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Inference in Probabilistic Ontologies with Attributive Concept Descriptions and
Nominals
Rodrigo Bellizia Polastro and Fabio Gagliardi Cozman
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Overall Purpose
Expand description logic to include uncertainty Define coherent semantics for a probabilistic logic Derive algorithms for inference in this logic
The probability that a particular wine is Merlot, given that its color is red.
For example:
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Goals
Extend previous work by: Handling realistic examples Add nominals to CRALC (credal ALC)
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Outline
Review definitions found in ALC Describe two semantics used in probabilistic
description logics Describe CRALC Show experimental results with Wine
Ontology & Kangaroo Ontology
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Definitions
Individuals, concepts, and roles Concepts and roles are combined to form
new concepts using constructors: Conjunction Disjunction Negation Existential restriction Value restriction
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Probabilistic Description Logics – the literature
Domain-based semantics (most common):
Interpretation-based semantics:
Direct inference:
The transfer of statistical information about domains to specific individuals. Problem with Domain-based semantics.
Tells us nothing about
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CRALC
Allows an ontology to be translated into a relational Bayesian network
Interpretation-based semantics Includes these constructs:
all constructs of ALC concept inclusions concept definitions individuals assertions
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CRALC
Probabilistic inclusions: read where D is a concept and C is a
concept name. only concept names are allowed in the
conditioned concept (no constructs) Semantics:
Semantics for roles:
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CRALC
Inference: The calculation of a query ,where A is a concept
and A is an Abox (set of assertions). Terminologies (graphs) are acyclic, and have nodes
for each concept, restriction, and role. Assumptions:
Homogeneity condition is a constant.
Unique names assumption (each element in the domain refers to a distinct individual)
Domain closure (the cardinality of a domain is fixed and known)
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Wine Ontology Experiment
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Wine Ontology Experiment
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Kangaroo Ontology Experiment
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Kangaroo Ontology Experiment
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Conclusions
CRALC has been improved Interpretation-based semantics has been
incorporated allowing for use of nominals CRALC has been demonstrated on realistic
examples The cost of using the interpretation-based
semantics is high (requires the construction of huge networks)
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Strengths
They show that CRALC works Rigorous mathematical motivation for their
choices Good background section for ALC and
probabilistic description logics
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Weaknesses
Don’t explain how Bayesian Networks are formed from ontology (probably in prior paper)
We don’t know how reasonable their results are as interpretations of the ontology.
Rigorous mathematical motivation for their choices