The mapping into description logic looks to make sense... On Thu, Apr 6, 2017 at 6:14 PM, 'Adam Gwizdala' via opencog <[email protected]> wrote: > 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]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/opencog. > To view this discussion on the web visit > https://groups.google.com/d/msgid/opencog/157e392d-63b1-4408-85c3-609e39e21dfa%40googlegroups.com. > For more options, visit https://groups.google.com/d/optout.
-- 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]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/opencog. To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CACYTDBe6KsxPoyLrG7k4HZCbo8t7%2BXJ7yAaKQxbKYt7nA7bXcQ%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
