Lesson-OWL.qmd

---
title: "Biostat 823 - Web Ontology Language"
author: "Hilmar Lapp"
institute: "Duke University, Department of Biostatistics & Bioinformatics"
date: "Sep 24, 2024"
format:
  revealjs:
    slide-number: true
knitr:
  opts_chunk:
    echo: TRUE
---

## OWL2: History {.smaller}

* Predecessors and major influences
  - 2000-2001 DARPA Agent Markup Language (DAML) and Ontology Inference Layer (OIL) ([DAML+OIL](https://www.w3.org/TR/daml+oil-reference/))
  - 2000-2004 Resource Description Framework Schema ([RDFS](https://en.wikipedia.org/wiki/RDF_Schema))
  - 2001-2004 W3C Web-Ontology Working Group
* Web-Ontology Language:
  - [OWL](https://www.w3.org/TR/owl-ref/): W3C recommended standard in 2004
  - [OWL2](https://www.w3.org/TR/owl2-overview/): W3C recommended standard in 2009
* Web-native: all identifiers are IRIs^[[Internationalized Resource Identifier](https://en.wikipedia.org/wiki/Internationalized_Resource_Identifier) (IRI) is a [Uniform Resource Identifier](https://en.wikipedia.org/wiki/Uniform_Resource_Identifier) (URI) that allows international characters. URLs are URIs that locate resources.]

## OWL2: Rich ecosystem

* Thriving community of ontology editors, semantic engineers, data scientists, and software developers
* [100s of ontologies](https://obofoundry.org) covering various domains across biology and biomedicine
* Open-source software tooling ecosystem:
  - [Protégé]() ontology editor
  - [Machine reasoners](http://owl.cs.manchester.ac.uk/tools/list-of-reasoners/)
  - [Command-line tooling](http://robot.obolibrary.org)
  - [Ontology development kit](https://github.com/INCATools/ontology-development-kit), [libraries and tools](https://github.com/INCATools/ontology-access-kit)

## OWL2: Terminology vs DL and FOL {.smaller}

* OWL and OWL2 are Description Logics (DLs), which are a fragment of FOL.

| FOL        | DL         | OWL        | Example    |
|------------|------------|------------|------------|
| constant         | individual | individual | 'my hand', 'Durham, NC'
| unary predicate  | concept    | class      | 'manus (hand)', 'city'
| binary predicate | role       | property   | 'part of', 'has parent'

* Individuals, classes, and properties are called _entities_ in OWL/OWL2.
* Properties hold between individuals, _not_ classes
  - Classes can have _property restrictions_, using existential or universal quantification, or specific cardinality.

::: aside
Individuals and classes are sometimes referred as _particulars_ and _universals_, respectively. Entities, and in particular classes, are often referred to as _terms_.
:::

## OWL2 constructs vs DL notation (I) {.smaller}

_C_ and _D_ are concepts, _R_ is a role (property). If $a\ R\ b$ then _b_ is connnected by R (_"R-successor"_).

| DL notation | Concept             | OWL2 (Functional Syntax)   |
|---------|-------------------------|----------------------------|
| $\top$  | Top concept    |`owl:Thing`        |
| $\bot$  | Bottom concept | `owl:Nothing`      |
| $C \sqcap D$ | Conjunction of concepts C and D | ObjectIntersectionOf( C D ) |
| $C \sqcup D$ | Disjunction of concepts C and D | ObjectUnionOf( C D )|
| $\neg C$     | Complement of concept C    | ObjectComplementOf( C ) |
| $\forall R.C$ | All connected by R are in C (universal quantification) | ObjectAllValuesFrom( R C ) |
| $\exists R.C$ | Some connected by R are in C (existential quantification) | ObjectSomeValuesFrom( R C ) |

Non-atomic concept definitions are called _class expressions_.

