Janos J. Sarbo
Institute for Computing and Information Sciences Radboud University, Nijmegen, The Netherlands
Common sense, naive logic, knowledge representation, signs, cognitive activity, Peirce, semiotics.
In order to endow computers with common sense with respect to specific domains we need to have a repre-
sentation of the world and make commitments about what knowledge is and how it is obtained. This paper is
an attempt to introduce such a representation and underlying ‘naive’ logic on the basis of an analysis of the
properties of cognitive activity. This paper is of interest to those engaged in the development of user interfaces
and ontologies, as well as to those interested in the semiotic aspects of problem specification and requirement
engineering. The focus of this paper is on the theory, applications are briefly mentioned due to lack of space.
According to a seminal paper by McCarthy and Hayes
(McCarthy and Hayes, 1969) “a computer program
capable of acting intelligently in the world must have
a general representation of the world in terms of
which its inputs are interpreted. Designing such a pro-
gram requires commitments about what knowledge is
and how it is obtained. The assumption taken by this
paper is that the world consists of phenomena that
are interactions and that knowledge arises from the
observation of such phenomena by means of signs.
An interaction may occur between entities, also called
qualities, that are in principle independent. An obser-
vation is a re-presentation of an interaction between
an external quality (input stimulus) and the observer,
in which both entities are interpreted as signs.
This representation by the observer, as an in-
terpreting system, has a ‘goal’, which is the
(re)cognition of the input stimulus as meaningful. For
example, the interaction between a piece of wood
and sufficient energy (qualities), appearing as burn-
ing (phenomenon), can be signified by the visual sign
of the arising smoke and fire. This sign, as a quality,
may interact with the eyes, and that event, as a sign,
may be recognized by the brain/mind as a representa-
tion of the burning phenomenon.
The observation of complex phenomena may re-
quire the representation of a series of interaction
events. As events governed by a goal are a process,
and, following our assumption, qualities and events
are interpreted as signs, we conclude that observations
and knowledge must be a process of sign interactions.
Human observation is a product of cognitive ac-
tivity by the brain/mind (Kalat, 2004), (Gazzaniga,
1998). This paper is an attempt to show that on the ba-
sis of an analysis of the properties of cognitive activ-
ity a representation for knowledge can be introduced.
Such a representation and the underlying logical in-
terpretation is what I shall call common sense and
‘naive’ logic. Other important elements of common
sense, such as intelligence and learning are beyond
the scope of this work.
According to Aristotle, the common sense (sen-
sus communis) is the hart where all information from
different senses are bound into an intelligible whole.
Following the common sensist, it is the sum of orig-
inal principles found in normal minds (Bergman,
2000). In the popular interpretation (Merriam-
Webster), it is a sound and prudent judgment based
on a simple perception of the situation or facts.
In this paper I take the popular view as my starting
point, skip the qualifications, “sound and prudent”,
and concentrate on the machinery implied: How do
we account for the relation between the simple per-
ception and the judgment? What is a simple percep-
J. Sarbo J. (2007).
In Proceedings of the Ninth International Conference on Enterprise Information Systems - ISAS, pages 395-400
DOI: 10.5220/0002405803950400
tion? How it is transformed into a judgment and what
is involved? To this end, I assume that common sense
is the brain’s potential for a process (re)cognizing the
‘naive’ or common sense meaning of the input stim-
ulus, as a sign. That potential and that type of pro-
cess must be common to all human interpreter, as it is
unlikely that cognitive activity as a process would be
different in each human and, yet, common concepts
can arise.
The duality involved in all phenomena is the key to
their interpretation as meaningful. For example, in
the observation of burning, the visual stimulus (first
quality) may trigger the eyes (second quality). This
interaction can be represented by the eyes, by means
of comparing the activation of the receptors triggered
by the current input, with the activation of those that
are not activated (the activation of the second type of
receptors may represent the background of the obser-
vation). The result of this comparison, a bio-electric
signal, is capable of re-presenting the input stimulus
(and, transitively so, the burning phenomenon) as a
change with respect to some earlier state. This bio-
electric signal may trigger the memory, and that in-
teraction may be recognized by the brain (possibly
through a sequence of re-presentation events) in a
meaningful reaction such as shouting Fire! or run-
ning away.
