consists of the following steps:
1. detection of minimally unsatisfiable subsets of KB ∪ {p}, called nogoods;
2. generation of the maximally satisfiable subsets of KB ∪ {p}, called goods;
3. revision of the credibility weights of axioms in KB ∪ {p};
4. choice of a preferred maximally consistent subset of KB ∪ {p} as the new
working ontology B ;
5. recalculation of “a posteriori” reliability of sources.
4.1 Symbolic steps
Step 1 and 2 are symbolical ATMS-style operations[22]. We define a nogood as
a minimally inconsistent subset of KB. Dually, we define a good as a maximally
consistent subset of KB.
Nogood detection can be demanded to a reasoner, such as Racer[23], FaCT[24],
Pellet[25]. The set of goods and nogoods are dual: if we remove from KB exactly
one element for each nogood, what remains is a good[26]. So, once an inference
engine finds out some nogoods, it is possible to use a set-covering algorithm, such
as the one introduced by Reiter for model-based diagnosis[27], to find out the
goods. This algorithm has already been succesfully used for belief revision[21].
An interesting property that the inference engine does not need to calculate
the collection of all nogoods (i.e. minimally inconsistent subsets of KB), but
just a collection of inconsistent subsets of KB, which is much easier.
4.2 Numerical steps
The numerical approach to ontology revision deal with the ontology as a set
of weighted axioms. Weights usually are reals between 0 and 1, representing
explicitly the credibility of the axioms.
ESOE, Busan - Korea, November 2007 63
Ontology Revision as Non-Prioritized Belief Revision 7
The numbers represent uncertainty caused by the not complete reliability
of the team members 3 . As the reliability of the source is strongly related to
the credibility of the information, it is necessary to deal with couples source,
axiom[28].
The numerical steps of the revision procedure are step 3–5.
Step 3 of the ontology revision process uses the belief function formalism,
as the one used by Shafer and Srivastava for auditing[29]. From the reliability
value of each source (a propability that the source gives correct information),
the credibility of the goods is determined by the Dempster rule of combination.
Thus, ontology revision consists in the reassignment of credibility to axioms in
the light of the incoming axiom. The credibility ordering reflects the collaborative
building of the ontology: the reliability and the number of different contributors
affect the credibility of the axiom and the converse.
The recalculation of credibility values involves all the collected axioms in
KB. The incoming axiom p is confronted not just with the current ontology B,
but with all KB, so that the weight of axioms in KB ∪ {p} are reviewed in a
broader and less prejudicial basis.
Step 4 is the selection of a new ontology B . The new ontology is the max-
imally consistent subset of KB ∪ {p} with the greater credibility. Since the
incoming information causes a recalculation of all the credibility values, and the
selected ontology is maximal, it is possible to rescue axioms from KB.
Even when the new contribution is compatible with the working ontology
(meaning that B ∪ {p} is satisfiable), not necessarily B = KB ∪ {p}, since the
global revision of numerical weight in step 3 may yield a totally different choice
of ontology in step 4. A previously rejected set of axioms r can be rescued if p
support r against a previously accepted set q.
In general, even when the new ontology B is syntactically equal to the pre-
vious B, meaning that p has been rejected, B may have a different credibility
distribution (assignment of weights) from B. The incoming contribution p might
be rejected even when a new ontology B , different from B, is selected, but
B ∪ {p} is still unsatisfiable.
Step 5 uses Bayesian conditioning to determine the probability that a source
give correct contributions, gives the new accepted ontology B . The main point is
that a reliable source can not give false informations, while an unreliable source
may occasionally give correct contributions.
As an alteration of the credibility of an axiom might result in the pertur-
bation of the credibility of all the axioms from the same source, thus causing a
completely different ontology to be selected at the next step.
3
Even the contribution from the agent self can be considered not completely reliable,
as this depends of the relative trust a contributor has on his work compared to trust
on other experts’ works.
64 International Workshop on Emergent Semantics and Ontology Evolution
8 Mauro Mazzieri and Aldo Franco Dragoni
5 Examples
We will show two examples, showing the symbolical and numerical steps respec-
tively. In both, we suppose that a group of domain experts are working on an
ontology of birds.
