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Topic: Sets as Memory traces.
Replies: 10   Last Post: Feb 11, 2013 12:48 AM

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JT

Posts: 1,149
Registered: 4/7/12
Re: Sets as Memory traces.
Posted: Feb 11, 2013 12:48 AM
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On 10 Feb, 21:13, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 11, 5:31 am, Zuhair <zaljo...@gmail.com> wrote:
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> > On Feb 8, 1:02 pm, Zuhair <zaljo...@gmail.com> wrote:
> > > On Feb 6, 9:17 pm, Zuhair <zaljo...@gmail.com> wrote:
> > > > On Feb 6, 2:14 pm, Zuhair <zaljo...@gmail.com> wrote:
>
> > > > > Suppose that we have three bricks, A,B,C, now one can understand the
> > > > > Whole of those bricks to be an object that have every part of it
> > > > > overlapping with brick A or B or C, lets denote that whole by W. Of
> > > > > course clearly W is not a brick, W is the totality of all the three
> > > > > above mentioned bricks. However here I want to capture the idea of
> > > > > 'membership' of that whole, more specifically what do we mean when we
> > > > > say that brick A is a 'member' of W. We know that A is a part of W,
> > > > > but being a part of W is not enough by itself to qualify A as being a
> > > > > member of W, one can observe that brick A itself can have many proper
> > > > > parts of it and those would be parts of W of course (since part-hood
> > > > > is transitive) and yet non of those is a member of W. So for a part of
> > > > > W to be a member of W there must be some property that it must
> > > > > satisfy. I'll add another primitive binary relation in addition to
> > > > > part-hood, and that binary relation I'll call as "contact". So we'll
> > > > > be working within a kind of Mereotopology. However axioms to
> > > > > characterize contact relation would be different from those of
> > > > > Mereotopology. Here only disjoint (non overlapping) objects are
> > > > > allowed to be in contact. When we say A is in contact with B then we
> > > > > mean that for some x,y where x is a part of A and y is a part of B
> > > > > there do not exist a gap between x and y, of course as said above
> > > > > provided that A and B are disjoint objects.

>
> > > > > Now we come to stipulate the sufficient condition for membership of a
> > > > > whole, this is:

>
> > > > > x is a member of y iff x part of y And (there do not exist a part of y
> > > > > that is in contact with x) And every proper part of x is in contact
> > > > > with some part of x.

>
> > > > > This supplies us with the impression that x is a 'solid' entity and
> > > > > yet x is separate (not in contact) from some other parts of y should
> > > > > those exist.

>
> > > > > However this interpretation of membership using this kind of
> > > > > mereotopology has its shortcomings, the greatest is that it is
> > > > > limiting in the sense that only one level of membership is possible,
> > > > > that is between solid blocks and collections of them, any collection
> > > > > of several blocks would not be able to be a member of any object since
> > > > > it does have separate proper parts. So this would only be enough to
> > > > > interpret flat sets.

>
> > > > > If we desire having a hierarchy of sets being members of other sets
> > > > > and if we want also to keep the above background of thinking of
> > > > > matters in terms of parts and wholes and contact etc.., then we need a
> > > > > more complex approach, one of those would be to invoke TIME in the
> > > > > picture!

>
> > > > > This without doubt would complicate the whole picture but yet it does
> > > > > supply us with some interpretation of sets and their membership.

>
> > > > > Now instead of having a binary relation C to represent contact, we
> > > > > upgrade that to a triple relation symbol C(x,y,t) to signify x in
> > > > > contact with y at moment t.

>
> > > > > This would revolutionize how matters are tackled here. So for example
> > > > > if at moment t1 we have a whole apple P being a solid block i.e. it is
> > > > > not in contact with any object and all its proper parts in contact
> > > > > with some proper part of it, then P would be said to be a block at t1.
> > > > > However this doesn't mean that apple P would also remain in this block
> > > > > status, possibly at moment t2 the same apple P had been cut into two
> > > > > separate halfs, so at moment t2 P is a whole of two separate blocks P1
> > > > > and P2 and no longer being as a solid block, so at moment t2 P cannot
> > > > > be an element of any object, while at moment t1 P could have been.

>
> > > > > This development would introduce us to the concept of MEMORY traces!
> > > > > and of course the introduction of a new binary primitive 'memorized
> > > > > in' or 'carved in'.

>
> > > > > A memory trace is supposed to be a record of objects in block status.
> > > > > So for example suppose that an rock was immersed in some mud at moment
> > > > > t1 and thus left its print on that piece of mud, then after a while
> > > > > that rock was broken into two smaller parts, and one part also fell
> > > > > down on another part of the mud and made another print on that piece
> > > > > of mud, so suppose that mud remained like that for years, now this
> > > > > piece of mud have the prints of the whole rock at solid status and
> > > > > also of a part of that rock at solid status, this piece of mud would
> > > > > be considered as a 'memory trace'.

