On 10/11/13 10:43, Niklas Laxström wrote:
> What is OWA?

John refers to the "Open World Assumption". This is an informal concept 
used in knowledge representation to describe the assumption that 
statements that are not made are "unknown" rather than "false". This is 
contrasted with the "Closed World Assumption" that is common in 
databases, where we assume that unspecified information is false.

For example, if the ACME company has a database that contains a table 
for employees, and this table does not contain "Bob", then one would 
assume that Bob is not an employee at ACME. In contrast, if an OWL 
ontology contains information about people (e.g., using FOAF), and the 
ontology does not contain Bob, one would not assume that Bob is not a 
person (maybe Bob just has not created a FOAF file). If we want to say 
that Bob is not a person in OWL, then we can do this directly by using 
negation; in databases, this is usually not possible and we simply 
assume that omitted information is negated.

OWA is closely related to what we call "monotonicity": the more 
information we enter into a system, the more informative it becomes. 
Databases are not monotonic in this sense: if I enter that Bob is an 
employee, then I add some information (that "Bob is an employee") but I 
also remove some information (that "Bob is not an employee"). OWL is 
monotonic, but other knowledge representation languages are not.

What John refers to is that SMW assumes a default type for properties 
(Page). Therefore, the input behaviour is not monotonic: if you specify 
another type later, then this will make the formerly true type Page 
false. However, this is not a "violation" of the OWA. Wikitext is just a 
surface syntax and not the internal knowledge model of SMW. Wikitext can 
never be monotonic: for example, if a page contains 
"[[someprop::somevalue]]" and you add an input character "X" to obtain 
"[X[someprop::somevaue]]" then SMW will no longer contain the fact. 
Parser functions, templates, comments, etc. will all lead to similar 
effects.

Clearly, it makes no sense for a surface syntax to be monotonic in this 
sense: a meaningful notion of monotonicity cannot refer to the character 
level. However, the only other structure that wikitext has is the DOM 
tree of templates and parser functions. Basic SMW fact syntax and MW 
category syntax does not feature there at all (it is just character 
data). So it does not work for defining a meaningful notion of 
monotonicity either. The simple conclusion is that wikitext is not a 
formal specification language, and that applying knowledge 
representation concepts like OWA and monotonicity to it is not meaningful.

If you want information specified in a formal knowledge representation 
format, then you can use the OWL/RDF exports of SMW. These exports have 
a monotonic semantics that is based on the OWA.

Markus



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