5.1 Symbolic Example
The initial knowledge base KB of one of those experts is made of the axiom
Bird F ly and the fact Bird(T weety), where Bird and F ly are classes (the
class of individuals that are birds, and the class of individuals that can fly,
respectively), while Tweety is an individual. The knowledge base is consistent,
so the initial ontology is B = KB.
The expert receive from a colleague (let’s call him source 1) the axiom
¬F ly(T weety). Now KB = {Bird F ly, Bird(T weety), ¬F ly(T weety)} is
unsatisfiable. If we would adopt the AGM principle of Priority to Incoming In-
formation, the new working ontology would be chosen among
1. B1 = {Bird F ly, ¬F ly(T weety)}
2. B2 = {Bird(T weety), ¬F ly(T weety)}
If we adopt the Principle of Recoverability instead, we have a third candidate
working copy,
3. B3 = B = {Bird F ly, Bird(T weety)}
Next, another expert (let’s call him source 2) affirms F ly(T weety).
If we use the AGM principles, the new working ontology would be, respec-
tively,
1. B1 = {Bird F ly, F ly(T weety)}, if B1 was chosen after the input from
source 1,
2. B2 = {Bird(T weety), F ly(T weety)}, if B2 was chosen.
If we allow the rejection of the new contribution, after the arrival of the
axiom from source 2, we can:
1. Reject the new axiom. Our working copy remain the same as after step 1.
2. Accept the new axiom.
(a) B1 = {Bird F ly, ¬F ly(T weety)}. We recover Bird(T weety), so
B1 = {Bird F ly, Bird(T weety), F ly(T weety)}.
(b) B2 = {Bird(T weety), ¬F ly(T weety)}. We recover Bird F ly, so
B2 = {Bird F ly, Bird(T weety), F ly(T weety)}.
(c) B3 = {Bird F ly, Bird(T weety)}. This is a simple expansion, so
B3 = {Bird F ly, Bird(T weety), F ly(T weety)}.
The example show that, if we consider the axiom F ly(T weety) more credible
than ¬F ly(T weety), our final working ontology would be the same, indepen-
dently from the choice made at the first step.
ESOE, Busan - Korea, November 2007 65
Ontology Revision as Non-Prioritized Belief Revision 9
5.2 Numerical Example
The initial knowledge base KB of one expert is made of the axiom Bird F ly
and the fact Bird(T weety).
The expert receives from source 1 the axiom ¬F ly(T weety) and chooses as
the new working ontology B2 = {Bird(T weety), ¬F ly(T weety)}.
Now suppose source 1 sends us the axiom ¬Bird(T weety). If we reject this
axiom, probably now our confidence in source 1 will be lower, as the credibility
of the information affects the reliability of its source[30].
A change on the credibility of an axiom provided by a source yields corre-
sponding changes in the credibility of the other axioms provided by the same
source, even if they are not logically related with each other. As a consequence
of this perturbation, a completely different working ontology might be chosen,
in the previous example B3 instead of B2 , thus rejecting the previously accepted
axiom from source 1. Since all the collected axioms are retained and their weights
can change, the new selection might reconsider some previously discarded axiom,
whether the incoming contribution is accepted or not.
Probably, the last come contribution decreases the credibility of the axioms it
would render unsatisfiable, even in the case it has been rejected. The same when
we receive an axiom which already belongs to the working ontology: it is not
the case that nothing happened, as AGM fourth postulate of expansion would
suggest[6, p. 49], since we are now, in general, more sure about the correctness
of the axiom.
6 Conclusions and Future works
When a group of peer tries to capture in an ontology a static domain, but
their domain’s knowledge is only partial and potentially unreliable, not all the
contribution can be taken as unconditionally useful. It is necessary to use an
ontology revision procedure that allows to discard the incoming information, if
there is no reason to consider it more reliable than other conflicting contributions,
and to rescue previously discarded axioms, if they are now compatible with the
current selected ontology.
In general, at each step there will be more than a consistent subset of the
ontology with maximal size (i.e., a good). There is the need of a rational criteria
to choose a good as the new working ontology. If we keep track of axioms’ sources
and give to each peer a a-priori reliability value, we can use the belief-function
formalism to estimate the reliability of each good and bayesian conditioning to
evaluate a new a-posteriori reliability value for the sources.