## OWL2 constructs vs DL notation (II) {.smaller}

_C_ and _D_ are concepts, _R_ is a role (property), _a_ and _b_ are individuals.

| DL notation | Axiom | OWL2 (Functional Syntax)      | Semantics |
|--|---------------|--------------------------------------------|-----|
| $C \sqsubseteq D$ | Concept inclusion | SubClassOf( C D ) | $\forall a\in C \rightarrow a\in D$ |
| $C \sqcap D \sqsubseteq \bot$ | Concept exclusion | DisjointClasses( C D ) | $\not\exists a\!: a\in C \wedge a\in D$
| $C \equiv D$ | Concept equivalency | EquivalentClasses( C D ) | $\forall (a\in C, b\in D) \rightarrow\\ a\in D \wedge b \in C$
| $C(a)$ | Concept member | ClassAssertion( C a ) | $a \in C$ |
| $R(a,b)$ | Role | ObjectPropertyAssertion( R a b ) |
| $R(a,\!'val')$ | Data value | DataPropertyAssertion(R a "val") |

_C_ and _D_ can be atomic concepts or class expressions. If the left hand side in a concept inclusion axiom is a class expression, it is called a General Class Inclusion (GCI) axiom.

## OWL2 property axioms {.smaller}

_C_ and _D_ are concepts; _P_, _R_ and _S_ are roles (properties); _a_ and _b_ are individuals.

| DL | Role ... | OWL2 (Functional Syntax)      | Semantics |
|--|---------------------|--------------------------------------------|-----|
| $R \sqsubseteq S$ | inclusion | SubObjectPropertyOf( R S ) | $\forall (a,b):\\ R(a,b) \rightarrow S(a,b)$ |
| $R \equiv S$ | equivalency | EquivalentObjectProperties( R S ) |
| $R \equiv S^-$ | inverse | InverseObjectProperty( R S ) | $\forall (a,b):\\ S(a,b) \rightarrow R(b,a)$ |
| $R \circ S \sqsubseteq P$ | chain | SubObjectPropertyOf( ObjectPropertyChain( R S ) P) | $\forall (a,b): R(a,z) \wedge S(z,b)\\ \rightarrow P(a,b)$
|  | Functional role | FunctionalObjectProperty( R ) | $\forall (a,b,c): R(a,b) \wedge R(a,c)\\ \rightarrow b \equiv c$
|  | Inverse functional | InverseFunctionalObjectProperty( R ) | $\forall (a,b,c): R(a,b) \wedge R(c,b)\\ \rightarrow a \equiv c$

* Properties can also be defined as (ir)reflexive, (a)symmetric, or transitive

## Domain and Range constraints

* Object property domain axiom:

  ObjectPropertyDomain( R C )
  - Semantics: $\forall a: R(a,\cdot) \rightarrow C(a)$

* Object property range axiom:

  ObjectPropertyRange( R D )
  - Semantics: $\forall a: R(\cdot,a) \rightarrow D(a)$

## Axioms about individuals vs classes {.smaller}

* OWL properties apply to individuals, both as subject and object:

  'my left index finger' :part_of 'my left hand'

* For classes ("universals"), must use property restriction ($\sqsubseteq\exists part\_of.hand$):

  'index finger' _SubClassOf_ :part_of _some_ 'hand'^[This and the below expression use [OWL-Manchester Syntax](https://www.w3.org/TR/owl2-manchester-syntax/), as opposed to [OWL Functional Syntax](https://www.w3.org/TR/owl-syntax/).]
  
  or more specifically ($\sqsubseteq anatomical\_structure \sqcap\exists part\_of.hand$):
  
  'index finger' _SubClassOf_ 'anatomical structure' _and_ :part_of _some_ 'hand'
  
* Note that existential quantification is "asymmetric", and the reverse with the inverse property does not necessarily follow:

  $index\_finger\sqsubseteq\exists part\_of.hand \wedge has\_part\equiv part\_of^- \not\rightarrow\\ hand\sqsubseteq\exists has\_part.index\_finger$

## Satisfiability and consistency {.smaller}

* In formal logic, a formula is satisfiable iff there is some assignment of values to variables that make it true.
* For ontologies, a class is unsatisfiable if no individual can exist that is a member of the class.
  - C is unsatisfiable iff $C\sqsubseteq\bot$ (in OWL this is `owl:Nothing`)
  - Often this is the result of a class C being (asserted or inferred as) a subclass of another class D and also the complement of D.
* An ontology is inconsistent if it asserts an individual as a member of an unsatisfiable class.
  - Most reasoners stop when encountering an inconsistency.

