this looks to me exactly like a definition for a description logic? except with some constraints on how you define the classes, properties and individuals so that they meet only the conditions of Word Grammar?
eg. --subordinate trans. looks like: 'x hasParent y' paired with respective inversion 'y isParentOf x' --sister trans. looks like a subproperty chain: 'x hasParent y isParentOf z' --proxy links look like another instance of a property and again a subproperty chain eg. 'x hasProxyLinkType1 y hasParent some z' --the head would a property defined to be the union of valid transitive subproperty chains (including the proxy link rule) to reach the root node? Your problem where words may be parents of each other, is a cyclic ontology feature, which messes up uniform interpolation eg. forgetting eg. can't represent it finitely, eg. non-terminating. Your operation solution looks similar to the fixpoint operators in the literature, but I'm getting out of my depth there So to my reckoning, you definition matches: SHIQ description logic where... ontology model where roles/individuals are words in the phrase(s) you have two properties: landmarks, proxy. where transitivity/inversions are allowed in certain cases you dont use classes/subclasses because you don't need them As for your weighted links... they don't fit anywhere :-) On Wednesday, 5 April 2017 23:26:20 UTC+1, Ben Goertzel wrote: > > Some quasi-mathematical-linguistic musings... > > Reviewing a bunch of familiar stuff in my mind, I’m trying to take an > algebraic view of Word Grammar…. This is presumably equivalent to > pregroup grammar under appropriate restrictions but it’s maybe a more > linguistics-ish way to look at it… > > Consider a set of words interlinked by ordered dependency links (so > each link has a head corresponding to the parent, and a tail > corresponding to the child). For reasons including those to be > described below, it is useful to consider these dependency links as > typed. > > Word Grammar tells us how, given such a set of words and links, to > construct a set of additional (ordered) “landmark links” between the > words. > > The rules thereof are as follows… > > The parent is the “landmark” of the child. > > In some cases a word may have more than one parent. In this case, the > rule is that the landmark is the one that is superordinate to all the > other parents. In the rare case that two words are each others’ > parents, then either may serve as the landmark. > > A Before landmark is one where the child is before the parent; an > After landmark is one where the child is after the parent. > > Rules of “landmark transitivity” are: > > * Subordinate transitivity: If A is a Before/After landmark for B, and > B is some kind of landmark for C, then A is a Before/After landmark > for C > > * Sister transitivity: If A is a landmark for B, and A is also a > landmark for C, then B is also a landmark for C > > * Proxy links: For certain special types T of dependency link, if A > and B are joined by a link of type T, then if A is a landmark for C, B > is also a landmark for C > > The “head” of a set of words is a root of the digraph of landmark > links in that set of words > > Restricting attention momentarily to the case of phrases with only one > head, one way to look at this is: The landmark transitivity rules tell > what happens when we carry out operations such as > > P1 +_T P2 > > (putting a dependency link between the head of P1 and the head of P2, > with P1 to the left and being at the child end of the link), or > > P1 +_T’ P2 > > (putting a dependency link between the head of P1 and the head of P2, > with P1 to the left and being at the parent end of the link) > > noting that this operation is not commutative, and also that the > dependency link may have a type T which may be important (e.g. due to > the existence of proxy links). > > These operations at on the space of graphs whose nodes are words and > whose linked are either typed, ordered dependency links, or ordered > landmark links; and for which the landmark links are consistent > according to the rules laid out above. > > The landmark transitivity rules tell where the landmark links go in > the combined structures P1 +_T P2 and P1 +_T’ P2, in a way that will > maintain the consistency of the rules regarding landmarks > > It is not hard to see that, according to the rules of landmark > transitivity, the free algebra formed by the multiple operations +_T, > +_T’ is distributive, associative, and noncommutative > > There is one hole in the above; we haven’t dealt with cases where a > phrase has more than one head, because two words are each others’ > parents. The easiest way to look at this formally seems to be to > introduce operations +_Tij, where > > P1 +_Tij P2 > > builds a dependency link of type T from the i’th head of P1 to the > j’th head of P2. We would also have operations of the form > > P1 +_Tij’ P2 > > We can then see that the free algebra formed by the multiple > operations +_T, +_T’, +_Tij, +_T’ij is distributive, associative, and > noncommutative... > > A next step would be to make all these links (represented here by + > operators) probabilistically weighted. But I'm out of time just now > so that will be saved for later ;) ... > > ben > > > > -- > Ben Goertzel, PhD > http://goertzel.org > > "I am God! I am nothing, I'm play, I am freedom, I am life. I am the > boundary, I am the peak." -- Alexander Scriabin > -- You received this message because you are subscribed to the Google Groups "opencog" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. 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