[FDM-TLO] Textual definitions - rules for identification or criteria of identity
Chris Partridge
Hi,
Mesbah (Khan) has been discussing with me an area in the extensional-intensional criteria of identity choice which may be of interest to some members of the forum. This relates to the use of textual definitions. I have tried to summarise our discussion.
What would be good is if people could review their favourite TLOs textual definitions and say whether they think they are more about giving a rule for what falls under the term – or the criteria of identity for what the term is (or refers to). Hopefully the rest of this email will give some idea of what the difference is.
Firstly, a clarification. In linguistics there is a distinction between intensional and extensional definitions. These are two ways of defining the meaning. An extensional definition will list the things – and intensional definition will give some rule for identification, often based on the meaning. The same set of objects, X say, can have equivalent extensional and an intensional definitions; for example, ‘the things currently on my table’ and ‘this pen, this cup and this book’. The goal of the definitions is to help identify what falls under the term.
The intensional and extensional criteria of identity are doing different work (as explained in the survey paper) – though one could – at a stretch – see some connections between the two distinctions. A criterion of identity is focused on the term (or what it refers to). If one took the two earlier definitions as capturing identity, then there would be two different collections not one.
TLOs and domain ontologies supplement their formal definitions with textual definitions of their objects. Some use textual definitions to help users understand the ontologies rather than as a component of the ontology itself. Others rely on textual definitions of their objects as a component of their ontologies, where the text may contain content that does not always map exactly or easily onto the formal ontology. (And, in a sense, undermining the move towards a purely formal ontology.)
This raises questions about the role of these textual definitions. Where these ontologies do not have a clear statement of their strategy for criteria of identity, an initially tempting assumption might be that these definitions are somehow implicitly a mechanism for implementing an (intensional) criteria of identity. Let’s see how that would work.
The machinery for deciding when two definitions have the same extension is usually simple and obvious. But deciding whether they have the same intension is more difficult without some guiding background framework.
This is perhaps best exemplified with definitions of general (rather than particular) objects. These typically define the things that fall under the general object – its extension. In the standard example, describing what an individual equilateral triangle is, rather than what the type ‘equilateral triangle’ is.
Here are two examples from OpenGIS® Geography Markup Language (GML) Encoding Standard - Version: 3.2.2
9.3.2 AbstractFeature
...
gml:AbstractFeature may be thought of as “anything that is a GML feature” and may be used to define variables or templates in which the value of a GML property is “any feature”. This occurs in particular in a GML feature collection (see 9.9) where the feature member properties contain one or multiple copies of gml:AbstractFeature respectively.
14.2.2.3 TimeInstant
gml:TimeInstant implements ISO 19108 TM_Instant (see D.2.5.2 and ISO 19108:2002, 5.2.3.2) and acts as a zero-dimensional geometric primitive that represents an identifiable position in time.
They both focus on instances (the term’s extension) and this would seem to imply they are pragmatically extensional rather than intensional. (They are of course intensional in the linguistic sense – as they do not list the instances.)
The background framework would have to deal with a variety of differences due the (informal) nature of text. Simple textual differences are easy to deal with. Presumably different inscriptions of the definitions will be counted as equivalent, even if they have different fonts and capitalisations. Similarly, pragmatically, translations into the same or different languages – with some notion of tolerance as there are unlikely to be exact equivalents across languages. There may be pragmatic ways of accounting for different phrasing when there is the same sense.
The ontological promiscuity (plenitude?) of intension remains. How does one deal with two definitions that have the same extension but use quite different terms; we have our standard example, ‘equilateral triangles’ and ‘equiangular triangles’. Having three equal sides seems to be quite a different property from having three equal angles. In this case, wouldn’t we want to say these are different definitions.
But it is not clear to me that the drafter of the definitions intended them to be used for more than either giving a reasonable sense of what is intended to help in pragmatically identifying the extension. They were not implicitly committing to intensional promiscuity. And, in practice, that is how they are used. If this is so, then the extensional/intension choice is still to be made.
Regards,
Chris Partridge
Chris Partridge |
Chief Ontologist | BORO Solutions Limited | www.BOROSolutions.co.uk
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