This work is just the beginning of an analysis of ontology revision process for
a distributed environment. Current research work involves the following subjects.
Collaborative Ontology Revision At the end of the work each expert has its
own version of the domain ontology. To extract the final result of the collective
work of the group of interacting experts, a voting mechanism is needed. The
66 International Workshop on Emergent Semantics and Ontology Evolution
10 Mauro Mazzieri and Aldo Franco Dragoni
integration of the different conceptualizations must not be performed by an
external supervisor, but it can be done by the group itself.
Ontology distribution To allow the distribution of individual fragments of the
ontology, it must be possible to partition it and then reconstruct it preserving
meaning.
For RDF, this bring to the definition of the minimal self-contained graph[31]
as the finer decomposition of a graph that would preserve meaning. This minimal
set consists in a statement and, recursively, all statements involving a blank node
already in the set.
Given the OWL RDF/XML syntax’s use of blank nodes to build complex
definitions, a similar concept can be applied to OWL. This decomposition allows
the distribution of the ontology between peers, as in the scenario introduced in
section 1.
User interaction A software supporting the collaborative building of an ontology
must be able to use an ontology revision mechanism to maintain a consistent
working ontology. Where inconsistencies arise and there is no other available
ranking, the choice among different maximally consistent subsets can only be
done by the user.
However, there are other times during the work when an user intervention
would be useful. Why don’t allow the user to explicitly mark a part of the ontol-
ogy as unreliable, not necessarily causing its deletion from the current working
set, but determining a change in the distribution of reliability among the sources?
Explicit reliability judgments by an human agent must be taken into account
when the system build a credibility ranking among the available sources.
Strong time-Independence Even if the new information has no priority for his
novelty, a complete independence of axiom’s weights from contributions’ arrival
time is not guaranteed. This, given the asynchronous setting, would be a desir-
able feature of the system.
Ontology versioning Ontology versioning is defined as the ability to handle an
evolving ontology by creating and managing different variants of it[2]. A com-
mon requirement between ontology versioning and the present ontology revision
framework is the ability to work with different versions of the ontology and to
recover previous parts of it. Thus the revision process for ontology revision can
be at some extent applied to ontology versioning.
References
1. Gruber, T.R.: A translation approach to portable ontology specifications. Knowl-
edge Acquisition 5(2) (1993) 199–220
2. Klein, M., D.Fensel: Ontology versioning on the semantic web. In: Proc. of the
Int. Semantic Web Working Symposium (SWWS). (2001) 75–91
ESOE, Busan - Korea, November 2007 67
Ontology Revision as Non-Prioritized Belief Revision 11
3. Flouris, G.: On Belief Change and Ontology Evolution. PhD thesis, Dept. of
Computer Science, University of Crete (February 2006)
4. Dou, D., McDermott, D., Qi, P.: Ontology translation on the semantic web. In:
International Conference on Ontologies, Databases and Applications of Semantics.
(2003)
5. Alchourrón, C.E., Gärdenfors, P., Mankinson, D.: On the logic of theory change:
partial meet contraction and revision functions. The Journal of Symbolic Logic 50
(1985) 510–530
6. Gärdenfors, P.: Knowledge in Flux: Modeling the Dynamics of Epistemic States.
MIT Press, Cambridge, MA (1988)
7. Ribeiro, M.M., Wassermann, R.: First steps towards revising ontologies. In: Proc.
of WONRO’2006. (2006)
8. Hansson, S.O.: A survey of non-prioritized belief revision. Erkenntnis 50 (1999)
413–427
9. Dragoni, A.F., Nissan, E.: Salvaging the spirit of the meter-models tradition: A
model of belief revision by way of an abstact idealization of responce to incoming
evidence delivery during the construction of proof in court. Applied Artificial
Intelligence 18 (2004) 277–303
10. Dragoni, A.F.: Belief revision: From theory to practice. The Knowledge Engineer-
ing Review 12(2) (1997)
11. Dragoni, A.F., Mascaretti, F., Puliti, P.: A generalized approach to consistency
based belief revision. In Gori, M., Soda, G., eds.: Topics in Artificial Intelligence,
Proc. of the 4th Conference of the Italian Association for Artificial Intelligence.
