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

The probability that a particular wine is Merlot, given that its color is red.

For example:

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)

Wine Ontology Experiment

Wine Ontology Experiment

Kangaroo Ontology Experiment

Kangaroo Ontology Experiment

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