ON THE LOGIC UNDERLYING COMMON SENSE

Janos J. Sarbo

Institute for Computing and Information Sciences Radboud University, Nijmegen, The Netherlands

Keywords:

Common sense, naive logic, knowledge representation, signs, cognitive activity, Peirce, semiotics.

Abstract:

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.

1 INTRODUCTION

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-

395

J. Sarbo J. (2007).

ON THE LOGIC UNDERLYING COMMON SENSE.

In Proceedings of the Ninth International Conference on Enterprise Information Systems - ISAS, pages 395-400

DOI: 10.5220/0002405803950400

 SciTePress

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.

2 A MODEL OF COGNITIVE

ACTIVITY

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

entities.

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

,C)

the linking of the qualia with their combinatory

properties ([C]);

(4) predication: (q

,C)–(q

,C)

the establishment of a relation between the com-

pleted qualia.

(1) sorting

(3) complementation

(4) predication

(2) abstraction

[C]

q q

[q q ]

(q ,C) − (q ,C)

(q ,C)

[q ][q ]

Figure 1: The processing schema of cognitive activity.

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396

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–¬B:

A is ‘known’, but B is ‘not known’ (completion of

the input state);

B–¬A:

B is ‘known’, but A is ‘not known’ (completion of

the input effect);

(A,¬B)–(B,¬A):

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) (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;

ON THE LOGIC UNDERLYING COMMON SENSE

397

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,

ambiguously.

]=A+B, [q

]=A∗B: 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 (A∗B), 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, ¬A∗B: 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+¬A∗B: 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 ¬A∗B 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)=A∗B+¬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)–(q

,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

]=A∗B; q

=[q

]\[q

(A+B)\(A∗B)=A∗¬B+¬A∗B; (q

,C)=¬q

: ¬(A∗¬B

+¬A∗B) =A∗B+¬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

,C).

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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398

A,B,~A,~B

~A+~B

~A*~B

A+B A*B

A+~B,~A+B

A is B

A*B+~A*~B

A*~B+~A*BA*~B,~A*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)–(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

(A∗B)+(¬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 ¬A∗B, to be used

interchangeably.

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.

3 A PEIRCEAN SEMIOTIC

INTERPRETATION

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,

corre-

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.

ON THE LOGIC UNDERLYING COMMON SENSE

399

connection

likeness actual event

quality

actual

rule

proposition

existence

qualitative

possibility

convention

Figure 4: The semiotic interpretation of logical signs and

interpretation moments.

index

icon sinsign

symbol

legisignrheme

dicent

qualisign

argument

Figure 5: Peirce’s nonadic classiﬁcation of signs.

4 SUMMARY AND FURTHER

RESEARCH

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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