On the basis of this example, a model of cogni-
tive activity, as a process, can be defined as follows.
In an observation the external stimulus (effect) is ef-
fecting the brain appearing as a state. This interac-
tion is re-presented by the brain through sampling the
sensory input in a percept (a percept is a collection
of qualia; qualities as perceived are called a quale in
cognitive theory (Harnad, 1987)). The current per-
cept is compared with the previous one, and this en-
ables the brain to distinguish between two sorts of in-
put qualia (in short, input): one, which was there and
remained there, which can be called a ‘state’; and an-
other, which, though it was not there, is there now,
which can be called an ‘effect’.
Let me emphasize that any quality can be inter-
preted as a state or an effect. Also, that there may be
any number of qualities involved in an interaction, but
according to the theory of this paper those qualities
are always distinguished by cognitive activity in two
collections, state and effect, that are treated as single
2.1 The Processing Schema
The interaction between the state and effect qualia ap-
pears as an event. Each occurrence of such an event
triggers the memory, generating a response. This
memory response is a representation of the brain’s
‘knowledge’, as an interpreting system, about the
properties of the external stimulus. Such properties,
that are learned in earlier observations, are an expres-
sion of the brain’s potential for combining with a type
of input effect, depending on the brain’s actual state.
The total of those properties is called the context of
the observation, containing all possible combinatory
properties associated with the input event.
The primary task of cognitive processing is the in-
terpretation of the external stimulus, in the light of its
context. Following the theory of this paper, first pre-
sented in (Farkas and Sarbo, 2000), I assume that the
input of cognitive processing consists of two types of
qualia, appearing as a ‘primordial soup’ ([q
]). The
stages of the recognition process can be defined as fol-
lows (see also fig. 1). I use the convention that square
brackets indicate that an entity is not yet interpreted
as a sign, and no bracketing or the usual bracket sym-
bols, if some interpretation is already available.
(1) sorting: [q
], [q
the identification of the two types of qualia in the
‘primordial soup’;
(2) abstraction: q
, q
the separation of the collections of the two types
of qualia;
(3) complementation: (q
,C), (q
the linking of the qualia with their combinatory
properties ([C]);
(4) predication: (q
the establishment of a relation between the com-
pleted qualia.
(1) sorting
(3) complementation
(4) predication
(2) abstraction
q q
[q q ]
(q ,C) − (q ,C)
(q ,C)
(q ,C)
[q ][q ]
Figure 1: The processing schema of cognitive activity.
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2.2 Perception and Cognition
In this paper I assume that cognitive activity can be
modeled by means of two processes that are isomor-
phic instances of the above schema. In the first pro-
cess, perception, the ‘goal’ is the interpretation of a
relation between the input qualia and the memory re-
sponse representing the context (in this process the
relation between the qualia themselves is secondary).
The memory response arises due to the triggering in-
put qualia. Depending on the activation of the mem-
ory, there may be qualia in the memory response hav-
ing an intensity: (i) above or (ii) below threshold, re-
spectively referring to an interpretation of the input
which is in the brain’s focus, and which is only com-
plementary. A memory response of type (i) signifies
the recognition of the input in the sense of agreement:
the input is recognized or ‘known’ as such an entity.
A type (ii) response refers to input recognition in the
sense of possibility: the input is not recognized or ‘not
known’, indicating that the memory response repre-
sents only a secondary or even less important aspect
of the input qualia.
This way, the brain can distinguish between four
different interpretations of the input stimulus: as a fo-
cused state (A) and effect (B), and a complementary
state (¬A) and effect (¬B). Notice that ¬ is used as
an indication of the denial of a positive identification,
not as a Boolean operator. A definition of perception
as an instance of the processing schema is omitted due
to lack of space. A full account of such a model can
be found in (Sarbo et al., 2006).
