Interpretation of Utterances based on Relevance Theory:
Toward the Formalization of Implicature with the Maximal Relevance
Sayaka Minewaki, Kazutaka Shimada and Tsutomu Endo
Department of Artificial Intelligence, Kyusyu Institute of Technology
Iizuka, Fukuoka, 820-8502, Japan

Abstract
This paper proposes an interpretation method of utterances using relevance theory. Sperber andWilson have said that humans adopt the maximal relevance in interpretation of utterances. The
maximal relevance has a high cognitive effect with low processing efforts. In relevance theory
the meaning of utterances is divided into explicatures and implicatures. We study to formalizeinterpretations with the maximal relevance. We focus on implicatures and define process ofderiving implicatures. In addition, we define the cognitive effect and the processing effort, andapply those to multi-objective optimization. We regard Pareto-optimal solutions as implicatureswith the maximal relevance. We exemplify the validity of our method. Future work is anexperiment using a method which combined this method with reported method.

1
Introduction
In daily conversation, human often use ambiguous
expression to utter. For example, syntactic
ambiguous expression, metaphor, irony, metonymy,
euphemism, humor, etc. Interpretation of utteranceswith ambiguous expression has been investigatedmany times in the past.
In this paper, we propose an interpretation
method of utterances, using relevance theory [1].
Relevance theory by Sperber and Wilson is thetheory in pragmatics about how a hearer interprets a
speaker's utterance. Sperber and Wilson have said,
essentially, that humans adopt the maximal relevancein interpretation of utterances. That is applicable tonot only interpretation of utterances but also generalhuman cognition. The interpretation with the
maximal relevance has a high cognitive effect withlow processing efforts. A processing effort isaccessibility of assumptions. A cognitive effect is
produced by the interaction of given information andnew information. In relevance theory, the meaning ofan utterance is divided into explicatures andimplicatures. Explicatures and implicatures are
explicitly and implicitly communicated meaning,respectively.
We focus on implicatures and study to derive
implicatures and calculate relevance. In order tocalculate relevance, we formalize the cognitive effect(CE) and the processing effort (PE) of implicatures.
We apply that CE and PE to multi-objective
optimization, regarding Pareto-optimal solutions asinterpretations with the maximal relevance.
The remainder of the paper is organized in thefollowing way: in Section 2, we outline relevancetheory. In Section 3, we present our method. In
Section 4, we exemplify the validity.
2
Relevance theory
Relevance theory proposed by Sperber and Wilson isa pragmatic framework. It is based on Grice's
principle. The goal of relevance theory is to explain
how a hearer infers a speaker's meaning on the basisof the evidence provided.
Sperber and Wilson argued that there are two
fundamentally different uses of language: descriptive
use and interpretive use. Descriptive use is use oftruth-conditional. Interpretive use is use ofresemblance. Utterances are interpretively used torepresent the thoughts of a speaker. That is,utterances are interpretations or interpretive
expressions of the thoughts that the speaker wants tocommunicate. In interpretive use, emphasis is on
how much a hearer faithfully reproduces theexpression of thoughts of the speaker. Sperber andWilson argued that interpretive use plays afundamental role in the analysis of non-literalutterances [2].
In general, communication has a stimulus tocommunicate something. A speaker attracts ahearer's attention by the stimulus, and distinctly
shows the hearer that the speaker wants tocommunicate something. The stimulus which attracts
the hearer's attention was called ostensive stimulus.
Communication based on ostensive stimulus wascalled ostensive communication. The typicalostensive communication is a dialogue. Ostensive
communication has an informative intention and acommunicative intention. The informative intention
is the intention to inform the hearer of something.
The communicative intention is the intention to
inform the hearer of one's informative intention.
Relevance
theorydeals
withostensivecommunication [3].
2.1 The principle of relevanceSperber and Wilson proposed two principles of
relevance as follows:
Cognitive Principle of Relevance:
Human cognition tends to be geared to the
maximisation of relevance.
Communicative Principle of Relevance:
Every act of ostensive communication
communicates a presumption of its own
optimal relevance.
Relevance is a potential property not only ofutterances and other observable phenomena, but ofthoughts, memories and conclusions of inferences.
Any external stimulus or internal representation
which provides an input to cognitive processes isrelevant to an individual. Cognitive principle of
relevance describes that human's cognitive resource
tends to process an input which is the most relevant
in available inputs. Communicative principle of
relevance describes that the ostensive stimulus has
optimal relevance with no exceptions. Sperber andWilson defined presumption of optimal relevance asfollows:
Presumption of Optimal Relevance:(a) The ostensive stimulus is relevant enoughfor it to be worth the addressee's effort toprocess it.
(b) The ostensive stimulus is the most relevant
one compatible with the communicator'sabilities and preferences.
According to these principles, the hearer, whoreceived the speaker's ostensive stimulus, expects
presumption of optimal relevance. Then the hearer
starts inferring in order to get the interpretation of
the maximal relevance.
Relevance is not just an all-or-none matter but amatter of degree. Relevance is assessed in terms ofthe cognitive effect and the processing effort. The
maximal relevance has a high cognitive effect withlow processing efforts.
The cognitive effect is a modification of a
cognitive environment by the interaction of the new
information with existing assumptions. The
cognitive environment of an individual is a set ofassumptions that are manifest to him. The
modification of the cognitive environment has three
types: contextual implication, strengthening ofexisting assumptions, and contradiction andelimination of existing assumptions.
The first modification of the cognitiveenvironment is addition of contextual implications tothe cognitive environment. The contextual
implication is a conclusion deducible from the input
and the context, which is new information. Consider
the following example:(1) X:Y:

