LINGUISTIC MODEL BASED ON THE GENERATIVE TOPOLOGICAL INFORMATION SPACE 
Seiichi Uchinami and Yoshikazu Tezuka 
Faculty of Engineering, Osaka University 
Yamada-Kami, Suita, Osaka, 565 JAPAN 
Based on the st~uctuzL~m, we propose a generative semantic model which 
has a topological information space generative grammar as basic rules. In 
this model a semantic map which is called a topological information space, 
is generated by the grammar,and the space can express implications and sim- 
ilarities among concepts. In the syntax, a syntactic generative grammar is 
defined based on the space grammar, and a mapping from the map to the lan- 
guage is defined. The mapping is composed of two mappings: one is a meaning 
affix mapping ~ which maps a conceptual area in the space to a token in the 
language,and the other is an operator mapping ~ which maps a generative rule 
in semantics to a rewriting rule in syntax. By these mappings, a derivation 
tree in semantics is mapped to a derivation tree in syntax, and vice versa. 
An algebraic system on the space is defined, and an algebraic system on 
the sentences is derived by the (~,~)-mappings. English will be analyzed 
according to this model and the algebraic systems on them. 
Finally an information processing model is described based on the model. 
The information processing in a natural language is carried out in the fol- 
lowing steps: recognizing the inputs, parsing, interpreting, deducing, up- 
dating them, and outputting. These processes are discussed in details. 
I. INTRODUCTION 
Linguistics has been investigated 
from three aspects: syntax, semantics, 
and pragmatics. 
As for syntax, many studies have been 
done since Chomsky presented a genera- 
tive grammar based on strueturalism, and 
splended accomplishments have been made. 
As for semantics, some reports have 
been published. In the standard theory 
and the Case grammar, syntactic rules 
are considered to be powerful enough to 
describe and manage meanings, but it is 
insufficient to describe meanings com- 
pletely with the discrete and branching 
rules, because meanings have continuous 
properties. 
In the stratificational grammar and 
the generative semantics,semantic compo- 
nents seem to be more important than in 
the standard theory, because semantic 
rules are used basically. But they have 
the similar defects as the standard 
theory, because these rules are discrete 
and branching ones. ' 
Lakoff and McCawley's generative 
semantics model are not enough to des- 
cribe meanings, because their semantic 
rules are treated with the same form of 
syntax. 
In general, their notations adopt 
classifications based on the categories 
or binary classifications. So it has the 
following weak points:lack of expressive 
power of similarity and distance, and 
ordering of property value of concepts. 
We have proposed to adopt a high 
dimensional semantic map (i.e. a topolo- 
gieal information space complementing 
for these defects. 
It is said that when one wants to 
express one's intention, not a sentence 
but a concept is formed in his brain at 
first, then it is translated into a sen- 
tential form, feeding back the differ- 
ence between the concept and the sen- 
tence translated, and at last it is ex- 
pressed as a speech or a writing. 
Therefore we have proposed the model 
that the concept which we want to utter 
is formed at first as a specified area 
in the semantic information space, next 
it is transformed into a phrase-marker 
(P-marker) in the deep structure, and at 
last it is transformed in the sentential 
form in the surface structure being fed- 
back in each stage. 
2. OUTLINE OF 
THE LINGUISTIC ACTIVITY MODEL 
There are two ways in describing mean- 
ings: one is connotational semantics; in 
this case meanings of sentences in a 
language A are described by sentences in 
a language B, for example, English is 
translated into Japanese. 
The other is the operational semantics; 
in programming language, input data are 
computed and the results are output. 
So the meanings of a programming lan- 
guage is expressed as an operator that 
prescribe input-output relation. 
In our model these two semantics are 
considered as follows. As for the con- 
notational semantics, we take the topol- 
ogical information space as the language 
that describes meanings. 
In this model we express the meanings 
of a natural language in the following 
way: we locate the concepts in the se- 
mantic map, i.e. the topological infor- 
mation space as follows; if a concept A 
implies a concept B, we assign them as 
the area B contains the area A, and if 
a similarity (or distance) between a con- 
cept A and B is greater than a similari- 
ty (or distance) between a concept A and 
93 
C, we locate the area B nearer ( or far- 
ther ) the area A than C. 
As for the operational semantics, 
there are two kinds of operators. One is 
responces or reactions against the re- 
ceived message, the other is updatings 
or rearrangements of the memory. The for- 
mer is carried out by responding with a 
speech, writing, or actions. The latter 
is carried out by updating the database. 
