1. Inference in Probabilistic Ontologies with Attributive Concept Descriptions and Nominals Rodrigo Bellizia Polastro and Fabio Gagliardi Cozman

2. 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:

3. Goals Extend previous work by: Handling realistic examples Add nominals to CRALC (credal ALC)

4. Outline Review definitions found in ALC Describe two semantics used in probabilistic description logics Describe CRALC Show experimental results with Wine Ontology & Kangaroo Ontology

5. Definitions Individuals, concepts, and roles Concepts and roles are combined to form new concepts using constructors: Conjunction Disjunction Negation Existential restriction Value restriction

6. 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

7. 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

8. 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:

9. 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)

10. Wine Ontology Experiment

12. Kangaroo Ontology Experiment

14. 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)

15. Strengths They show that CRALC works Rigorous mathematical motivation for their choices Good background section for ALC and probabilistic description logics

16. 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