Do you like cats?
I don't like any animals.
a. Cats are animals.
b. Y doesn't like cats.

In understanding Y's utterance, X has an assumption(1a) which was included in his cognitiveenvironment, and X deduces a contextual
implication (1b). X's cognitive environment is
modified by addition of the contextual implication(1b) to X's cognitive environment.
The second modification of the cognitiveenvironmentisstrengtheningofexisting
assumptions, by providing further evidence.
Consider the following example:(2) a.

If Y is afraid of cats, Y doesn't like cats.

b.

Y is afraid of cats.

(2a) and (2b) are added to (1) as new information. X
deduces (1b) from (2a) and (2b). (1b) is an existing
assumption, not a contextual implication. (1b) isstrengthened by new information (2).
The third modification of the cognitiveenvironment is elimination of existing assumptions
that appear to be false. If new information and an
existing assumption are contradiction, weak one iseliminated. Consider the following example:(3) a.
b.
c.

If Y has cats, Y likes cats.
Y has a cat.
Y likes cats.

(3) is added to (1) as new information. X deduces acontextual implication (3c) from (3a) and (3b), but(3c) contradicts the (1b). If (1b) is weaker than (3c),(1b) is eliminated. On the other hand, if (3c) is
weaker than (1b), (3c) is eliminated.
Each assumption has a confirmation value,
which is degree of confidence. Modification of theconfirmation value yields the cognitive effect. In thecase of addition of contextual implication, theconfirmation value is provided. In the case ofstrengthening of existing assumptions, theconfirmation value of an existing assumption
increases. In the case of elimination of existing
assumptions, the confirmation value of an eliminatedassumption is lost.
Processing effort is determined by three main
factors [4] as follows:(a) The complexity of the utterance: the more
complex the utterance the greater the processing
effort.
(b) The size of the context: the larger the context,
the greater the processing effort.
(c) The accessibility of the context: the lessaccessible the context, the greater theprocessing effort.
The accessibility has two characteristics as follows:(a) One is that recently accessed assumptions are
more accessible than assumptions not recently
accessed.

(b) Another is that assumptions frequently accessed
are more accessible than assumptions
infrequently accessed.
2.2 The meaning of an utterance
According to the relevance-theoretic account, themeaning of an utterance is divided into explicaturesand implicatures. These definitions are as follows:(I) An assumption communicated by an utterance
U is EXPLICIT [hence an "explicature"] if andonly if it is a development of a logical form
encoded by U.
(II) An assumption communicated by U which is
not explicit is IMPLICIT [hence an"implicature"].
Explicatures are derived by disambiguation,
saturation, free enrichment, and ad hoc concept
construction. Implicatures are derived by inference.
Implicatures come in two sorts: implicated premises
and implicated conclusions. Implicated premises area subset of the contextual assumptions used inprocessing the utterance. Implicated conclusions area subset of its contextual implications. Explicaturesand implicatures are derived in parallel [6].
Each implicature has strength. Consider thefollowing example of a strong implicature:(4) X:
Y:

Would you drive a Mercedes?
I wouldn't drive any expensive car.
a. Y wouldn't drive any expensive car.
b. A Mercedes is an expensive car.
c. Y wouldn't drive a Mercedes.

