Hi Wacek,
There's actually a system that supports attaching sentences computationally to predicates along the lines you suggest.
Here's an ontological example that one can run using the system.
| This example is from "Relations in biomedical ontologies" by Barry Smith et al,
| Genome Biology 2005. http://genomebiology.com/2005/6/5/R46
|
| 3. C part_of C1 = [definition] for all c, t, if Cct then
| there is some c1 such that C1c1t and c part_of c1 at t.
for all c, t, if eg-C c t then there is some c1 such that eg-C1 c1 t and c part_of c1 at t
------------------------------------------------------------------------------------------
3. that-C is a part_of the Continuant class that-C1
(A c,t) [ eg-C c t => (E c1) [ eg-C1 c1 t and c part_of c1 at t ] ]
------------------------------------------------------------------------------------------
for all c, t, if eg-C c t then there is some c1 such that eg-C1 c1 t and c part_of c1 at t
some-C and some-C1 are two different Non-process classes with instances
not : (E c,t) [ that-C c t and not (E c1) [ that-C1 c1 t and c part_of c1 at t ] ]
-----------------------------------------------------------------------------------
(A c,t) [ that-C c t => (E c1) [ that-C1 c1 t and c part_of c1 at t ] ]
some-C and some-C1 are two different Non-process classes with instances
some-c is an instance_of that-C at some-t
not : (E c1) [ that-C1 c1 that-t and that-c part_of c1 at that-t ]
----------------------------------------------------------------------------
(E c,t) [ that-C c t and not (E c1) [ that-C1 c1 t and c part_of c1 at t ] ]
some-c1 is an instance_of some-C1 at some-t
some-c is a part_of that-c1 at that-t
------------------------------------------------------------
(E c1) [ that-C1 c1 that-t and that-c part_of c1 at that-t ]
this-item is an instance_of this-Class at this-t
========================================================
c1 C1 1
c C 1
c1 C1 2
c C 2
this-item1 is a part_of this-item2 at this-t
=============================================
c c1 1
c c1 2
the class this-class is of type this-type
==========================================
C Non-process
C1 Non-process
the class some-C is of type Non-process and has at least one instance
the class some-C1 is of type Non-process and has at least one instance
that-C and that-C1 are different
-----------------------------------------------------------------------
that-C and that-C1 are two different Non-process classes with instances
the class some-C is of type Non-process
some-c is an instance_of that-C at some-t
--------------------------------------------------------------------
the class that-C is of type Non-process and has at least one instance
some-t1 is less than some-t2
-------------------------------------
that-t1 is earlier than that-t2
some-C1 is not equal some-C2
-------------------------------
that-C1 and that-C2 are different
One can view, run and change the example by pointing a browser to the site below and selecting RelBioOntDefn3 . One can also write and run new examples. The vocabulary is open, and so to a large extent is the syntax.
I hope this may be of interest.
-- Adrian
Internet Business Logic
A Wiki and SOA Endpoint for Executable Open Vocabulary English Q/A over SQL and RDF
Online at www.reengineeringllc.com
Shared use is free, and there are no advertisements
Adrian Walker
Reengineering
Phone: USA 860 830 2085
On Thu, Feb 3, 2011 at 11:35 AM, Wacek Kusnierczyk <waku@xxxxxxxxxxx> wrote:
On 2/3/11 3:37 AM, Pat Hayes wrote:
> Ian, here's a non-philosophical way to characterize it. Start with an atomic sentence of the form R(a, b), with no time involved, and suppose that a and b here are ordinary uncontroversial physical objects, say. Intuitively, they are 3D things. Now add time, t. Where do we put the time parameter? Several answers can be given.
>
> 1. Attach it to the sentence, meaning that the sentence R(a,b) is true at the time t. This gives you a hybrid or context logic where the times are possible temporal worlds/indices or contexts, to which truth is relativized. But the sentences being so relativized do not themselves make any reference to time. Call this 3D.
>
> 2. Attach it to the relation as an extra argument, and call the relation a 'fluent': R(a, b, t) This gives you the classical AI/KR approach which used to be called the situation calculus, where one quantifies over times in the KR language itself, but the object terms are still thought of as denoting 3D rather than 4D entities. Call this 3D+1.
>
> 3. Attach it to the object terms (using a suitable function, written here as an infix @): R(a@t, b@t) This requires us to make sense of this @ operation, and it seems natural to say that it means the t-slice of the thing named, which now has to be re-thought as a 4D entity. So the a, b things have morphed form being 3D (but lasting through time) to being genuinely 4D, and having temporal slices or parts. Call this 4D.
>
> For some folk this last step is apparently mind-boggling, although to me it is puzzling how one can think of something being 3D and also extended in time and have it *not* be 4D. For yet other people (think OBO), there are apparently two kinds of thing in the world, one kind (continuants) which must be described using the 3D+1 style , the other (occurrents) which should be described using the 4D style. God alone knows why anyone would believe that there are two ways to exist in time, but there's nowt as queer as folk, as someone's grandmother used to say.
>
> What I like about this way of contrasting the options is that it makes it be simply a matter of syntax - where in the sentence to attach the temporal parameter - and not one of metaphysics. Syntax is way easier than metaphysics. It also means that one can see quite clearly how to make the various formal techniques work together, by allowing the temporal parameter to 'float'. In fact, with a bit of extra work one can embed almost all the necessary temporal reasoning into a generalized unification algorithm which extracts temporal constraints during the unification process. I have all the details somewhere if you (or anyone else) are interested.
>
By way of a naive, as usual, question, I wonder if the above could not
be syntactically summarized as
1. R(a,b)@t
2. R@t(a,b)
3. R(a@t,b@t)
vQ
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