Pattern Logic Series, Part VI: Disambiguating “is”
Grounding meaning in a fixed and computable system of pattern is the ultimate aim of this series on pattern logic. In this Part VI, we will begin to see how we can move from ambiguous assertions to clear and distinct ones.
When we say to each other that “some concept is some concept” it is easy to overlook the ambiguity in the assertion. This ambiguity of meaning is one of natural language’s most useful features because it grants a communicator greater efficiency in being able to assume multiple possible interpretations wherein listeners can usually supply the required specificity on their own given the context. But disambiguating words like “is”, “and” and “or” becomes especially helpful when we need to make our communication more precise, and this is certainly the case when modeling knowledge for machine interpretation. Pattern logic helps us to do this in a systematic method.
In part I of this series we introduced the concept of simple limitation and defined this as a relation composed as a portion limited by an extent. The portion, the limitation and the extent are three distinct parts, and in the special case that all three of these represent logical universals, we have called this type of relationship a predication. When logical individuals get pulled into the pattern as the portion and/or the extent of the limitation we saw how we get other relationships like instantiation, extension and composition.
In part II we looked at compound limitations involving the predication variant of limitation and identified three basic serial arrangements of three concepts and two limitations, and called these mediation, overlap and union.
When we look through the lens of language, these three basic arrangements of mediation, overlap and union correspond respectively to an ambiguous usage of the words “is”, “and”, and “or”.
In part III we have examined patterns of ‘imperfect limitation” and discussed the Frame-Region diagram as a helpful means of diagramming the logical meanings of many ADEPT LION patterns. What we will now investigate is how these additional patterns can be employed to turn the ambivalent basic expressions into precise ones.
This is analogous to the contextualizing that a listener does when making sense of the ambiguity in a word like “is”. This contextualizing process is so automatic for us that it requires a surprising degree of focus to tease this processing apart. Fortunately, pattern logic supplies a methodology that helps us to be not only systematic, but also thorough in our investigation. What will remain to be done at the end of these next three parts of our exploration is to determine what has been omitted from the resultant scope of disambiguated meanings then available for the words “is”, “and”, and “or”.
The four meanings of “is”
In this braid diagram we see the basic pattern of mediation in which a concept beta is the extent of a limitation involving the portion concept alpha, which in turn is also the portion of a limitation with the concept gamma as the extent. This mediation arrangement is ambiguously expressing in common English some concept beta which can be stated as “something alpha is something gamma”. Mediation is therefore what we call the basic compound limitation that corresponds to our use of “is” when relating two universals.
Let’s look at the following four uses of “is”:
1. Crimson is deep red.
2. Burgundy is a red (dark red).
3. Navy is blue (navy blue).
4. Kleenex is facial tissue.
These four assertions represent four distinctly different meanings of the word “is”. These differences are subtle, but this is where the ADEPT LION trickle diagrams and frame-region diagrams can help bring insight.
Restatement
In the first example we want the “is” to convey that “crimson” and “deep red” are the same thing. By adding the two redundant limitations shown in the trickle diagram at the upper left, we get the corresponding frame region diagram arrangement of restatement between these three concepts:
· alpha = “crimson”
· beta = “crimson is deep red”
· gamma = “deep red”
We should pause here to convince ourselves that if somebody were to communicate to us any of the three quoted concepts of alpha, beta or gamma above, they would only be restating one concept in three ways. For the sake of this example, we need to consider these terms of “crimson” and “deep red” to be completely interchangeable. If we assert some additional synonym like “ruby”, this should not change the equivalence that is being assumed between “crimson” and “deep red” and “ruby”…
Due to the features of the pattern necessary to assert this disambiguated meaning, we call this a “mediation with a double redundancy”.
Proper Hierarchy
The second example seems indistinguishable: “burgundy is a red (dark red)”. The distinction is that there are other concepts that would exist within both the concepts of red (like light red) and of dark red (like maroon) that would not be synonymous with the terms expressed. In order to assert this existence of non-synonymous alternatives, we need not know what they are however. All that is needed in the pattern is the additional expression of a “proper part”. The imperfect limitation of non-predication when added to a limitation between two concepts accomplishes this distinction.