(4a) is an explicature which was derived bysaturation, (4b) is an implicated premise, and (4c) is
an implicated conclusion. In this conversation, Y did
not answer X directly. However, Y gives X
immediate access to X's encyclopedic information
about expensive cars, the information in (4b). If X
retrieves assumption (4b) from X's memory and adds
to X's context, X would derive the contextual
implication (4c). Hence, X assumes that Y does not
drive a Mercedes. (4b) and (4c) are strong
implicatures.
Y's utterance in (4) gives X access to X's
encyclopedic information about expensive cars.

Hence it would be reasonable for X to add premises(5a) and (6a), and derive conclusions (5b) and (6b).
Or X could construct some premise such as (7a), andderive conclusion (7b).

utterances. In [6] we have reported a method ofinterpretation for explicatures. In this paper, we
propose a method to model the relevance of
implicatures.

(5) a.
b.
(6) a.
b.
(7) a.

3.1 Process of deriving implicatures
Implicatures are supplied wholly by inference.
Typical inference consists of deduction andinduction. According to the relevance-theoretic
account, the human deductive device has access only
to the following elimination rules. Let P and Q
denote assumptions.

b.

A Rolls-Royce is an expensive car.
Y wouldn't drive a Rolls-Royce.
A Cadillac is an expensive car.
Y wouldn't drive a Cadillac.
If x would not drive expensive cars, then x
disapproves of displays of wealth.
Y disapproves of displays of wealth.

It is clear that (5-7) are not what Y wanted tocommunicate. Because Y does not force X to use(5-7). Hence, (5-7) are weak implicatures, which X
chose freely from a wider range of context. Usingsuch weak implicature is the X's sole responsibility.
Distinction between strong implicatures and weak
implicatures is whether the hearer supplied premises
along an encouragement given by the speaker. It
seems that the encouragement given by the speakeris included in the speaker's utterance.
Consider another example of the weak
implicature:(8) His ink is pale.
(9) a. He has the character of a man who would
use pale ink.
b. His writing lacks contrasts.
c. There is something weak in his writing.
d. He does not put his whole heart into his
work.

And-elimination(a) Input: (P and Q)
Output: P(b) Input: (P and Q)
Output: Q
Modus ponendo ponens
Input:(i) P(ii) (If P then Q)
Output: Q
Modus tollendo ponens(a) Input:(i) (P or Q)(ii) (not P)
Output: Q(b) Input:(i) (P or Q)(ii) (not Q)
Output: P

In the case of an interpretation consistent with theprinciple of relevance composed of various
implicatures, the result of deduction is also the weak
implicature. (8) did not require deriving specificimplicatures. There are not strong implicatures. A
hearer searches weak implicatures (9) from extensive
context in order to interpret the meaning of (8). In
this case, hearer's confidence is less strong than thecase (4).

Implicatures come in two sorts: implicatedpremises and implicated conclusions. Implicatedpremises are premises of deduction, and implicatedconclusions are conclusions of deduction. We show aprocess of deriving implicatures. This process
consists of two sub processes: first, retrieval of
implicated premises existing in a memory; second,deduction of implicated conclusions from implicatedpremises which were retrieved.
We define implicated premise formats asfollows:

3
Methods
Relevance theory has not applied enough in thecomputer science field yet. Our goal is to formalize
relevance theory for an interpretation method of(a) IF-THEN rule: 'IF P then Q,' where P and Q are
propositional forms or assumption schemata.
(b) ISA relationship: 'A is B,' where A and B arewords or phrases or propositional forms or avariable (when one is the variable, other isnever the variable) or assumption schemata.

(12) X:Y:

Examples are as follows:(10) a.
b.
c.
d.

If it is winter, then it is cold.
If x has cats, then x like cats.
Cats are animals.
'x is awake' is 'x is not sleeping.'(10a, b) are IF-THEN rule formats, (10c, d) are ISA
relationship formats.
We define selection rules of implicatedpremises and derivation processes of implicatedconclusions. An implicated conclusion is deduced
from an implicated premise and a literal meaning or
an explicature or an implicated conclusion which
was deduced previously. It seems that retrieval cuesof the strong implicated premises are included in the
speaker's utterance. Let P0 denote the literal meaningor the explicature or the implicated conclusion,
which was deduced previously.
(a) IF-THEN rule(i) P is the propositional form: when P0
corresponded to the antecedent P, or P0 was
an analytic implication of P, the consequent
Q is the implicated conclusion.
Consider the following example:(11) X:Y:

Shall we play tennis?
It's raining.
a. If it's raining then it's not a good idea
to play tennis.
b. It's not a good idea to play tennis.