The model has four description levels: 
(i) Expression level ( utterances, 
writings, and actions ) 
(2) Surface level ( sentences ) 
(3) Deep level ( phrase-markers ) 
(4) Semantic level ( information space ). 
In the expression level, one's inten- 
tion is expressed through one's organs. 
The surface level is the level of the 
language which we use in the daily life, 
and the set of sentences compose ele- 
ments in this level. 
In the deep level, each element is a 
generator of a surface description, and 
is in the form of P-marker, i.e. so 
called a derivation tree. 
In the semantic level, the concept 
is expressed as an area or a file of 
areas in the information space, where 
the information space is something like 
a semantic map, and is made up of the 
neighbourhood system or the metric space, 
and has topological properties, which 
can express distances, similarities and 
inclusions so on. 
In the functional point of view, the 
information space is composed of a mean- 
ing subspace and an estimating subspace, 
where the meaning subspace expresses 
topological relations among concepts, 
the estimating subspace expresses vari- 
ous estimated yalues in the process of 
management. The estimating subspace has 
an activity axis, an occurrence proba- 
bility axis and so on. 
There are three levels of processing 
on them as follows: 
(I) Expression processing 
(expression level ÷~surface level ~ ), 
(2) Syntactic processing 
( surface level ÷~ deep level ~ ), 
(3) Semantic processing 
( deep level ÷÷ semantic level ~ ). 
The expression processing is to 
utter, write or act, and in the opposite 
direction to recognize the received 
signs. The syntactic processing is map- 
pings from the deep level to the surface 
level and vice versa, in other words, 
mappings from P-markers to the sentences 
and the mappings among P-markers. 
A syntactic structure consists of two 
level elements and the algebraic struc- 
tures on them. 
The semantic processing is mappings 
from the semantic level to the deep 
level and vice versa, and mappings among 
the semantic level, in other words map- 
pings from domains in the information 
space to P-markers and vice versa, and 
the mappings among domains in the infor- 
mation space. A semantic structure con- 
sists of two level elements and the 
algebraic structures on them. 
The correspondence between the seman- 
tic structure and the syntactic struc- 
ture is as follows. There are two map- 
pings which connect two structures, one 
is a meaning affix mapping ~ that maps 
an area in the space to a word in the 
syntactic grammar, the other is an oper- 
ator mapping ~ that maps an operator on 
the space to a production rule in the 
syntactic grammar. 
The algebra on the syntactic and the 
semantic structure are defined. 
3. TOPOLOGICAL INFORMATION SPACE 
In the syntax-generative grammar, it 
is of no use to introduce relations 
among sentences, because there are no 
semantic relations among sentences which 
are generated by the grammar. But in the 
semantic-generative grammar, not only 
elements but also a topology over them 
should be generated. Because interpret- 
ing meanings of sentences, distances, 
similarities and inclusions among con- 
cepts which are expressed by points or 
areas, are very important. 
In an algebraic point of view, a to- 
pological space is defined by an ordered 
pair (X,T), where X is a support (set of 
points), and T is a topology on X. 
The whole topological space is gener- 
ated as a dictionary, or a thesaurus, or 
the universe of knowledge. In conversa- 
tion with someone or a description of 
one's concept, a particular area is 
pointed out to communicate one's inten- 
tion with others. Then we need two kinds 
of production rules: one is the universe 
generative rules which generate the 
whole topological space, i.e. elements 
set and a topology on them, and the other 
is the utterance generative rules which 
generate distinct conceptual areas. 
In terms of sorts of topology, we 
investigated topology-types which are 
required to express properties of mean- 
ings of about one thousand Chinese 
characters for ordinary use. Following 
types of topology are listed up; 
I) Linear number axis. In this type, a 
property value is expressed in a numeri- 
cal value such as an integer or a real 
number, e.g. a weight axis: 150 Ibs. 
2) Cyclic number axis. Property values 
are expressed in numerical values in a 
given closed interval, and both end 
points are identified, i.e. a number 
sequence is defined cyclically, e.g. a 
time axis; one o'clock, two o'clock, .. 
twelve o'clock, one o'clock, .. . 
3) Ordinal axis. Property values can not 
be expressed in numerical expression, 
--94- • 
but property values are lined up in 
order along its strength and weakness, 
e.g. a sensation of warmth axis; cold 
cool, comfortable, warm, hot, heated. 
4) Cyclic ordinal axis. Property values 
are lined up in order cyclically, for 
example, a season axis; spring, summer, 
autumn, winter, spring,.. . 
