Open World Assumptions
- 5 minsOWA and CWA
Checkout previous post on Temporal Databases & Time Series
Greater Than First Order Logic & C.W.A. vs O.W.A.
Closed World Assumption (CWA) - temporal databases hold complete information about the truth
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*we state what is possible* needs a place to put it.
Open World Assumption (OWA) - The alternative: to treat the relational structures representing temporal databases as incomplete specifications and use the OW Assumption to answer queries
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*we state what is not possible* {} empty OWA - everything is possible; then constrain ontology iteratively, making it more restrictive as we go. - NaF (Negation as Failure)
| Animal | CanFly? |
|---|---|
| Penguine | No |
| Shark | No |
| Hummingbird | Yes |
Can pigs fly? - CWA = False: table does not contain fact. - OWA = We don’t know: unless we can infer “pigs can or cannot fly” - NaF = only false if “pigs cannot fly” OWA assumes incomplete information by default
- We can intentionally underspecify and allow others to reuse and extend
- e.g. All Sharks liveInHabitat; some waterHabitat
- Are there fresh/ seawater sharks?
- Do we care? Someone might.
- It can be useful to reuse
Ontology
Ontology Mapping
Ontology Engineering
Ontology Development
A Property Chain
Extending Ontology: we can add statements, but cannot take any away.
- Monotonic: in extending ontology all existing true statements remain true.
UNAs: Unique Name Assumptions: Objects have different IDs by default
- CWA creates UNA
- OWA doesnt create UNA
- to allow later assertion that two things are the same or different (or this maybe inferred)
- Negation is Required for Distinctness.
- RDF cannot make assertions about objects being different
- OW language and other logics can.
Constraints: can mean
- Integrity Constraints (CWA)
- prevents invalid values from being asserted in a model
- used for validation/parsing/data input
- single model: constraints only facts are asserted
- Logical Axioms (OWA)
- restrictions, property domain/range
- everything can be true unless proven otherwise
- multiple possible models can satisfy the axioms
- this may cause some unintuitive inferences
Choosing OWA vs CWA
Analyzing problem domains
| Open World Problem | Closed World Problem |
|---|---|
| Does Rupaul know Kurt Cobain? | Is there a bus from downtown to ocean beach in 5 mins? (only x trains & y destinations) |
| What are the potential side effects of drug x? (answers maybe found in other resources) | Find me drugs that are not licensed for x? (would need closure for each) |
| What are the factors affecting climate change? (new studies may improve or validate other factors) | When was the worst climate change instance ever recorded? |
Why Open World
Underspecification
- Abstract, nested and unnamed entities Easily reusable (and extendable) Good at knowledge level (Ontology) Good at “schema”-“schema” mapping
- Asserting/Inferring equivalents They naturally deal with incomplete information
- Domain knowledge where answers are evolving (e.g. science) Making an inference
Why Closed Worl
Paradigm Shift
- Involves Technology/Experience Catch u Some problems are inherently closed world (often those that we ask “which are not… “ or have a finite number of elements)
- but is possible to close the open world (later Dealing with Defaults & Exception Dealing with Schema-Data mapping
- integrity constraints, validation (parsing from generation)
- data structures are typically close Meta-query
- What do we know??
Interpreting Knowledge on problems
I. Problem Domain A
Will there be a host for the pre-show?
| Time | Activity | Hosts / Awardees |
|---|---|---|
| 5:00pm | Pre-show | __ |
| 7:00pm | Enter | 1993 VMA doors open |
| 7:10 | First Performance | Madonna “bye bye baby” |
| 7:30pm | Introduction | Christian Slater |
| 8:000pm | Best Dance Video - “Free Your Mind” | Shaquille O’Neal introduces En Vogue |
| 8:15pm | Best Rap Video - “People Everyday” | Martin Lawrence introduces Arrested Development |
| 8:30pm | Best Alternative Video - “In Bloom” | Michael Richards introduces Nirvana |
| 8:45pm | Viewer’s Choice Award - “Living on the Edge”** | RuPaul & Milton Berle introduces Aerosmith |
| 9:00pm | Best Direction in Video - “Jeremy by Pearl Jam” | Sharon Stone introduces Director Mark Pellington |
*Order made up for demonstration purposes. Data gathered from ff resources:*
VMA-Rupaul-Nirvana | MTV Awards List
- Database says “No” OWA says “Don’t know” unless a blank is interpreted as “Activity and not(hasSpeaker)”
II. Problem Domain B I want to treat my patient with a painkiller that is not an anticoagulant
| Drug | Effect |
|---|---|
| Aspirin | Painkiller |
| Wharfarin | Anticoagulant |
| Paracetemol | Painkiller |
- Database says “Aspirin”, “Paracetamol”
- OWA can’t say this unless we make explicit “Paracetamol is not an anticoagulant”
OWA is good for describing knowledge in a way that is extensible
CWA is good for constraining and validating data
Resources: PDF - Open World Assumption -University of Manchester Ontology Engineering
| Elephants in the Room | Elephants in the Room project on Github |
ERD - Entity Relationship Diagram for Elephants in the Room 
Maximo Nakpil
Full-Stack Web Dev Exploring Data and Design Disciplines