Number 992 in LNAI, Florence, Italy, Springer-Verlag (October 11–13 1995) 231–
236
12. Bechhofeer, S., van Harmelen, F., Hendler, J., Horrocks, I., McGuinness, D., Patel-
Schneider, P., Stein, L.A.: OWL web ontology language reference. Recommenda-
tion, W3C (10 February 2004)
13. Hayes, P.: RDF Semantics. Recommendation, W3C (February 10, 2004)
14. Baader, F., McGuinness, D., Nardi, D., Patel-Schneider, P., eds.: Description Logic
Handbook: Theory, implementation and applications. Cambridge University Press
(2002)
15. Patel-Schneider, P.F., Hayes, P., Horrocks, I.: OWL web ontology language seman-
tics and abstract syntax. Recommendation, W3C (February 2004)
16. Heflin, J., Hendler, J.: Dynamic ontologies on the web. In: Proc. of the 17th Nat.
Conf. on Artificial Intelligence, Austin, Texas (30 Jul – 3 Aug. 2000) 443–449
17. Foo, N.: Ontology revision. Lecture Notes in Computer Science 954 (1995) 16–??
18. Halaschek-Wiener, C., Katz, Y.: Belief base revision for expressive description
logics. In: Proc. of the OWLED’06. (2006)
19. Qi, G., Liu, W., Bell, D.: Knowledge base revision in description logics. In: Proc.
of 10th European Conf. on Logics in Artificial Intelligence (JELIA’06). Number
386-398, Springer Verlag (SEP 2006)
20. Haase, P., Stojanovic, L.: Consistent evolution of OWL ontologies. In: Proc. of
the 2nd European Semantic Web Conf. (ESWC-05). (2005)
21. Dragoni, A.F., Giorgini, P.: Distributed belief revision. Autonomous Agents and
Multi-Agent Systems 6 (2003) 115–143
22. de Kleer, J.: An assumption-based truth maintenance system. Artificial Intelligence
(28) (1986) 127–162
23. Haarslev, V., Möller, R.: Racer system description. In: Proc. of the Int. Joint
Conf. on Automated Reasoning (IJCAR 2001). Volume 2083 of Lecture Notes in
Artificial Intelligence., Springer (2001) 701–705
68 International Workshop on Emergent Semantics and Ontology Evolution
12 Mauro Mazzieri and Aldo Franco Dragoni
24. Horrocks, I.: The FaCT system. In de Swart, H., ed.: Proc. of TABLEAUX98.
Number 1397 in LNAI, Springer (1998) 307–312
25. Sirin, E., Parsia, B., Grau, B.C., Kalyanpur, A., Katz, Y.: Pellet: A practical
OWL-DL reasoner. Technical Report 2005-68, University of Maryland, Institute
for Advanced Computes Studies (UMIACS) (2005)
26. Roos, N.: A logic for reasoning with inconsistent knowledge. Artificial Intelligence
57 (1992) 69–103
27. Reiter, R.: A theory of diagnosis from first principles. Artificial Intelligence 32
(1987) 57–59
28. Dragoni, A.F.: A model for belief revision in a multi-agent environment. In De-
mazeau, Y., Werner, E., eds.: Decentralized A.I. Volume 3., North Holland Elsevier
Science Publisher (1992) 103–112
29. Shafer, G., Srivastava, R.: The bayesian and belief-function formalisms a gen-
eral perspective for auditing. In Shafer, G., Pearl, J., eds.: Reading in Uncertain
Reasoning. Morgan Kaufmann Publishers (1990)
30. Mazzieri, M., Dragoni, A.F.: On the relation between trust on input and reliability
of output. In: Demos and Posters of the 3rd European Semantic Web Conference
(ESWC 2006). (2006)
31. Tummarello, G., Morbidoni, C., Puliti, P., Piazza, F.: Signing individual fragments
of an RDF graph. In: Proc. of the World Wide Web Conference (WWW2005).
(2005)
ESOE, Busan - Korea, November 2007 69