5) More general topology. Property 
values can not be expressed in type i)- 
4), and are given weaker topology as 
near-and-far relations or similarity 
relations among elements, for example, 
chromaticity diagram on color; yellow, 
red, blue, green, etc. 
6) Simple set. There is no topology on 
elements, so only a medley of elements 
constitutes a set, e.g. a set of terms 
which expresses aspects or units. 
We'll formalize the model that can 
cover all sorts of topology listed above. 
A topological information space 
generative grammar (TISG) consists of 
three levels of production rules which 
are restricted in the rewriting order. 
Def.l Space Constitution Grammar : Gi 
G1 = < VNi' VTi' Pl' S1 > (i) 
where Vi= VNiU VTi , VNi~ VTi = ~ (2) 
D = { • , # , I } (3) 
LA(v,D)={(a~)*~I a,SgV, ~ D } (4) 
V\] is a finite set ( vocabulary ), VN\] 
arid V~ 1 are called a nonterminal vocEDu- 
lary, ~ terminal vocabulary respectively. 
S. is a subset of VNi (initial vocabu- 
lary), and Pi is a T1nite set of produc- 
tion rules ( rewriting rules ) of the 
form: P1 : A ÷ ~ (5) 
where A eVNi ' ~e LA(Vi,D). 
D is a space constitutor set, and con- 
sists of direct product: • , connected 
sum: # , and direct sum: I • 
Def.2 Space Property Grammar : G2 
~2 = < VN2 ' VT2 ' P2 ' $2 > (6) 
where V 2 = VN2U VT2 , VN2nVT2 = 
property production rule P2 is a finite 
set of production rules of the form: 
P2 : A ÷ ~ , where Ae VN2 , (7) 
g { a, ~ , ca, aa -l, aba-lb -I, 
abe-1 }, a,b eV~ . (8) 
A grammar G2 generates properties of sub- 
spaces. Sorts of properties are as fol- 
iOWS: 
(i) Line axis ( a ) 
(ii) Cyclic axis ( a ) 
(J i i) Sphere axis (Sphere) ( aa-1 ) 
(iv) Projective axis ( aa ) 
(Projective plane) 
(v) Torus axis (Torus) (aba-lb "1) 
(vi) Boundary axis ( abe -1 ) 
(Surface with boundary) 
where type (id)-(vi) are of polyhedral 
forms of manifold. 
Def.3 Topology Prescription Grammar:G3 
G3 = < VN3 ' VT3 ' P3 ' S3 > (9) 
where V 3 = VN3UVT3 , VN3~VT3 = 
P3 consists of two parts, one is P^_ 
which generates the universe, the ~her 
is P~A which generates a specified area 
to p~int out a concept. 
P3T : A ÷ ~ (i0) 
e{ topological spaces of each types } 
P3A : A * ~ (ii) 
6 ( areas of topological spaces } 
G3 generates the topology of each sub- 
space, then following types of topolo- 
gies are adopted adaptively: To, Ti, T2, 
R, T3, CR, T, N, T4, T~, T , Compact, 
Metric, Uniform, SeparableVand so on. 
Def.4 The Topological Information 
Space Generative Grammar : G I 
G I = < G1, G2, G3>, (12) 
where G1, G2 and G3 are sub-grammars 
defined above. And the relations among 
three levels are as follows: 
S 1 = S, S 2 = VTi, S 3 = VT2 
Def.5 The Topological Information 
Space : I I = I(Gi) (13) 
The topological information space 
generated by G T is written as eq.(13) 
Def.6 The Syntax Generative Grammar:'G 
G s = < V N , V T , R , S > (14) s 
where S is an initial vocabulary, and 
subset of V., R is a set of phrase 
structure r~writing rules. 
The other side V is divided into two: 
V=V U V a, where V is significant voca- 
bulary, aYidVG is g~ammatical vocabulary. 
An intersectlon of V with V~ is not 
always null. P 
A generation tree, i.e. derivation 
tree of a sentence is called a P.marker 
(phrase marker), and the set of all P- 
markers generated by G is written as 
P=P(G). The terminal string extracted 
from the treetop of the P-marker is 
called a sentence, and the set of all 
sentences generated by G, is written as 
L(G), and is called the language gene- 
rated from the grammar G. 
The P-marker sets and the set of all 
sub-P-markers gotten by decomposing P 
are called ~niverse of P-markers, and 
written as P. 
