The genotype langage and formal semantics

Abstract

The work is based on the hypothesis of the common semiotic basis
for natural languages. The hypothesis explains the human ability of interlinguistic communication, i.e; the possibility of translating from one
language into another. The common semiotic basis of natural languages
is conceived of as abstract language which is called the genotype language.
The genotype language is constructed as an expanding deductive
system which is defined by mathematical rules envisaging the construction
of linguistic object and their derivation from the primitive linguistic
object. The system of these rules is called the applicative grammar because
of the operation of application which plays a fundamental role in the
construction of the genotype objects. The applicative grammar procedes
from the most primitive system of linguistic objects and gradually expands
according to definite rules. The most primitive linguistic objects are the
following : 1) names of objects; 2) names of situations; 3) transformers.
Names of objects are nouns and noun phrases. À situation is either a whole
consisting of some objects and some property attributed to it, or a whole
consisting of objects and a relation hetween objects ascribed to them.
The objects are called participants of the situa . A simple situation is
among whose participants there is at least one situation. Names of the partipants situations are sentences. Names of properties and relations are predicates. Names of the participants are arguments of the predicates of terms.
Transformers are linguistic objects which change the linguistic objects
of one class into cither the linguistic objects of one class, into either of the
linguistic objects of another class or into the linguistic objects of the same
class.
Terms and sentences are regarded as the basic classes of linguistic
objects. The transformers applied to the basic classes generate an infinite
number of the classes of linguistic objects. These classes are called episemions and regarded as universal linguistic categories. The linguistic
objects which belong to episemions are called semions. The episemions
are given an abstract and empirical interpretation.
The primitive form of the genotype language is defined by the semion
calculus. The sole operation of the calculus is the application of the semionoperator to the semion-operand. Thus obtained, the semions simulate
LANGUE GENOTYPIQUE ET SEMANTIQUE FORMELLE. 99
words. word combinations and sentences of natural languages. The derivation rules of the cpisemions and semions define the formal syntax of the genotype language.
The genotype language is expanded by means of splitting terms, taking into account their situational roles. The following new terms are introduced : agentive. instrumentive. affective. locative and completive. The expanded
genotype language makes it possible to delve deeper into the study of natural languages.
A subset of the expanded genotype language is effected by means of combinatory operators. The combinatory operators are employed in the rules of derivation by means of which complex semions are obtained from the semantic axioms. The formal semantics of the genotype language is defined ty these derivation rules. The formal semantics is a tool for simulating the essential semantic processes of natural languages. It must be emphasised that the applicative grammar is the simplest of all possible semiotic systems because all its objects are constructed by means of the binary operation of application: Thus the applicative grammar is based the principle of binarism.