=Paper=
{{Paper
|id=Vol-173/paper-15
|storemode=property
|title=Statistical Reasoning - A Foundation for Semantic Web Reasoning
|pdfUrl=https://ceur-ws.org/Vol-173/pos_paper6.pdf
|volume=Vol-173
}}
==Statistical Reasoning - A Foundation for Semantic Web Reasoning==
https://ceur-ws.org/Vol-173/pos_paper6.pdf
Statistical Reasoning – A Foundation for Semantic Web Reasoning
Shashi Kant • Evangelos Mamas
Massachusetts Institute of Technology
Cambridge, MA 02139
skant@sloan.mit.edu • emamas@sloan.mit.edu
Abstract tion, and Robotics etc. The Semantic Web would do well to
re-use some of these efforts in building this underlying
There has been considerable debate as to the merits framework.
and the applicability of probabilistic or statistical
reasoning to Semantic Web. Much of this debate
seems to have centered on the applicability of sta- 2 Ontologies and Probabilistic Models
tistical methods in a supposedly deterministic set- We introduce the notion that Probabilistic Graph Models
ting. In this paper, we argue that statistical reason- (PGM) or Bayesian Networks can be viewed as fuzzy On-
ing (“reasoning with uncertainty”) need not be a tologies; conversely an Ontology can be viewed as a crisper
substitute for traditional Description Logic (DL) / Bayesian Networks. In our proposed architecture, there may
First-Order Logic (FOL) reasoning, instead statisti- not be a clear dividing line between them. A good way of
cal methods can serve as a complement to logic- visualizing this relation would be to view Ontologies and
based reasoning systems in two ways: (i) Offer a Bayesian Networks as ships floating in a sea of statistical
meta-reasoning (or audit) mechanism to validate “metadata”. We use this metaphor to describe the notion
logical reasoning, and (ii) Act as a “filler” where that the sea of statistical metadata fills-in the gaps between
Ontological information either does not exist, or is the islands of Ontologies. Lately there have been some ef-
insufficient to reason conclusively. forts to develop Probabilistic Ontologies by annotating
OWL or RDF Ontologies with probabilistic information e.g.
1 Introduction BayesOWL [Ding,Peng 2004]. We argue against this ap-
proach, and suggest that probabilistic and logic-based rea-
Much of the Semantic Web effort has focused on the design
soning approaches should be viewed as orthogonal to each
and development of Ontologies and related technologies.
other. It makes most sense to keep the Ontological informa-
This approach presupposes that a critical mass of Ontologies tion separate from the statistical data, along the lines of how
will exist that can sufficiently and accurately respond to
the WWW operates - in which an HTML page links to a
reasoning queries. As Sir Tim Berners-Lee puts it [Berners-
“FTP” site or a “mailto” to an email hyperlink and the nec-
Lee, 1998]: "The choice of classical logic for the Semantic essary protocols invoked only when clicked.
web is not an arbitrary choice among equals. Classical
logic is the only way that inference can scale across the
Figure 1 illustrates a hierarchical mechanism of aligned On-
web." tologies and Bayesian Networks. At the very top are the top-
level Ontologies on which there is general agreement and
However, a pure logic-based approach looks increasingly
acceptance, at the bottom are the fuzzier, grayer-scale
implausible given the paucity of Ontologies and the diffi- Bayesian Networks which represent relations between re-
culty in constructing and maintaining Ontologies. Just like
sources using probabilistic mechanisms.
the World Wide Web (WWW) had a ready and mature plat-
form to run on i.e. the Internet - which had been in existence
BayesianAbstract
Ontological Details Fuzzy
Crisp
for a long time prior to the emergence of the WWW, we feel
that the Semantic Web needs an underlying platform, upon
which Ontologies can function and interoperate.
We argue that this platform should be a web of statistical
“metadata” – which expresses semantic relations in prob-
abilistic terms. Such systems (e.g. Bayesian Networks, Ontological Abstract Crisp
Probabilistic Relational Models) have also been in existence Bayesian Details Fuzzy
for a while and are used in various Machine Learning and Query
AI applications such as Machine Vision, Speech Recogni-
Figure 1: Ontologies vis-à-vis Bayesian Networks
We suggest, that probabilistic (or statistical) information be 4 Conclusion
encoded using any of the widely accepted Bayesian Inter-
change Formats such as XML-BIF [Cozman, 1998], or Mi- “Reasoning with Uncertainty” is probably a misnomer to
crosoft Research’s XBN [Microsoft, 1998] or Hugin.net describe the efforts required in this area - a more appropriate
[Jensen, 2004] format. We propose that the Ontological phraseology would be “reasoning without certainty”. While
model encapsulate what it is designed for - expressing logi- the difference may seem pedantic, the underlying notion is
cal relations between resources, and the probabilistic model that “uncertainty” is not a state unto itself, but merely the
express the statistical relation between them. We do not see absence of certainty. In a Semantic Web sense, it is a state
a need to mix-and-match as they offer very different views where Ontological information is non-existent, incomplete
on the same information-set and are perceptually orthogo- or inconclusive. Statistical reasoning could therefore be the
nal. bedrock upon which DL/FOL based querying and reasoning
can be performed.
3 A Hybrid Reasoning Model This means that the semantic web can operate in areas cur-
Reasoning using Ontologies is based on predicate logic and rently out-of-bounds because of a lack of Ontological in-
belongs in the classical tradition of monotonic deductive formation. We therefore hypothesize that statistical “meta-
reasoning i.e. propositions are either true or false. But this data” could be the building-block of the Semantic Web lead-
proposed framework provides a mechanism for handling ing to better and more accurate reasoning mechanisms.
fuzzier, incomplete and inaccurate inputs. In this model,
reasoning can be performed using a “bottom-up” approach 5 Acknowledgments
where a query unanswered by a pure Ontological match is
extended further up the hierarchy (Fig 1.) until all required We would like to acknowledge the gracious help and sup-
information is found. An adjunct application might be to port of the members of the World Wide Web Consortium
validate traditional reasoning with a mathematical confi- (W3C) and faculty of MIT-CSAIL for their help and sup-
dence level (meta-reasoning). port. We would especially like to thank Ralph Swick and Sir
Tim Berners-Lee for their critique and feedback.
Some examples of the reasoning activities possible using
this system are: 6 References
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