Def.7 The Semantic Algebraic System:~i 
The semantic algebraic systen~ ~I is defined as 
~I = < I, I I, E I> (15) 
where I is the information space defined 
by GT, and IT, E T are the interior and 
extePior operators on I respectively. 
Generally speaking interior operators 
are functlons I I (n~2), and exterior 
operators are functions I×2÷I, where 
is an exterior operator. 
Def.8 The Syntactic Algebraic S~tem:~s 
The syntactic algebraic system is defined as 
~s = < P' Is' Es > (16) 
where ~ is a set of P-markers generated 
by G, and I and E are the interior and 
exterior op~ratorsSon ~. 
--95-- 
Def.9 The meaning affix mapping : 
f , (17) ~' : D ÷ Vp 
where D is the set of all areas in the 
space I. @' assigns an area ( a concept 
in semantic map ) to a token or string 
of tokens ( words ) in the syntactic 
level. We interpretea sentence through 
used-rewriting rules, so in order to 
avoid ambiguity we extend V ¢ to P, i.e. 
: D ÷ P P (18) 
Def.lO The operator mapping : 
: O I ~ O s (19) 
where 01 = Pi U ~u IiU E I (20) 
O s = RUVGU IsU E s (21) 
assigns the semantic operator in 
the semantic space to the syntactic 
operator in the syntax. 
4. THE SEMANTIC ALGEBRAIC SYSTEM 
IN ENGLISH 
We will show the semantic algebraic 
system in English briefly. Fig.l shows 
the outline of G I. 
\[\]\] The organization of the support 
in E.n.gl.ish .--% o.rganization of 
the .meaning subs.p.ac.e. --- 
The mean'ing subspace is used to ex- 
press the topology among concepts. It 
consists of three subspaces: intellec- 
tual, feeling, and ordering subspaces. 
The intellectual subspace is a field 
to represent, state and judge. 
The feeling subspace is a field to ex- 
press out actions, emotions and senses. 
The ordering subspace is a field to 
express the ordering of events or the 
informations. ~ 
(I) The intellectual s.u.bspace 
In Engl'ish there are four typical 
intellectual subspaces: {i} nouns or 
noun phrases, {2} adjectives or adjec~ve 
phrases, {3} adverbs, {4} verbs. 
These four subspaces are written as IN, 
IA, ID, and I v respectively. 
They constitute the support of the 
system, but some of adverbs correspond 
to the operators, for example, "very". 
These four subspaces are composed to the 
higher level by nesting each other. 
(2) The feeling subspace 
The feeling subspace is divided into 
three subspaces: action driving, emo- 
tional and sense subspaces. 
(i) The action driving subspace 
This subspace expresses forms of 
actions and action-driving potentials. 
The forms of actions are imperative, 
prohibition, request, hope, desire, 
petition, question, doubt, obligation, 
permission, causative, voluntary and 
intention so on. 
This subspace is divided into the 
reply and the action subspaces, in the 
functional point of view. The reply sub- 
space expresses " answer by language ", 
and the action subpace expresses the 
actions except utterance, e.g. eat. 
The words are mapped from the areas 
in the space by the meaning affix map- 
ping @ and the operator mapping ~ as 
follows: if one receives words which 
arouse actions, one finds form of actions 
in this subspace by ~-~ and finds 
driving potentials by ~-~. 
The meaning affix mapping ~ is defined 
on the following types of words: verbs 
which arouse actions (for example, ask, 
order etc.), imperative and interroga- 
tive forms of verbs, and auxiliary verbs 
of prohibition and wish so on. 
The meaning affix mapping designates 
only " forms of actions aroused ", and 
" the content of actions " is designated 
by the area in I . For example, impera- 
tive sentence " VRead " is managed as 
follows. The form of action is desig- 
nated " ordinary imperative ", and a 
action " to read " is designated as a 
corresponding area in I subspace. 
• V The operator mapping ~ has following 
functions, As for verbs listed above, 
the aroused degree of the action is 
designated. And if there is an adverb 
that modifies a verb, and its adverb 
expresses the degree, $ is designated 
by the degree expressed by the adverb, 
for example, a word " abs0\]ute\]y " 
designates " extreme " degree. 
(ii) The emotional subspace 
The emotional subspace is used to ex- 
press emotions of a speaker and a hearer, 
and to modify a criterion level of decision 
of taking action, and this subspace does 
not arouse immediate actions. 
i<information space> ÷ <meaming ss>.<estimating ss> 
Pl <meaning subspace> ÷ <intellectual ss>.<feeling ss>.<ordering ss> 
<estimating subspace> ÷ <reliability ax>.<activity ax>.<occurrence probabilLty ax>.< . .>. .. 
