Reasoning the FMA Ontologies with TrOWL Jeff Z. Pan, Yuan Ren, Nophadol Jekjantuk, and Jhonatan Garcia University of Aberdeen, UK ORE2013

The FMA ontology The Foundational Model of Anatomy ontology is “an evolving computer-based knowledge source for biomedical informatics” – Developed with Protégé as a FRAME-BASED system – Consists of several components such as Metaknowledge – Evolves (latest version released in 2010) – Highly expressive Several OWL translations – DLR and FullR: OWL DL/FULL versions without/with metamodelling – Constitutional: alternative OWL DL translation with metamodelling – OWL2G_noMTC: OWL2 translation from FAM 3.0 without metamodelling – DLR_M1/M2: portion of DLR enriched with the class-based approach (Glimm et al., 2010) to accommodate metaclasses

TrOWL: Tractable reasoning infrastructure for OWL 2 Semantic Approximation (AAAI2007) – Pre-compute and compile the materialisation of OWL 2 ontologies in OWL 2 QL – Sound and complete for conjunctive queries without non- distinguished variables – Tractable in run-time Syntactic Approximation (AAAI2010) – Normalise OWL 2 axioms into nominal-safe EL++ with additional data structures to maintain non-EL semantics – Approximate deduction on the normalisation results – Sound, incomplete but practically high recall for many ontologies – Tractable TBox classification and ABox materialisation Oracle 11g support, SPARQL 1.1 query answering (leveraging OWL- BGP), local closed world reasoning, Jena API, etc.

Syntactic Approximation Normalisation – Representing non-EL expressions with fresh names – Maintain complementary relations Deduction – CEL rules – Additional rules E.g. A subClassOf B => not B subClassOf not A Example ontology: – A subClassOf forall r B – forall r C subClassOf D – B subClassOf C – => – A subClassOf D ALL r r B B A A C C D D Some r r nB A A nC Some D D B B C C X1 X2

Metamodelling in FMA Ontology FMA frame-based ontology contains metamodelling – E.g. Physical_anatomical_entity instanceOf Anatomical_entity_template – Physical_anatomical_entity subClassOf Anatomical_entity Different implementations in OWL ontologies – FMA FullR uses OWL Full; – FMA Consititutional encodes metaclass assertions with class subsumptions, metaproperty assertions with existential and universal restrictions; – OWL 2 DL with punning semantics A class and an individual with same IRI will still be treated as different entities, leading to incomplete results – OWL 2 DL with class-based approach Introducing representative individual of each concept Encoding subsumptions/class assertions with object property relations

Evaluation Results FMA ontologies are in general very difficult to reason with – Especially with Metamodelling involved TrOWL performs generally well on FMA ontologies – Generally faster than fully-fledged, universal, intractable reasoners; – The only one to classify FMA-OWL2G_noMTC TBox in 1 hour; – Practically high recall

Dealing with Unsatisfiable Concepts Translated versions of FMA contain many unsatisfiabilities – FMA Constitutional: 33,433 / 41,648 – FMA OWL2G_noMTC: 67,771 / 85,005 Investigating such unsatisfiabilities is difficult – Hard to compute justifications Requires a lot of entailment checkings – Too many unsatisfiability to look into We want to get into the core of the problem efficiently

Just. (A subClassOf Bot) Finding the Core Unsatisfiabilities Kalyanpur et al.’s root and derived unsatisfiable concepts – B is parent of A – A is derived – Non-derived unsatisfiable concept is root A derived concept can have alternative justification that contains no parent – Eliminating all root concepts do not necessarily eliminate all unsatisfiability Still need to compute justifications and entailment checkings Just. (B subClassOf Bot)

Finding the Core Unsatisfiabilities Type I and Type II unsatisfiable concepts – Purely based on the derivation relations between axioms – Suitable with a forward-chaining completion-based algorithm Type I concepts are full-unsatisfiable in reasoning Type II concepts are semi-unsatisfiable in reasoning – not immediately subsumed by all concepts – propagates Type II – Can become Type I if appropriate inference occurs axiom1 axiom2 axiom3 A subClassOf Bot B subClassOf Bot

Application on FMAs Repairing the Type I concepts will resolve all existing unsatisfiabilities – From TrOWL’s perspective Fewer enough Type I makes debugging much easier – E.g. 145 Type I in FMA Constitutional, only 0.43% of all the unsatisfiable concepts; 6 axioms directly involved, out of the 122,136 logical axioms

Summary and Future Work TrOWL and its syntactic approximation facility is well suited for the reasoning, metamodelling and debugging of the FMA ontologies – Striking a balance among expressiveness, performance and quality Future works – A completeness-guarantee? Why does TrOWL have high recalls on certain ontologies? A potential tractable DL that covers FMA family? – A fully-fledged completion-based reasoner for OWL2 DL? Will be intractable – Parallelisation? Changing CEL rules to ELK rules? Parallelising the additional approximate deduction rules – Improved entailment checking Currently using the dual-ontology classification algorithm from CEL Changing to a goal-driven algorithm?

Thank You!