(11a) is an implicated premise. Y's utterance
corresponds to the antecedent of (11a). Hence theconsequent of (11a) is an implicated conclusion(11b).
(ii) P is the assumption schema: when P wasable to be unified with P0, the consequent Q
is the implicated conclusion.

Do you like cats?
I have a cat.
a. Y has a cat.
b. If x has cats, then x like cats.
c. If Y has cats, then Y likes cats.
d. Y like cats.

(12a) is an explicature of Y's utterance. (12b) is an
assumption schema which was retrieved from X's
memory. If x gets unified with Y, an implicatedpremise (12c) is formed. (12d) is an implicatedconclusion derived from (12a) and (12c).
(b) ISA relationship (A is B)(i) A (B) is the word or the phrase: when a wordor phrase which is included in P0 matched to
A (B), or it was the analytic implication of A
(B), new P0 which changed it into B (A) is theimplicated conclusion.
For example, the explicature of Y's utterance in(1) is 'Y doesn't like cats' is explicature wasderived by saturation. 'Any animals', included in
the explicature of Y's utterance and is the analytic
implication of 'animals'. New assumption whichchanged 'animals' into 'cats' is the implicatedconclusion (1b).
(ii) A (B) is the propositional form: when P0
matched to A (B), B (A) is the implicatedconclusion.
(iii) A is the variable and B is a word or thephrase: if a word or phrase which is includedin P0 matched to B, or it was the analytic
implication of B, then new P0 which changed
the word or phrase into A, which is unified, isthe implicated conclusion.
Consider the following example:(13) X:Y:

Have you read Z's book?
I don't read any autobiography.
a. Y doesn't read any autobiography.
b. x is an autobiography.
c. Z's book is an autobiography.
d. Y doesn't read Z's book.

Consider the following example:(13a) is an explicature of Y's utterance, (13b) is anassumption schema which was retrieved from X's
memory, (13c) is an implicated premise which X
formed based on (13b), and (13d) is an implicatedconclusion derived from (13a) and (13c).
(iv) A (B) is the assumption schema: when A (B)was able to be unified with P0, B (A) is theimplicated conclusion.
3.2 Formalization of relevanceIn this section, we formalize the degree of relevance.
Relevance is a matter of degree, and depends on the
cognitive effect and the processing effort. There istrade-off between the cognitive effect and theprocessing effort. First, we discuss clues to define
the relevance of implicatures. Next, we define thecognitive effect and the processing effort, and apply
those to multi-objective optimization.
First, we discuss clues to define the relevanceof implicatures. The implicated conclusion deduced
from specific implicated premises is strong. In thecase of implicated premises accessed from extensive
context, the implicated conclusion is weak. In short,the strength of implicated conclusions depends on
the strength of implicated premises. The strong
implicature has specific implicated premises andimplicated conclusions which are deduced from
specific implicated premises. On the other hand, theweak implicature is implicated premises accessedfrom extensive context and implicated conclusions
deduced from them.
The strength of implicatures has the following
relations with the processing effort, the cognitiveeffect and relevance:(a) The strong implicature is more accessible than
the weak one. In other words, the processing
effort of the strong one is less than the weakone.
(b) The degree of the cognitive effect depends on
how much a confirmation value of assumptions
increased:• In the contextual implication, when theimplicature with high confirmation value
was deduced, the cognitive effect is high.
• In strengthening of existing assumptions,when a confirmation value was muchincreased, the cognitive effect is high.

From (a) and (b), we add a supposition as follows:(c) The strong implicature is more relevant than the
weak one: the strong implicature has highcognitive effect with low processing efforts.
On the basis of those relations, we define thecognitive effect and the processing effort. The degreeof the cognitive effect depends on a confirmation
value of an implicated conclusion. The confirmation
value of the implicated conclusion depends on two
things: (1) confirmation values of premises used bydeduction; (2) the degree of resemblance between an
implicated conclusion the hearer deduced andexplicit responses that a speaker would have wanted
to communicate. With regard to (2), it seems that oneof the role of inference is recovery of implicitly
conveyed. Hence, the implicated conclusion with astrong resemblance should have high cognitiveeffect.
We define a calculation of the confirmation
value. Let P0 denote the literal meaning or the
explicature or the implicated conclusion, which was
deduced previously. Let IP and IC denoterespectively the implicated premise and theimplicated conclusion which is a contextual
implication. Let CV(x) denote the confirmation
value of x. The calculation of CV applied
Conjunctive Rules of MYCIN's certainty factor [7].
CV(IC) is calculated by the following formula:CV( IC ) = CV( P0 ) × CV( IP)Here, CV ranges from 0 to 1. If CV(x) = 0, x is not
an assumption existing in cognitive environment.
The more CV increases, the more the confidence of x
becomes strong.
If deduction is repeated many times, theconfirmation value decreases.
(14) a.
b.
c.
d.
e.
f.
g.