In example two we have achieved a proper three tiered hierarchy, or in frame-region diagrams, a proper nesting of three distinct concepts. We have already introduced the notation of “trunk” for the general, “leaf” for the specific and “branch” for the intermediate concept in part II. In this case the trunk of our hierarchy is the concept “red”, the branch is the concept “Burgundy is red” and the leaf is the concept “burgundy”. Notice that in order to be clear about the middle/branch level of this hierarchy, it is helpful to re-name the sense in which “burgundy is red”, specifically that “burgundy” is a proper part of an intermediate concept which we can call “dark red”, which in turn, is a proper part of the more general concept of “red”.
We can call this form of disambiguation a “mediation with a hierarchical branch”.
Restatement of a Subordinate
In the third example of “navy is blue (navy blue)” we have given the parenthetical addition in order to make explicit the sense in which navy is blue. Specifically, “navy blue” is the sense in which “navy is blue”. Because “navy blue” is a proper part of the concept “blue” but also indistinguishable from the concept of “navy” as a color, we have an additional disambiguated meaning of “is” which we can call “mediation with a redundant subordinate”.
Pause to convince yourself that any reference made to “navy” as a color concept, is the same as the only-slightly-more-verbose reference to the color concept of “navy blue”.
We are also assuming here that the most-general-concept “blue” is a color. This could most certainly be explicitly asserted with the addition of a “color” concept delta, but that would stretch our model beyond the three concepts we are allowing ourselves.
Restatement of a Superordinate
Whereas the third example generalized the leaf into the branch, the fourth example generalizes the branch into the trunk. When we assert that “Kleenex is facial tissue” and by this we are giving our listener license to substitute the concept “Kleenex” whenever they more generally mean to say “facial tissue” then we will have arrived at the sense of “is” that we call “mediation with a redundant superordinate”.
This disambiguation is achieved much like the third variety, with redundant and non-predication pattern additions, but they have been swapped in their positions relative to the starting base pattern of mediation.
Discussion
So we have disambiguate “is” into four distinguishable sub-varieties, namely:
1. mediation with a double redundancy = three equivalent concepts
2. mediation with a hierarchical branch = three properly nested concepts
3. mediation with a redundant subordinate = equivalence of leaf and branch concepts
4. medication with a redundant superordinate = equivalence of branch and trunk concepts
Note that in the basic arrangement of mediation that we started with, the alpha, beta and gamma concepts were all uncommitted, meaning that they had no dependency of their meaning upon some other occasion in the pattern. Our acts of disambiguation have changed this flexibility to some extent. Looking back at the diagrams, we have lightly shaded the concepts that are now committed. In short, declaring a proper part requires a commitment but declaring a restatement or equivalence of concepts does not require a commitment. Thus the proper hierarchy is the most committed pattern of the four.
Let’s consider the utility of this disambiguation of “is” in the context of machine interpretation of some asserted knowledge. We have used redundant and imperfect limitation to specify equivalence and proper parthood upon the mediation pattern in order to make these assertions less ambiguous. Removing the “guess work” for the machine is clearly useful whether our aim is clear communication of context or correct inferencing when we reason over the connection of these concepts to others.
But have we completely disambiguated “is”? In other words, have all senses of “is” been identified with sufficient clarity. The answer is most certainly “no!”. The word “is” clearly has many other uses that we have not even begun to explore. For instance, we have already seen in our discussion of the “problem of universals” that it is helpful to have patterns that distinguish between logical universals and logical individuals.
But for the limited scope of this discussion involving relations between two universal concepts modeled as an “is” predication, we do have identified something truly useful. Given inferencing over transitive patterns and some additional redundancies that we have not discussed, we already know that there is truly an infinite number of variations possible for the word “is”. This realization is reassuring and not necessarily overwhelming, because these variations remain computable.
Perhaps the most immediate application of this disambiguation of “is” would be within a taxonomy of words such as Princeton’s WordNet. There we find a corpus of words that are arranged through concepts like synonym, hypernym and hyponym that we could translate to the grounded patterns of double redundancy, proper hierarchy, superordinate and subordinate that we have been exploring.
There would be little to gain by only replicating an existing representation of knowledge about words such as is found in WordNet. And pattern logic is offering more than a new representation. Systematic reasoning, both deductively, inductively and abductively is now on the table with knowledge grounded in pattern because the mechanics of sound reasoning are embedded in the logical structure of the patterns. But we are getting ahead of ourselves. We still need to disambiguate “and” and “or”, which is what we will do in the next two parts of our series.
