On 10 Feb, 21:13, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Feb 11, 5:31 am, Zuhair <zaljo...@gmail.com> wrote: > > > > > > > > > > > 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.