PPSWR 2006 - Automated Reasoning Support for FOL Onto logies 1 Fabian M. Suchanek presented at the 4 th Workshop on Principles and Practice of Semantic Web Reasoning (PPSWR 2006) Peter Baumgartner (National ICT Australia, Canberra/Australia) Fabian M. Suchanek (Max-Planck-Institute for CS, Saarbruecken/Germany) Automated Reasoning Support for First-Order Ontologies
37
Embed
Fabian M. SuchanekPPSWR 2006 - Automated Reasoning Support for FOL Ontologies 1 presented at the 4 th Workshop on Principles and Practice of Semantic Web.
Fabian M. SuchanekPPSWR Automated Reasoning Support for FOL Ontologies 3 Model Computation Ontology (set of FOL formulae) Model (set of derivable facts) x singer(x) => sings(x) singer(elvis) sings(elvis). singer(elvis).
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 1Fabian M. Suchanek
presented at the4th Workshop on Principles and Practice
of Semantic Web Reasoning (PPSWR 2006)
Peter Baumgartner (National ICT Australia, Canberra/Australia)
Fabian M. Suchanek (Max-Planck-Institute for CS, Saarbruecken/Germany)
Automated Reasoning Support
for First-Order Ontologies
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 2Fabian M. Suchanek
Automated Reasoning Support for FOLOs
Motivation ر
Our Transformation from FOL to DLPs ر
Existentially Quantified Formulae ر
Equality ر
Conclusion ر
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 3Fabian M. Suchanek
Model Computation
Ontology (set of FOL formulae)
Model (set of derivable facts)
x singer(x) => sings(x)
singer(elvis)
sings(elvis).
singer(elvis).
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 4Fabian M. Suchanek
Use of Model Computation
Model computation can be used for:
Finding contradictions in the ontology ر
(there is a model only iff the ontology is consistent)
Debugging the ontology ر
Proving/disproving conjectures ر
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 5Fabian M. Suchanek
Undecidability of Model Computation
Model Computation is only semi-decidable for FOL:
we can (in principle) always detect unsatisfiability ر
we cannot always detect satisfiability (for principal reasons) ر
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 6Fabian M. Suchanek
Existing Approaches
There exist model generation systems (e.g. MACE4 and Paradox).
Problems:
They try to map all constants to the same domain element ر
They have difficulties if there are many distinct constants ر
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 7Fabian M. Suchanek
Existing Approaches
p(c1,...cn).p(x1,...,xi-1, x ,xi+1...,xj-1, x ,xj+1,...xn). for all 1<i<j<n
Fails for n>8
There exist model generation systems (e.g. MACE4 and Paradox).
Problems:
They try to map all constants to the same domain element ر
They have difficulties if there are many distinct constants ر
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 8Fabian M. Suchanek
Our Approach
DLP KRHyper/ smodels / dlv
Transform
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 9Fabian M. Suchanek
Disjunctive Logic Programs (DLPs)
r(a) v p(x,y) :- q(x,y), r(z), not(s(a,x)).
A Disjunctive Logic Program (DLP) is a set of rules.
Rule:
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 10Fabian M. Suchanek
Our Transformation from FOL to DLPs
Prenex Negation Normal Form
x inCharge(x) => onLeave(x) v y refersTo(x,y)
x[…] y[…] [Qz…] inCharge(x) v onLeave(x) v refersTo(x,y)
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 11Fabian M. Suchanek
Our Transformation from FOL to DLPs
x[…] y[…] [Qz…] inCharge(x) v onLeave(x) v refersTo(x,y)
x inCharge(x) => onLeave(x) v y refersTo(x,y)
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 12Fabian M. Suchanek
Our Transformation from FOL to DLPs
Disjuncts without existential or following variables
Disjuncts with existential or following variables
x[…] y[…] [Qz…] inCharge(x) v onLeave(x) v refersTo(x,y)
x inCharge(x) => onLeave(x) v y refersTo(x,y)
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 13Fabian M. Suchanek
Our Transformation from FOL to DLPs
Disjuncts without existential or following variables
Disjuncts with existential or following variables
x[…] y[…] [Qz…] inCharge(x) v onLeave(x) v refersTo(x,y)
x inCharge(x) => onLeave(x) v y refersTo(x,y)
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 14Fabian M. Suchanek
Our Transformation from FOL to DLPs
negative literals
Disjuncts without existential or following variables
Disjuncts with existential or following variables
x[…] y[…] [Qz…] inCharge(x) v onLeave(x) v refersTo(x,y)
x inCharge(x) => onLeave(x) v y refersTo(x,y)
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 15Fabian M. Suchanek
Our Transformation from FOL to DLPs
Option 1: Usual Skolemization
x y inCharge(x) v onLeave(x) v refersTo(x,y)
prev(x) v is_sat(x) v onLeave(x) v refersTo(x,sk(x)) :- inCharge(x).
Problem:
onLeave(Smith)
refersTo(Smith,Miller)
refersTo(Smith,sk(Smith)).
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 16Fabian M. Suchanek
Our Transformation from FOL to DLPs
Option 2: Recyling
false :- is_sat(x),
not(refersTo(x,y)).
(simplified. See paper)
prev(x) v is_sat(x) v onLeave(x) v refersTo(x,sk(x)) :- inCharge(x).
Problem:
onLeave(Smith)
refersTo(Smith,Miller)
refersTo(Smith,sk(Smith)).
x y inCharge(x) v onLeave(x) v refersTo(x,y)
PPSWR 2006 - Automated Reasoning Support for FOL Ontologies 17Fabian M. Suchanek