## OWL uses Open World Assumption {.smaller}

* Closed World Assumption (CWA):
  - Facts that are not known are assumed to be false.
  - Databases and database queries are most common example:
    ```sql
    SELECT Instructor_Name FROM Lesson_Instructors WHERE ...
    ```
    The result set is assumed to contain all values that can possibly match (i.e., that exist).
* Open World Assumption (OWA):
  - Facts that are not known are undefined (neither assumed true nor false).
  - For example, an individual asserted only as a member of class C cannot be assumed as not being a member of class D (unless C and D are asserted as disjoint).

## Tbox and Abox

* All axioms (statements) about classes (concepts) form the Tbox, the *t*erminological component of an ontology.
* All axioms about individuals form the Abox, the *a*ssertional component of an ontology.
* An ontology O consists of Tbox and Abox: $O=\{\mathcal{T},\mathcal{A}\}$

## Semantic entailment

* An ontology semantically entails a statement $\phi$ if $\phi$ is true in _all_ models (valid interpretations) of the ontology.
* Reasoners compute semantic entailments.
* A reasoner is
  - _sound_ if every semantic entailment it computes is correct;
  - _complete_ if it computes all possible semantic entailments.
* To be useful, reasoners need to be both sound _and_ complete.

## Reasoning services {.smaller}

- Semantic entailment
- Satisfiability and consistency
- Classification
  * Inference of class subsumption hierarchy
  * Inference of individuals' class membership
- Conjunctive query answering ("DL queries")
  ```
  'anatomical structure' and 'part of' some 'hand'
  ```
  The [DL Query tutorial](https://oboacademy.github.io/obook/tutorial/basic-dl-query/) in the OBOOK (OBO Organized Knowledge) collection of training and tutorial materials on ontology development and use provides a good introduction.
- Explanation

## OWL2 profiles and decidability {.smaller}

* OWL/OWL2 DL:
  - Maximum expressivity while maintaining computational completeness and decidability
  - Allows well-performing reasoners
  - Some restrictions that in practice are rarely relevant (individuals and classes must be distinct; some cardinality restriction constraints for transitive properties)
* OWL2 defines several expressivity profiles: [OWL2-EL](https://www.w3.org/TR/owl2-profiles/#OWL_2_EL), [OWL2-QL](https://www.w3.org/TR/owl2-profiles/#OWL_2_QL), and [OWL2-RL](https://www.w3.org/TR/owl2-profiles/#OWL_2_RL)
* OWL2-EL Profile:
  - Decidable in polynomial time, allows for very effective reasoners
  - Unsupported constructs include universal quantification; cardinality restrictions; disjunction; class negation; inverse, functional, (a)symmetric object properties.
  - Supported constructs are sufficient for most bio-ontologies, including those that are very large (Gene Ontology (GO), UBERON, SNOMED-CT)

## Resources: Reasoners

* OWL2 DL reasoners
  - Many based on the [Analytic Tableaux algorithm](https://en.wikipedia.org/wiki/Method_of_analytic_tableaux)
  - [Fact++](http://owl.man.ac.uk/factplusplus/)
  - [Hermit](https://www.cs.ox.ac.uk/isg/tools/HermiT/)
  - [Racer](https://www.ifis.uni-luebeck.de/~moeller/racer/)
* OWL2 EL reasoners
  - [ELK](https://github.com/liveontologies/elk-reasoner)
* [More complete list with details](http://owl.cs.manchester.ac.uk/tools/list-of-reasoners/)

## Symbolic and Neural AI (I) {.smaller}

* AI approaches relying on formal logic knowledge representation and reasoning fall under _Symbolic AI_.
  - _Symbolic AI_ stands in contrast to _neural_ AI approaches (ANNs, Deep Learning, etc; also called "connectionist")
* Neuro-symbolic AI approaches attempt to integrate these to complement each other

| Issue         | Symbolic AI   | Neural AI    |
|---------------|---------------|--------------|
| Decisions        | Self-explanatory | Black box |
| Expert knowledge | Readily utilized | Difficult to utilize | 
| Trainability     | Typically not    | Trainable from raw data |
| Susceptibility to data errors | High, brittle      | Low, robust |
| Speed            | Slow on large expressive KB     | Fast once trained |

