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Inference in Probabilistic Ontologies with Attributive Concept Descriptions and Nominals. Rodrigo Bellizia Polastro and Fabio Gagliardi Cozman. Overall Purpose. Expand description logic to include uncertainty Define coherent semantics for a probabilistic logic
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Inference in Probabilistic Ontologies with Attributive Concept Descriptions and Nominals Rodrigo Bellizia Polastro and Fabio Gagliardi Cozman
Overall Purpose • Expand description logic to include uncertainty • Define coherent semantics for a probabilistic logic • Derive algorithms for inference in this logic For example: The probability that a particular wine is Merlot, given that its color is red.
Goals • Extend previous work by: • Handling realistic examples • Add nominals to CRALC (credal ALC)
Outline • Review definitions found in ALC • Describe two semantics used in probabilistic description logics • Describe CRALC • Show experimental results with Wine Ontology & Kangaroo Ontology
Definitions • Individuals, concepts, and roles • Concepts and roles are combined to form new concepts using constructors: • Conjunction • Disjunction • Negation • Existential restriction • Value restriction
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
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
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:
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)
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)
Strengths • They show that CRALC works • Rigorous mathematical motivation for their choices • Good background section for ALC and probabilistic description logics
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