In the second process, cognition, the final signs
generated by perception are interpreted as input
qualia. In this process, the ‘goal’ is establishing a re-
lation between the qualia themselves (now it is the re-
lation between the input qualia and the context that is
secondary). More specifically, the ‘goal’ of this pro-
cess is a relation between the input qualia that are in
the focus (A, B), in the light of the qualia that are com-
plementary (¬A, ¬B). In accordance with the current
‘goal’, the context ([C]) contains relational informa-
tion about the input qualia.
The input signs appear as a ‘primordial soup’. The
important representation moment is step 3, in which,
the input qualia are linked with background informa-
tion (context). In conformity with the condition set
for an interaction, there may be an interaction be-
tween A and ¬B, and between ¬A and B, but no in-
teraction may occur between A and ¬A, or B and ¬B.
This is because A and ¬A (but also B and ¬B) arise
due to the same input trigger, indicating that the two
signs are not independent. The (re)cognition process
is completed in step 4, in which, a relation between
A and B is established. Cognition as a process is de-
picted in fig. 2.
The three relations, which correspond to the three
types of interactions between the input qualia, can be
characterized by means of the meaning of their con-
stituents, as follows (an interaction, which is a rela-
tion, computationally, is denoted by a ‘–’ symbol):
A is ‘known’, but B is ‘not known’ (completion of
the input state);
B is ‘known’, but A is ‘not known’ (completion of
the input effect);
both A and B are ‘known’ (establishment of the
input relation).
If both A and B are ‘not known’, interpretation ter-
minates, meaning that cognition, as a process, does
not actually happen. Let me emphasize the mediation
function of the context signs, in step 3. Through the
common meaning shared by the two signs, ¬A and
¬B, the context implicitly determines the interpreta-
tion of the relation between A and B. That relation
can be called a ‘proposition’ which is a hypothesis
(A ‘is related to’ B or, briefly, A is B), but only if we
agree that the input qualia are impossible to correct
and that the relation ‘generated’ may represent only
one of their aspects. The processing schema can be
used recursively, by means of degenerately represent-
ing the final sign of the recognition process, as a qual-
ity. Recursive analysis can be necessary for the recog-
nition of complex phenomena.
(1) sorting
(3) complementation
(4) predication
(2) abstraction
(A,~B) (B,~A)
[A B]
A ‘is’ B
Figure 2: The signs generated by cognition as a process.
2.3 Logical Analysis
The interpretation of cognitive activity as the gener-
ation of three types of meaningful interactions illus-
trates the completeness of this process. This aspect
becomes even more clear from the logical analysis of
the processing schema. In this section I make an at-
tempt to elaborate such an analysis, on the basis of the
model of cognitive activity introduced in the previous
section (the focus will be on cognition as a process;
a similar analysis of perception can be made easily).
First I associate a logical expression to each interpre-
tation moment, on the basis of the common logical as-
pects exhibited by both of them. Second I introduce
operations transforming those expressions to formal
expressions generated by a Boolean logic. The hid-
den agenda of this section is a tacit introduction of
logical concepts, in the process model of cognition.
What makes this step especially important is that log-
ical concepts have a precise meaning.
An essential element of a logical interpretation of
cognitive activity as a process, is the abstraction of
a common meaning of the two types of input qualia,
which is the concept of a logical variable. In virtue
of the duality of the input, the logical interpretation
requires the introduction of two variables, which are
denoted by A and B. The collections of qualia that
are in the focus, and that are complementary are rep-
resented, respectively, by means of a logical variable
which is stated positively and negatively.
Perceived state and effect qualia that are in the fo-
cus are denoted, respectively, by A and B; those that
are complementary by ¬A and ¬B. Notice the use of
¬ as logical negation, which is relative difference
with respect to the collection of a type of qualia rep-
resented as a set. For example, the complementary
subsets of the A-type qualia are denoted by A and ¬A,
]=A+B, [q
]=AB: The expression of the pres-
ence of the input qualia which are in the fo-
cus, as a meaningful co-existence (A+B) and co-
occurrence (AB), respectively, in the sense of
possibility (‘+’) and agreement (‘’). As A and
B are commonly interpreted as logical variables,
the separate representation of any one of the two
types of input qualia contains a reference to both
variables. The difference between the two types
of relations between the input qualia is expressed
by means of the difference between the two oper-
ators, + and ’.