<i~teIiectu~ subspace> + <noun ss>|<adjective ss> l<adverb ss>I<verb ss> 
<feeling subspace> ÷ <action d~iving ss>.<emotio~l ss>.<sense ss> 
<action driving subspace> + <reply ss>.<action ss> 
<emotional subspace> ÷ <state of emotions ss>.<degree of emotions ss> 
<ordering subspace> ÷ <events ordering ss>.<cau~ality ordering ss> 
<events ordering subspace> ÷ <seasons> <months> l <times> I< ...71... 
p2:<reliability axis> + I . . 
<seasons> ÷ S, .. '. i where ss means "subspace", and ax means "axis" ) 
I ÷ × , ( O<x<l ) I ÷ \[0,\]\] , ... P3A: $ ÷ 
P3T: 5 + <spring> <samm~z > <autumn> <wimZ~> <s p~ing > l <~m~ > l <a~tamn> l <wi~ > 
Fig.\] A part of the rewriting ru\]es Jn the information space generative grammar 
96- 
This subspace is divided into two: 
the state of emotions and the degree of 
emotion's subspaces. 
Usually the area is computed both on 
the subject and the indirect object. 
Sorts of emotions are joy, anger, pity, 
fear, love, hatred and sadness etc. 
is computed by adjectives, verbs 
and nouns that express emotions, and 
interjections. And ~ is determined by 
the degree of words listed above, ad- 
verbs, and emphasizing styles. 
(~i) The sense subspace 
Kinds of senses are the senes of 
sight, hearing, smell, taste, touch, and 
internal organs. These senses are awoke 
by direct excitations and by particular 
words in conversation. Incase of words, 
there are two types as follows: 
{I} The words which designate a certain 
sense area in the space, for example, 
dazzling, hungry. These words are mapped 
by @-i into the sense subspace. 
{2} The words which activate the poten- 
tial of a certain area in the sense esti- 
mating subspace. For example, a word 
" rain " arouses the sense of cold and 
chilly in Japan. The sense potential is 
raised by these words, and the degree is 
computed by ~-i 
The stimuli from the five organs of 
sense are gained by actual experiences, 
but the stimuli by words request to 
image the same experience as a speaker. 
(3) The o.rd.ering subspace 
This subspace expresses ordering 
series of domains in time or in logic. 
Usually the ordering axis is a real time 
axis of (-~,~), and is divided into 
three areas: past, present, and future. 
But present is the relative value, and 
has meaning of only a time base. 
(i) Ordering the events 
This designates the occurrence time 
of the contents described in the inte- 
llectual and feeling subspaces. 
There are two kinds of time assign- 
ment, one is simple: past, present, or 
future. The other is composite: perfect, 
simultaneous, or delay. The composite 
assignment designates ordering in time 
or in logic among clauses or events. 
(ii) Ordering the causality 
As for logic, input clauses are 
classified into two groups: one is a 
group of assumption or causes, the other 
is a group of conclusion or effects. And 
a suitable causality type is assigned to 
each clause. 
\[2\] OPERATORS IN ENGLISH 
(i) The intelle'ctual subspace 
(i) The exterior operators The ex- 
terior operators modify or restrict the 
conceptual area in a specified axis, and 
there are two types as follows: the 
value-shift type and the quantifier type. 
For example, let u ~Vpf , v ~VG¢ , and d: 
an area in the space, w:exterior operator 
on the space, if ~-1(u)=d and ~-1(v)=~, 
then the area corresponding to a phrase 
" uv " is formed by " md " in the space. 
There are four types in the exterior 
operators as follows: 
(a) Restricting to limit, e.g. very 
(b) Settlement of range, 
(i) Extension of range, e.g. all 
(2) Reduction of range, e.g. small 
(c) Inversion of range, e.g. unpresant 
(d) Shift or limit the value of reliability in 
the estimating subspace, e.g. infer. 
Sorts of limiting are conclusion, 
presumption, hearsay, degree, possibi- 
lity, question, negation & emphasis. 
(ii) The interior operators There 
are four levels in the interior operators 
as follows: words, phrases, clauses and 
sentences. Let a,c ~Vp%, beVG%, ¢-1(a)=a, 
~-1(c)=y, ~-1(b)=B, a,T ~ D, B ~{binary 
operators over the space}. Then 
6=~-l(abc)=~'l(a).~-l(b).~-l(c)=~T. 
