Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

[Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>]

Dear Gary, John and Mike 

===========================================
Gary,

Glad to be of help. We can actually develop some rough guidelines from these.

Imagine you have a theory, T0, and you realize you would like to extend via terms A and B. 

A extends the theory conservatively, while B does so nonconservatively. If possible, what would be ideal would be to create three new theories: 
     T0c and T0n and also T0*,  each with different metadata.


T0c would be a novel theory (module in the repository) which is T0 extended conservatively with A (specialization via A in John's terminology).  So metadata (T0c extends T0), (T0 conservativeExt T0)
T0n would be also be a novel theory / module which is T0 extended non-conservatively with B (also specialization via B in John's terminology). (T0n extends T0), (T0n nonConservativeExt T0)

T0* would be yet another module, which is the conservative extension of T0n, and a nonconservative extension of T0c  (also specialization).  (T0' extends T0c), (T0* extends T0n), etc...

While this might seem like extra work, what it does is clearly specify how the theory evolved, and more importantly, it would help you identify possible modules much more easily, and make changes much more easily as well.

===========================================

John and Mike,

> [JFS] Another operator is what I call analogy:  taking one theory and
>
>
> renaming some of the labels (i.e. names of relations, types, or
> individuals) to create another theory that is isomorphic with
> the first.

Two observations here.

1) A note about terminology, in our work we called this "conceptual or structural metaphor" (reusing work done by Lakoff 1980, Danesi 2002 and Pinker 2007, creating a lineage and linkages for this idea to other disciplines). More importantly, this "analogy" need not lead to an isomorphism, which leads me to the second point.

I'll quote this passage from Lakoff from _Metaphors We Live By_ in the chapter on "Grounding of Structural Metaphors" from the 2003 edition:

> A material resource is a kind of substance
>
>      can be quantified fairly precisely
>      can be assigned a value per unit quantity
>      serves a purposeful end
>      is used up progressively as it serves its purpose
>             (page 65)

I don't mean to suggest this particular metaphor is necessarily apt (i'm sure there are many philosophical quibbles with this particular exposition), I include it simply to demonstrate how it can take effect as a partial metaphor.

2) From a logical perspective, there is nothing special about this term. It is special only when one considers the "intended meaning" of the labels. From the logical perspective, this operation can be one of a number of interpretations. This also explains why it need not be an isomorphism. The three types of mappings in the FOIS2010 paper support three types of metaphor / analogy. One is complete (definable equivalence), which does indeed lead to isomorphism. The other two, faithful and relative (and a fourth, weaker one called partial to appear later), result in a partial mapping of the terms from one theory to another.

The latter type of interpretation supports the case when only some labels make sense to map. An example is the "metaphor" or "analogy" between a biological cell membrane and an electronic circuit.

The mapping might capture (permeability --> resistance),  (diffusivity --> current flow), and (membrane potential --> voltage). For a more complete exposition of this look at: http://en.wikipedia.org/wiki/Membrane_potential#Equivalent_circuit but have no clear analog for Na, K, Cl etc..

Indicating that not all aspects of the cell are analogous to electrical circuits, so we might only attain a partial "analogy".

But the larger point is that a metaphor/analogy is really like any other mapping from a logical perspective: you are mapping the logical (sub)structures of one theory to another. The analogy/metaphor label simply indicates that the "intended meanings" are different. Or not even, simply that the application domains of the labels are different (since two people using "Biological Entity" and mapping into one another might have different intending meanings, but we would be hard pressed to say that we are creating a metaphor for Biological_Entity_A to Biological_Entity_B.)

In this parlance, we might say that PSL has a partial structural metaphor with Graphs and Linear Orderings etc. We wouldn't say that a manufacturing process by company C has an analogy to a PSL theory, even though the intended meanings might differ (if it is a partial metaphor).

Cheers,
Ali
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