=A∗¬B, ¬AB: The logical abstraction of the in-
put qualia which are in the focus as constituents,
irrespective of the actually co-occurring other
type of qualia. It is this perspective that makes the
two signs synonymous (the “, in the definition of
is a representation of this equivalence).
=A∗¬B+¬AB: The expression of the input as
an abstract event, defined by the possible co-
existence or ‘compatibility’ of its abstract con-
stituents (which are now interpreted differently).
The context ([C]) is defined by the complementary
qualia represented as a co-existence (¬A+¬B)
and a co-occurrence relation (¬A∗¬B). The syn-
onymous representation of these signs is an ex-
pression of the secondary meaning of the context.
,C)=A+¬B, ¬A+B: The abstract constituents (q
completed with the context ([C]) or, alternatively,
the actual meaning of the input qualia as con-
stituents. For example, the meaning of ¬AB in
context, is defined by the qualia complementing
this abstract representation, which are: A and ¬B.
Alternatively, the actual meaning of A, as a con-
stituent, is defined by A itself and also by ¬B, the
complementary qualia, linking A with B implicitly
(as the relation between A and B is not yet real-
ized, the qualia denoted by B cannot contribute to
this interpretation of A). As the two expressions
of A, as an actual constituent, are related to each
other by the relation of co-existence, the logical
meaning of (q
,C) can be represented as A+¬B.
For the same reason, as in q
, the two representa-
tions of (q
,C) are interpreted as synonyms.
,C)=AB+¬A∗¬B: The abstract compatibility re-
lation in context, interpreting the input as a char-
acteristic property appearing as an event. That
event, which is a representation of the interaction
between A and B, is alternatively signified by the
interaction between ¬A and ¬B. The two signs
signify the interaction which is in the focus, re-
spectively, positively and negatively.
,C)=A is B: The expression of the logical
relation between the input qualia which are in the
focus, as a syllogistic proposition.
The above classification can be interpreted as a
formal logic defined by a single operation, relative
difference (‘\’), which has three types: relative differ-
ence with respect to the type of quality itself (sorting);
with respect to the other type of input qualia (abstrac-
tion); and, with respect to the input as a whole (com-
plementation). For example, [q
]=AB; q
(A+B)\(AB)=A∗¬B+¬AB; (q
: ¬(A∗¬B
+¬AB) =AB+¬A∗¬B. In the last example, rela-
tive difference with respect to the context ([C]) is in-
terpreted as relative difference with respect to the uni-
verse (‘1’), which explains the use of negation (‘¬’)
in the definition of (q
Notice in fig. 3 the presence of all Boolean re-
lations on two variables, reinforcing our conjecture
about the completeness of the cognitive process (‘0’
and ‘1’ can be defined as a representation of a ‘not-
valid’ and a ‘valid’ input, respectively). The results of
this analysis indicate that ‘naive’ logical signs hence
also the concepts of cognitive activity, as a process,
can be defined as an interaction (relation) between
neighboring signs. In fig. 3, such signs are connected
with a horizontal line. In a computational interpre-
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A is B
Figure 3: Logical interpretation of cognitive activity.
tation, the combinatory properties of the signs can
be represented by finite sets, and the interactions be-
tween signs by Boolean operations on sets. A full
account of ‘naive’ logic can be found in (Sarbo and
Farkas, 2001).
The processing schema can be used recursively,
in which case the final sign generated by one process
can be subject to sorting by a subsequent next process.
That (q
,C) is suited for this operation can be
justified by the logical analysis of the constituents of
predication. This reveals that (q
,C) and (q
,C) can be
interpreted, respectively, as a co-existence (‘+’), and
a co-occurrence relation (‘’) defined on same terms:
,C)= (A+¬B, ¬A+B)
,C)= (A+¬B)(¬A+B)
Notice that the above expression of (q
,C) is an
alternative form for its logical representation as
(AB)+(¬A∗¬B). In logic, recursion can be syntac-
tically represented by means of nesting (parenthesis).
