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Comments on Precisiated Natural Language (PNL)
Dr. Zadeh's recent papers and UAI postings on Precisiated Natural Language (PNL) put forward a new language based approach to uncertain reasoning. The key claim is that a basic function of language is to provide a means of describing perceptions and that since perceptions are essentially imprecise and fuzzy, natural language descriptions of them are necessarily so as well. Moreover, many scientific theories are largely concerned with formalizing aspects of the physical world which are only experienced through our senses (i.e. perceptually) and existing bivalent logic based descriptions of such theories are inadequate. As an alternative, Dr. Zadeh's proposes the use of PNL to express such theories using the analogy to linear (bi-valent logic) versus non-linear mathematics (PNL) to make his point. Dr. Zadeh's goal is to provide a system for "precisiating" (or making precise) linguistic descriptions to support reasoning over them and to support an improved, yet language based formulation of scientific theories. Dr. Zadeh's goal is highly laudable and worthy of pursuing.
A key element of PNL is the definition of a Global Constraint Language (GCL). The translation of natural language into GCL is a basic mechanism of precisiation. In GCL, all constraints are expressed by the form
X isr R
where X is a variable for an individual (or individuals) R is a relation (or attribute) and "isr" ascribes the relation to the individual with a modality (e.g. possibilistic, probabilistic, veristic) specified by the "r" in "isr". The mapping from natural language to GCL is facilitated by the availability of a dictionary for translating from natural language to GCL. For example, the linguistic _expression_ "Eva is young" can be looked up in the dictionary and translated into
Age(Eva) is (possibilistic) Young.
To support reasoning, GLC statements can be abstracted into various protoforms, with reasoning mechansims defined over the protoforms. "Eva is young" can be abstracted to the protoform "A(B) is C" (i.e. "Age(Eva) is young") and any rules of reasoning which apply to this abstracted form can be used to support reasoning over the more specific representation.
My own research is concerned with the construction of meaning representations from linguistic input (for details see www.DoubleRTheory.com) and I share Dr. Zadeh's interests in this regard. I currently do not have a mechanism for reasoning over the constructed representations and I am excited about the prospects of using Dr. Zadeh's research to provide such a mechanism.
The mapping from Double R representations (i.e. representations of referential and relational meaning) to GCL is complicated by the restricted form of GCL and by the compositional nature of Double R representations which precludes use of a dictionary to provide a full mapping. Ultimately, I suspect that the basic GCL form:
X isr R
will need to be supplemented to support precisiation of the full range of meanings that occur in Natural Language. Otherwise, many meaning contrasts will remain implicit. For example, how are such things as specification (i.e. identification of referring expressions), modification, quantification, conjunction, disjunction, complementation (i.e. intransitive, transitive, ditransitive, clausal complement), tense, aspect, genericity, etc., consistently mapped from Natural Language to GCL.
For example, the linguistic _expression_ "Eva is young" is represented in Double R as:
Situation-Referring-_expression_ / \ Subject Predicate | | Object-Referring-_expression_ Predicate-Referring _expression_ | / \ Head Specifier Head | | | Eva is young
That is, "Eva is young" refers to a situation consisting of the subject "Eva" which refers to an individual and the predicate "is young" which refers to an attribute that is predicated of "Eva". According to Dr. Zadeh, the fully abstract protoform corresponding to this _expression_ has the form
A(B) is C where A corresponds to "Age", B to "Eva" and C to "young"
Note that the type of the attribute "young", namely "age", is not explicitly expressed in the linguistic _expression_. Translating the linguistic _expression_ into this protoform will require making this type explicit. But in Dr. Zadeh's protoform for "Most Swedes are tall"
Q A's are B's where Q corresponds to "Most", A to "Swedes" and B to "tall"
the "height" attribute remains implicit as it does in the linguistic _expression_ and the focus is on explicitly representing the quantifier "most" in the protoform. It should be noted that there is an implicit quantifier in the linguistic _expression_ "Eva is young" which is also implicit in the "A(B) is C" protoform. In general, some mechanism is needed for consistently mapping quantification and attribute type into GCL notation.
It is clear from Dr. Zadeh's writings that an important goal is to provide a GCL that is expressive enough to cover the full subset of natural language that is precisiable. Dr. Zadeh claims, and I agree with him, that bivalent logic is inadequately expressive for this purpose. It is my belief that more expressive logics tend to have more of the features of natural language and this being the case, why not simplify the mapping from natural language into logic, rather than focusing on simplifying the logical form. In the past, the main reason for keeping the logical form simple was to support reasoning, but Dr. Zadeh's protoforms provide a means for supporting reasoning which is abstracted from the more specialized GCL expressions which capture the full, unabstracted meaning of the linguistic input. Of course, it is also important to keep the mapping from GCL to protoforms as simple as possible. Here again, dictionary lookup will only work for the noncompositional cases.
I like very much Dr. Zadeh's idea of building dictionaries with both human precise and machine precise entries. However, these dictionaries will need to be supplemented with knowledge about how to combine the individual dictionary entries to support the building of compositional representations of meaning. If the machine precisiated entries and compositional knowledge were coded in an XML based version of PNL, they would have considerable potential for wide use in NLP applications.
Very respectfully,
Jerry
Jerry T. Ball Senior Research Psychologist Human Effectiveness Directorate Air Force Research Laboratory [EMAIL PROTECTED] www.DoubleRTheory.com
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