representation of parsimonious covering theory in owl-dl

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

1

OWL Experiences and Directions (OWLED 2011)

Representation of Parsimonious Covering Theory

in OWL-DL

Cory Henson, Krishnaprasad Thirunarayan, Amit Sheth, Pascal Hitzler

Ohio Center of Excellence in Knowledge-enabled Computing (Kno.e.sis)

Wright State University, Dayton, Ohio, USA

Paper at http://bit.ly/k-pct

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

2

Find a set of entities (in the world) that

explain a given set of sensor observations

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

3

Characteristics of a Solution

1. Handle incomplete information (graceful degradation)

2. Minimize explanations with additional information (anti-monotonic)

3. Reason over data on the Web (i.e., RDF on LOD)

4. Scalable (tractable)

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

4

http://linkedsensordata.com

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

5

Semantic Sensor Network (SSN) Ontology

http://www.w3.org/2005/Incubator/ssn/wiki/

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

6

minimizeexplanations

degrade gracefullytractable

Parsimonious Covering Theory (PCT)

Web OntologyLanguage (OWL)

Convert PCT to OWL

Web reasoning

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

7

Parsimonious Covering Theory

• Goal is to account for observed symptoms with plausible explanatory hypotheses (abductive logic)

• Driven by background knowledge modeled as a bipartite graph causally linking disorders to manifestations

Yun Peng, James A. Reggia, "Abductive Inference Models for Diagnostic Problem-Solving"

m1

m2

m3

d1

d2

d3m4

disorder manifestationcauses

explanationobservations

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

8

PCT Parsimonious Cover

• coverage: an explanation is a cover if, for each observation, there is a causal relation from a disorder contained in the explanation to the observation

• parsimony: an explanation is parsimonious, or best, if it contains only a single disorder (single disorder assumption)

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

9

Given

PCT problem P is a 4-tuple D, M, C, Γ⟨ ⟩

• D is a finite set of disorders• M is a finite set of manifestations• C is the causation function [C : D Powerset(M)]⟶• Γ is the set of observations [Γ M ]⊆

Δ is a valid explanation (i.e., is a parsimonious cover)

Goal

Translate P into OWL, o(P), such that o(P) ⊧ Δ

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

10

headache

extreme exhaustion

severe ache and pain

stuffy nose

sneezing

sore throat

severe cough

mild ache and pain

mild cough

flu

cold

fever

disorder manifestationcauses

PCT Background

Knowledge in OWL

disorders (D)

for all d ∈ D, write d rdf:type Disorderex: flu rdf:type Disorder

cold rdf:type Disorder

manifestations (M)

for all m ∈ M, write m rdf:type Manifestation

ex: fever rdf:type Manifestationheadache rdf:type Manifestation …

causes relations (C)

for all (d, m) ∈ C, write d causes mex: flu causes fever

flu causes headache …

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

11

PCT Observations and

Explanations in OWL

observations (Γ)

for mi ∈ Γ, i =1 … n, write

Explanation owl:equivalentClasscauses value m1 and … causes value mn

ex: Explanation owl:equivalentClasscauses value sneezing andcauses value sore-throat causes value mild-cough

explanation (Δ)

Δ rdf:type Explanation, is deduced

ex: cold rdf:type Explanationflu rdf:type Explanation

and

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

Ohio Center of Excellence on Knowledge-Enabled Computing (Kno.e.sis)

12

thank you, and please visit us at

http://semantic-sensor-web.com

Kno.e.sis – Ohio Center of Excellence in Knowledge-enabled ComputingWright State University, Dayton, Ohio, USA