Conclusion - Computational Linguistics and Talking Robots - page 241

may be viewed as rudimentary parts of speech: f is like a two-place verb, while
a and b are like nouns serving as subject and object. 15
The corresponding constructs in DBS are features, defined as attribute-value
pairs, using noun, verb ,and adj as the core attributes of proplets. By distin-
guishing between the attribute and the value(s), there may be features such as
[noun: dog] which are more differentiated and intuitive than the individual
constants a 1 ,a 2 ,a 2 , ...of Symbolic Logic, without any loss of generality. 16 In
DBS, a functor-argument like f(a,b) of predicate calculus is shown by example
in 3.2.5 and represented abstractly as the schema 3.2.6.
In any semantics, there are two kinds of meaningful elements, (i) logical and
(ii) contingent . In predicate calculus, the logical elements are the connectives,
the quantifiers, the variables, and a certain bracket syntax, while the contingent
elements are letters for constants. In Database Semantics, the logical elements
are the attributes and the variables in the proplets, while the non-variable val-
ues, i.e., the symbols, indexicals, and names, are contingent.
The traits common to Symbolic Logic and DBS may be increased further by
taking the liberty to reinterpret the semantic interpretation of a sign-oriented
approach as the hear mode of an agent-oriented approach. 17 In this way, the
sign-oriented approach may be taken to cover one of the three steps of the
natural language communication cycle.
This holds especially for Montague (1974), who shows in PTQ how to se-
mantically interpret surfaces of English by translating them into formulas of
predicate calculus. The translation is quasi-mechanical in that the reader can
go mentally through the rule applications and the lambda reductions as if going
through the steps of a proof. Montague formalizes the translation mechanism
as a Categorial Grammar with (i) a cleverly structured set-theoretical inter-
pretation and (ii) the reduction mechanism of typed lambda calculus (lambda
reduction). 18
From the viewpoint of this agent-oriented reinterpretation, DBS may be seen
as completing Montague grammar in two ways. One completion is the exten-
sion of Montague grammar to the full cycle of natural natural language com-
munication by adding the think and the speak mode. The other completion is
15 Using typed lambda calculus, Montague (1974) worked hard to formalize functors and arguments set-
theoretically as semantic types with corresponding syntactic categories, fitting into the rule schemata
of Categorial Grammar. Lambda reduction in a typed lambda calculus may be viewed as a souped-up
version of the categorial canceling rules.
16 If needed, a feature may be represented abstractly as a pattern with the attribute and the values repre-
sented by variables. Cf. NLC'06, Sect. 4.1.
17 This reinterpretation is the founding assumption of SCG'84.