{1} The interior operators common 
to each level (space) 
(operators) (syntaxi synthesis of areas 
+ enumeration in, by+ 
Sum: parallel logical sum 
ex. red and white tulips, 
Selection: selection exclusive or 
ex, either You or I, 
Product: series logical product 
ex. beautiful and healthy. 
{2} The interior operators in words 
Compound words in syntax are corres- 
ponding to these operators. Usually the 
operator is designated by a rewriting 
rule in the syntax, and V G does not 
appear in the compound words. This oper- 
ator limits the area expressed by the 
main word in the compound word by the 
area expressed by the subordinated word. 
For example, the conceptual area of " 
letter paper " is the restricted area of 
" paper " for a letter. 
{3} The interior operators in phrases 
These operators resemble to the oper- 
ators in the words. But in this level, 
not only rewriting rules but, also V~ such 
as " the monkey in a cage designates 
an operator too. In case of noun phrases 
there are two kernels:V and one VG, and 
these are mapped to oneParea. In case of 
adjective phrases or adverb phrases such 
as " in a cage ", there are one kernel 
V and one V~, so the lack of V_ causes F 
t~at these phrases are mapped to unary 
operators in the space. 
A phrase has a ease, and each phrase 
is attached a pair of the concept and 
its case. 
{4} The interior operators in clauses 
The process of composing clauses 
from words and phrases is corresponding 
to the unification of some conceptual 
areas as follows. There are three main 
--97- 
concepts: subject, object and action. 
And there are three types of unifica- 
tions as follows; 
*Mutual dependency: composition of tran- 
sitive verb with direct object, and com- 
position of direct object with indirect 
object. 
*Uni-directional dependency: composition 
of the subject and verb ( phrase ). 
*Mutual independency: composition of two 
clauses by a coordinate conjunction. 
{5} The interior operators in sentences 
There are two methods of composition 
by a coordinate junction or nesting. 
(2) The feeling subspace 
This information does not always 
appear, but if it appears it designates 
the state of feeling between the sender 
and the receiver. 
(3) The ordering subspace 
(i) The exterior operators 
A shift or limitation of the value 
in the ordering axis is designated by 
the inflection of verbs and tense. 
(~) The interior operators 
Conjunctions designate interior 
operators. The operators are classified 
into subjunctive, indicative and impera- 
tive groups in the modal point of view, 
Also operators are divided into copula- 
tive, alternative, adversative, disjunc- 
tive and illative conjunctive groups in 
the conjunctive point of view. 
5. INFORMATION PROCESSING MODEL 
ON TIIE INFORMATION SPACE MODEL 
Our communication is carried out bi- 
directionary. On sending we compose a 
concept which we want to communicate oth- 
ers, next point out a corresponding area 
in the topological information space, map 
an area or areas to tokens in the syntax 
by the meaning affix mapping ~ or oper- 
ator mapping ~, form the P-marker in the 
deep level, get the sentences, and at 
last speak or write sentences. 
Descriptions of entities and relation- 
ships are managed as follows: 
(i) when we quote one entity, or when we 
express one entity's properties, a par- 
ticular area in the information space is 
pointed out. 
(2) when we express two or more entities 
and relationships among them, a direct 
product of two or more areas of entitie~ 
and an area of the relationship is 
pointed out. Both entity-subspace and 
a relationship-subspace are topological 
information spaces. Then the composed 
space become a topological space too. 
On receiving we listen or read the 
sentences, analyze them lexically, parse 
them, get the P-marker in the surface 
level, transform it to the deep P-marker, 
map it to the derivation tree of the 
topological information space generative 
grammar, find the corresponding areas, 
compose the areas and relationship among 
them, interprete the message, update the 
memory, and respond the required actions. 
These two processes are inverse 
relation, so we here describe in detail 
these processes in the latter case. 
We depict processing steps in Fig.2. 
\[\]\] Lexical analysis and Parsing 
In this step syntactic processing is 
carried out. There are four recognition 
levels of syntax as follows: 
(i) Rec.og.nizing phonemes & characters 
The received phonemes or' ch'aracters 
are checked whether they belong to per- 
missible phonemes or characters. 
(2) Lexical analysis Input strings 
are divided by the word delimiters, and 
recognized as words. Words are checked 
whether they are contained in the token- 
dictionary or not. 
(3) Parsing & Deriving P-markers 
Delimiters of sentences are searched and 
each sentence is parsed. If ambiguity 
occurs in parsing, all feasible P-markers 
are listed up. 