>
> > > > > Now we would coin another interpretation of 'set' as a 'memory trace'.
> > > > > Membership would be of objects in solid status carved in the memory
> > > > > trace.

>
> > > > > so x carved in y  or x memorized in y is taken to mean that x is a
> > > > > solid block at some moment t and memorized as such in y.

>
> > > > > So we have the axiom.
>
> > > > > x M y -> Exist t. x is solid at t.
>
> > > > Even more appropriate is to stipulate 'carved in' as a three place
> > > > relation symbol, so Cv(x,y,t) would mean x is carved in y at moment t.

>
> > > > Now we can 'define' a binary relation M standing for 'memorized in'
> > > > as:

>
> > > > x M y <-> Exist t. x is solid at t & Cv(x,y,t)
>
> > > > here of course what is meant by x M y is: x memorized as a solid
> > > > object in y. And of course we can interpret set membership by the
> > > > relation M defined above, and of course sets would be memory traces.

>
> > > > Zuhair
>
> > > > > So membership can be interpreted as this memorizing relation and sets
> > > > > can be interpreted as 'memory traces'

>
> > > > > It is natural to assume identity of memory traces after what is
> > > > > memorized in them.

>
> > > > > It needs to be stressed that memory traces are NOT the wholes of what
> > > > > is memorized in them! since the whole of an apple and a half of it is
> > > > > the apple itself and it is not different from the whole of three
> > > > > thirds of it, but the memory traces of those are different!

>
> > > > > However if an object do not change its solid status over time, i.e. if
> > > > > we have the following property:

>
> > > > > for all t. x is solid at t
>
> > > > > then wholes (i.e. totalities) of such objects can be taken to be
> > > > > memory traces of them since time is not having any differential effect
> > > > > on those kinds of objects.

>
> > > > > So all in all, sets here can be interpreted as memory traces and set
> > > > > membership as memorizing objects in solid block status.

>
> > > > > Zuhair
>
> > > If we take the fossil example as a case of memory trace, then what is
> > > imprinted in the fossil is the image of the memorized object not the
> > > object itself. This gives me the idea of memory traces being of images
> > > of memorized object as it occurs actually normally everyday in our
> > > minds. We need to stipulate that an image preserves the contact status
> > > of the imaged. However it is also plausible to state that all images
> > > are disjoint.

>
> > In reality what is plausible is to state that all images of objects in
> > solid status
> > are disjoint.

>
> > Also it is desirable to have a unique image of an object at solid
> > status.

>
> > To make the formal workup we need to introduce the primitive three
> > place
> > relation symbol  Img(x',x,t) to signify x' is the image of x at moment
> > t.

>
> > Now the memorizing relation M would be defined as:
>
> > x M y iff  Exist x',t. x is solid at t & Img(x',x,t) & x' Part of y.
>
> > Of course we need y to be a whole of images of objects at solid status
> > and this what memory trace would mean.

>
> > Anyhow this needs further workup to be completed.
>
> > So the images of an apple and its half at another moment
>
> "temporal reasoning in artificial intelligence"
>
> About 1,950,000 results (0.40 seconds)
>
> http://www.cs.brandeis.edu/~cs112/cs112-2004/newReadings/allen-time-a...
>
> Time and Time Again: The Many Ways to Represent Time
> James F Allen
> The University of Rochester
>
> I. Representations Based on Dating Schemes
>
> A good representation of time for instantaneous events, if it is
> possible, is using an absolute dating system. This involves time
> stamping each event with an absolute real-time, say taken off the
> system clock on the machine, or some other coarser-grained system such
> as we use for dating in everyday life. For instance, a convenient
> dating scheme could be a tuple consisting of the year
>
> II. Constraint Propagation Approaches
>
> There has been a considerable amount of work in Artificial
> Intelligence in defining temporal reasoning systems that used the
> technique of constraint propagation. These systems use a graph-based
> representation where each time is linked to each other time with an
> arc labeled with the possible temporal relationships between the times
>
> III. Duration-Based Representations
>
> With the exception of the first technique using absolute dates, we
> have been ignoring the problem of representing temporal durations. In
> this section we will examine some representations that operate
> primarily using duration information. The basic technique for dealing
> with duration information is seen in PERT networks. This
> representation maintains a partial ordering of events in an acyclic
> directed graph that
> has both a distinguished beginning and ending event. Each node in the
> graph represents an event and has an associated duration.
>
> IV. Temporal Logics
>
> So far we have only discussed the representation of...
>
> läs mer »


Truth is the human have a very limited concept of time and order since
evolutionary not been that important, we can memorise a timestamp with
an event, an AI could do so much better.




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