## Neuro-symbolic AI resources {.smaller}

* Recent overviews:
  - Hitzler P, Eberhart A, Ebrahimi M, Sarker MK, Zhou L. (2022). [Neuro-symbolic approaches in artificial intelligence](https://doi.org/10.1093/nsr/nwac035). Natl Sci Rev. 2022 Mar 4;9(6):nwac035.
  - Sarker, M. K., Zhou, L., Eberhart, A., & Hitzler, P. (2022). [Neuro-symbolic artificial intelligence: Current Trends](https://daselab.cs.ksu.edu/sites/default/files/2021_AIC_NeSy.pdf). AI Communications, 34(3), 197–209.

* Deep learning-based reasoners
  - Ebrahimi, M., Eberhart, A., Bianchi, F., & Hitzler, P. (2021). [Towards bridging the neuro-symbolic gap: deep deductive reasoners](https://daselab.cs.ksu.edu/sites/default/files/APIN2021.pdf). Applied Intelligence, 51(9), 6326–6348.
  - Tang, Z., Hinnerichs, T., Peng, X., Zhang, X., & Hoehndorf, R. (2022). [FALCON: Sound and Complete Neural Semantic Entailment over $\mathcal{ALC}$ Ontologies](http://arxiv.org/abs/2208.07628). arXiv:2208.07628 [cs.AI].

## Resources: OWL Ontologies {.smaller}

- Primers, Tutorials
  * [OWL2 Primer](https://www.w3.org/TR/owl2-primer/)
  * [Ontology 101](https://ontology101tutorial.readthedocs.io/) Tutorial
- Software
  * [Protégé](https://protege.stanford.edu) -- authoring/editing ontologies
  * [Ontology Development Kit](https://github.com/INCATools/ontology-development-kit) (ODK) -- initiate an ontology following OBO Library practices
  * [Ontology Access Kit](https://github.com/INCATools/ontology-access-kit) (OAK) -- Python library and CLI
  * [ROBOT](http://robot.obolibrary.org) -- command line tool
  * [OWLAPI](https://github.com/owlcs/owlapi) -- library (Java) and reference implementation 
  
## Resources: Ontologies in Bio {.smaller}

- Ontologies for biology & biomedicine
  * [OBO Ontologies](https://obofoundry.org)
- Tutorials and Training
  * [OBO Semantic Engineering Training](https://oboacademy.github.io/obook/)
  * [ICBO OBO Tutorial 2022](https://oboacademy.github.io/obook/courses/icbo2022/)
- Publications
  * The Gene Ontology Consortium (2000). [Gene ontology: tool for the unification of biology](http://dx.doi.org/10.1038/75556). Nature Genetics, 25(1), 25–29.
  * Dececchi TA, Balhoff JP, Lapp H, & Mabee PM (2015). [Toward Synthesizing Our Knowledge of Morphology: Using Ontologies and Machine Reasoning to Extract Presence/Absence Evolutionary Phenotypes across Studies](http://dx.doi.org/10.1093/sysbio/syv031). Systematic Biology, 64(6), 936–952.
  * Haendel MA, Chute CG, and Robinson PN (2018) [Classification, Ontology, and Precision Medicine](https://doi.org/10.1056/NEJMra1615014). New England Journal of Medicine 379 (15): 1452–62.
  
## Other resources

* Nicole Vasilevsky's [curated list of ontology resources](https://nicolevasilevsky.github.io/ontology_resources/)
* Michael DeBellis (2021) [A Practical Guide To Building OWL Ontologies Using Protégé 5.5 and Plugins](https://drive.google.com/file/d/1UqI19JiGnJwzKx_JQ7qRAz7bmCzyqZpj/view). Edition 1.4.
  - [Pizza Ontology](https://github.com/owlcs/pizza-ontology/blob/master/pizza.owl)
* [OBO Organized Knowledge](https://oboacademy.github.io/obook/) (OBOOK) collection of training and tutorial materials on developing and using ontologies in life science.