Input 
~I Lexicai Analysis~ O~_erational semantics I 
I Parsing 1 ~ -~ ~ -~ •'~-- -~ : ~1 
'\]' A-1 % ~< S ntax .... > ( P-markers ) % ~yn~ax l~Ctlonary 
* , % ~, ! 
>I Range check I 
I Concept Prescriptionl -- i; \[ 
! Integration check 
( Conceptual areas )--~ Feeling, Ordering --~(F e) 
  ' ~ Interpretation 
--< Knowledge Dictionary J 
i Output Utterance ::: 
Description 
(P-mar%.ers) 
Sentence I 
Generation 
~(File) 
I Updating 
Induction 
Deduction 
Evaluation 
Fig.2 The Information Processing Model 
--98-- 
(4) Reduction of P-markers to generator P-mar- 
kers The parsed P-marker in the sur- 
face level is transformed into a genera- 
tive P-marker in the deep level. 
If recognition is failed in each step, 
the degree of potential for question is 
increased. And if the degree of poten- 
tial for question exceeds the threshold, 
a question to resolve the ambiguity is 
formed, and is utterd. 
\[2\] Range check 
The value of property of the input 
data is checked whether it is out of 
range of permissible interval or not, 
i.e. range check of property value is 
carried out. Because in the information 
space, the domain of property value is 
defined by the topological information 
space generative grammar. This process 
is divided into two sub-processes: 
(i) the validity judgement of the con- 
ceptual area that is mapped from the 
words or phrases in the input sentences, 
i.e. the check for grammatical sentence~ 
(~) meta-description of a virtual world, 
i.e. the definition of words or assumtion 
of property values etc. "' A ' is defined 
to be ' B '" is interpreted that the 
range of @(B) is adjusted to @(A) by 
modifying the characteristic functions 
of A for the virtual view. 
\[3\] Intellectual interpretation 
The object is definitely prescribed 
to be in such a situation, and is managed 
as follows. 
(i) The intellectual prescription 
In this step the focussed conceptual 
area is pointed out to interprete the 
communicated intention, and the area is 
mapped from the words, phrases, clauses 
or sentences. This means the specializa- 
tion of universal predicates. An element 
of direct product of IA, IN, Iv, .. etc. 
are pointed out. 
(2) Correlation 
The corr'elation between subject and 
object in the sentence is clarified, and 
the relationship among entities are 
investigated, and the cases of each word 
is made clear; there are following cases 
Agentive, Factitive, Objective, Dative, 
State, Action arousing, Emotional, Feel- 
ing, Time, Cause, Result, Degree, Loca- 
tive and Goal cases so on. As for cases 
we don't make verbs special treatment as 
the dependency model, so verbs are as- 
signed cases, too. 
The correlated tuples of conceptual 
areas are filed with cases. 
\[4\] Integration check 
In bussiness database systems, the 
conceptual schema for the enterprise is 
analyzed at set-up-time, and the most 
suitable schema is selected, and is not 
time-variant. And the correspondence 
between the external schema and the con- 
ceptual schema is preset, so the input 
data is integrated to the conceptual 
schema automatically. 
On the contrary, in the academic use 
of the database or in our thinking, the 
universe of knowledge is not fixed, and 
is growing according to the input data 
from the circumstances. 
So we introduce View (Aspect) for 
integrating the same object in different 
records. A group of experimental data, a 
group of sentences in a book, etc., have 
the same view. This view is different 
from the view in the relational model. 
A group of fragmentary data with the 
same view is checked whether they can 
be integrated to one object if they ex- 
press the same object. A group of frag- 
mentary data, which has the view that 
contains or is contained by the input 
data view, is checked whether they can 
be integrated to one object or not. 
\[5\] Feeling and Ordering interpretation 
(I) The feeling interpretation 
In the action arousing subspace, 
whether action is required or not is 
examined, where the action means res- 
ponses by hands, speech or writing so o~ 
There are emotional and feeling sub- 
spaces. As for the emotional-state, the 
conditions of the sender and the recei- 
ver are judges by particular words con- 
cerning emotions. As for the emotional 
state, the same judgement is executed. 
(2) Ordering information interpretation 
For described events, before-and- 
after relations on time, and cause-and- 
effect relations are judged. 
These informations are used in deduction 
and induction of theorems from axioms, 
and in management of subjunctive mode. 