2.4 Naive Versus Boolean Logic
In virtue of its relation with cognitive activity, ‘naive’
logic can be more powerful than Boolean logic. For
example, the synonymous interpretation of q
, as a
constituent state and event, enables the correspond-
ing logical expressions, A∗¬B and ¬AB, to be used
This dexterity of ‘naive’ logic is opposed to the ef-
ficiency of Boolean logic. By refraining from the syn-
onymous representation of ‘naive’ logical signs and
defining a suitable calculus, Boolean logic introduces
an interpretation that can be computationally more ef-
ficient. While ‘naive’ logic may only establish a re-
lation between two variables at a time, and the order
of logical computations is dictated by the processing
schema, Boolean logic may combine variables and
compute operations in any order. A final difference
between ‘naive’ and Boolean logic is due to the dif-
ferent interpretation of the logical values ‘true’ and
‘false’. In Boolean logic those values are defined as
constants. Not in ‘naive’ logic, in which ‘true’ and
‘false’ are interpreted as a representation of the status
of the sign recognition process, that can be ‘valid’ or
‘not valid’.
Can ‘naive’ logic be useful in practice? No, if we
only use the computer for doing calculations. Yes,
if such calculations have to be communicated with
the human user. Following the theory of this paper,
the formal computations by the computer can be pre-
sented as the signs of a recognition process of some
phenomenon. The conjecture of this research is that
such a presentation may enable the human user to
more directly conceptualize information generated by
the computer, as knowledge. A phenomenon, similar
to this one, is apparent motion perception, in which,
pictures presented in a certain way are experienced as
motion. Individual pictures representing static infor-
mation correspond to a percept; the experience of a
series of pictures as motion, to a meaningful interpre-
tation of subsequent percepts.
That the intuitive and the formal logical interpretation
of a sign are tightly related to each other must be clear
from our earlier explanation of the logical relations of
cognition. This dependency forms the basis for the
semiotic interpretation of the nine types of logical re-
lations and interpretation moments. For example, [q
] represents that the aspect of quality is present in
the appearance of the input as a ‘primordial soup’;
] represents that the aspect of simultaneity is a pri-
mary element of the input, as an appearance (event)
that happens now; q
represents that the compatibility
of the abstract meaning of the input qualia is expres-
sive of a rule-like relation. A complete overview of
the meaning aspects exhibited by the logical relations
as well as the interpretation moments of the process-
ing schema is given in fig. 4.
From this semiotic interpretation of the logical re-
lations, the analogy with Peirce’s nine signs, as mean-
ing aspects, follows trivially. For example, [q
], [q
and q
, this time interpreted as proto-signs,
sponds to the Peircean concept of a qualisign, sinsign,
and legisign, respectively (Sarbo, 2006). The classifi-
cation of Peirce’s nine signs is depicted in fig. 5.
In summary, the logical interpretation of the pro-
cessing schema opens the way to a Peircean semiotic
account of our model, revealing the existence of a re-
lation between the interpretation moments, and the
nine kinds of aspects or parameters of (full) meaning,
defined by Ch.S. Peirce (Peirce, 1931).
Proto-signs are in a process of becoming a sign.
likeness actual event
Figure 4: The semiotic interpretation of logical signs and
interpretation moments.
icon sinsign
Figure 5: Peirce’s nonadic classification of signs.
In past research we applied our process model of cog-
nitive activity for knowledge representation in differ-
ent domains, such as, natural language, ‘naive’ rea-
soning and mathematics (the conception of number).
We have shown that the processing schema is also
suited for a computational interpretation. The combi-
natory properties of signs can be represented by finite
sets, and interactions between signs by Boolean op-
erations on sets. The resulting formal model can be
proved to be linearly complex in the number of input
qualia (Sarbo and Farkas, 2002).
In virtue of its importance for cognitive activity,
‘naive’ logic can be practical for the development of
user interfaces and ontologies (Sarbo et al., 2006).
Most recently we applied the theory for requirement
engineering, in particular in the initial conceptual-
ization phase of problem specification (van Breemen
et al., 2007).
While the focus of past research has been on a jus-
tification of the theory, by means of testing it in differ-
ent domains of human knowledge, current research is
centered around the embedding of the process model
of cognitive activity in the Peircean theory of inter-
pretants (van Breemen and Sarbo, 2007).
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