E6\] Evaluation of the received contents 
After the grammatical valuation of 
input sentences and semantic interpreta- 
tion in the space, following managements 
are carried out: evaluation of communi- 
cated contents, and judgement of logical 
validity. These managements are executed 
by inferences using deductions, induc- 
tions and arithmetic operations on areas 
in the space. By these.processing, con- 
firming the validity on the communicated 
contents, and drawing new conclusions 
from inputs and knowledge, are executed. 
(I) Arithmetic operations 
Arithmetic operations are used in 
deduction, induction and other manage- 
m~nts. There are following property-types: 
D: a power set of areas, 
H: a power set of hyperplanes, 
V: a power set of values P 
E: a power set of estimating value. 
And following kinds of operations exist. 
D × H ×V × *D × H × V × E 
(2) Evaluation of Declaration 
The input informations are checked 
whether they contradict with the data 
that are already input and confirmed, 
(3) Deduction and Induction 
--99-- 
(i) Deduction 
The question is rewritted to the ques- 
tions on the space. Using the algebraic 
properties, the equation is transformed 
and solved. In case that the algorithm 
is cataloged, a suitable procedure is 
searched and triggered. Also suitable 
procedures are triggered if the estimat- 
ing value exceeds the threshold in each 
process. 
In case that the algorithm is not 
cataloged, or the input is not a ques- 
tion, deductions from the input is exe- 
cuted. We communicate each other with 
some view, and the received information 
is interpreted in that view, i.e. if the 
received data contradicts with the same 
view data, the input data must be checked 
whether it is right or not. And if a 
contradiction is not deduced, the valua- 
ble data deduced from the input are 
arranged and stored. In these processes, 
the deduction is executed by syllogisms 
or resolution. 
(2) Induction 
The induction is executed as follows: 
at first some special predicates in the 
same view are selected, common variables 
are searched, universal special predi- 
cates are reconstructured by choosing 
the domain appropreately from the exis- 
tential special predicates. These exis- 
tential predicates are not always valid, 
but if the contradiction is not found by 
checking the domain in the information 
space feeding back the result, the 
Predicates ~re regarded to be correct 
probably, and are stored as a hypothesis, 
and output. Where induction is exe- 
cuted on the data which have the same 
view, and the predicates are selected 
from the predicates which have the same 
properties in the same view data. 
This operation is useful in creative 
thinking, for example, from the data 
gathered, common properties are extracted, 
and the induction is executed to the 
predicates which contain the common prop- 
erties. As a result, from the experimen- 
tal data or the observational field data, 
some valuable hypotheses are generated. 
(4) Updating the Memory or Database 
The received message are parsed and 
mapped to the semantic level, interpreted 
and deduced. As a result new facts or new 
informations are clarified. These data 
are stored in the database. There are 
two ways of updatings: one is a permanent 
amendment: if the data is a principle 
one, modifications of the information 
space are needed, so the information 
space generative grammar is reconstructed, 
and the corresponding amendments of files 
are carried out. The other is a temporary 
modification in an interim file. 
C7\] Composition of Intention & Utterance 
If the question is ambiguous or the 
answer is not deducible from the database 
and inputs, the action-driving potential 
to fill up the information insufficiency 
is elevated, then the question to resolve 
the ambiguities is composed and utterd. 
If the question is correct and the answer 
is deducible from the dictionary and 
inputs, the answer file in the semantic 
level is translated into the P-marker, 
and is utterd. If the input is not an 
interrogation, then the database is up- 
dated, and no answer or agreeable res- 
ponces are made, In every case, the 
intention is described in file form in 
the semantic level, i.e. tuples of con- 
ceptual areas with cases. The file is 
recomposed to the derivation tree in the 
syntactic level by 0 and $, transformed 
to the surface description, and uttered. 
6. CONCLUSION 
A generative semantics model based on 
the topological space generative grammar 
was proposed. This model has more de- 
scriptive power than other models because 
both implications and similarities can 
be generated in the basic level. 
The aim of this model is to describe and 
manage the semantics algebraically, and 
for that purpose English was arranged 
based on the model. 
The question-answering process in a 
natural language was clarified. In this 
model not only a concept but also esti- 
mation of the information is considered. 
Then the motivation for next actions can 
be interpreted. Based on the model, we 
are now implementing a research-DBMS. 
Using it we can built up and test hypo- 
theses by KJ-methods and so on. 

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2.Fillmore,J.C."The Case for Case", In Univer- 
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3. Jackendoff,R.S." Semantic Interpretation in 
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4.CODASYL Dev. Committee, "An Information Algebr~ 
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5.Uchinami,S.,Tezuka,Y. and Kasahara,Y." A Model 
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