P0
(If P0 then P1)
P1(If P1 then P2)
P2(If P2 then P3)
P3

(14a) is an assumption, (14b) is an implicatedpremise, and (14c) is an implicated conclusion
derived from (14a) and (14b). (14d) is an implicatedpremise, and (14e) is an implicated conclusion
derived from (14c) and (14d). (14f) is an implicatedpremise, and (14g) is an implicated conclusion
derived from (14e) and (14f). The confirmation
value of P1, P2 and P3 is calculated respectively as
follows:
CV( P1 ) = CV( P0 ) × CV( IP)= 0.8 × 0.8= 0.64
CV( P2 ) = CV( P1 ) × CV( IP)= 0.64 × 0.8= 0.512CV( P3 ) = CV( P2 ) × CV( IP)= 0.512 × 0.8= 0.4096
Here, we assume that the confirmation value of P0
and all implicated premises (IP) is 0.8. If n is large,
CV(Pn) ≈ 0. However, humans often conclude a
relevant implicature, even though deduction isrepeated many times. A hearer supposes explicit
responses that a speaker would have wanted tocommunicate. If an implicated conclusion is similar
to one of explicit responses, the implicatedconclusion would be relevant. That is, by comparing
the implicated conclusion with explicit responses,
the degree of resemblance is provided.
Consider (4)-(7) again. X asks Y whether Y
would drive a Mercedes. X supposes that (1) “Ywould drive a Mercedes” and (2) “Y would not drivea Mercedes”. They are direct responses X supposes.
We think that they are included in X's cognitiveenvironment. X retrieves implicated premises (4b),(5a), (6a) and (7a). Then X deduces implicatedconclusions (4c), (5b), (6b) and (7b). (4c)corresponds to one of direct responses in implicatedconclusions. By modus tollendo ponens, the direct
response (1) is eliminated and the direct response (2)is strengthened. The confirmation value of (4c) is
greater than that of other implicated conclusions.
We redefine the calculation of the confirmation
value. If IC corresponds to one of the direct
responses which a hearer supposes or IC was ananalytic implication of that,CV( IC ) =CV( P0 ) × CV( IP) + 1
2

elsewhere,
CV( IC ) = CV( P0 ) × CV( IP)
We define the degree of the cognitive effect asfollows: in the case of contextual implication,
CE = CV( x i )in the case of strengthening,
CE = α (CV( x i ) − CV( x j ))where xi is an implicated conclusion as a contextual
implication. xj is an existing assumption and this
propositional form is same as xi. α is a parameter thatemphasizes either the contextual implication orstrengthening.
The degree of the processing effort depends onaccessibility of implicated premises. We regard theprocessing effort as a summation of costs of
implicated premises, and define the cost of an
implicated premise ai. The cost is based on two
characteristics of the accessibility:β cost(a i ) = min mα ,n + 1 where mα is a cost of an assumption accessed whena hearer interpreted speaker's utterance before mtimes. β/(n+1) is a cost of an assumption accessed ntimes in the past. α and β are arbitrary constants.
Definition of the processing effort is as follows:
PE = ∑ cost( a i )Relevance is a matter of degree, and depends onthe cognitive effect and the processing effort. Thereis trade-off between the cognitive effect and theprocessing effort. We apply those to multi-objective
optimization.
Multi-objective optimization is an approachwhich allows balancing among many different
functions. An optimum solution set which isbalanced is called Pareto-optimal solutions. There is
no dominant strategy in Pareto-optimal solutions.
We regard Pareto-optimal solutions as implicatureswith the maximal relevance. Definition is as follows:
max CE( x i ), min PE( x i )s.t. x i ∈ F

where xi is an implicated conclusion, F is set of all
implicated conclusions possible.
4
ExampleIn this section, we derive implicatures, calculate
relevance defined in Section 3, and exemplify thevalidity of our method.
Consider following dialogue. X makes his firstutterance to Y after dinner.
(15) X:
Y:

Would you like a cup of coffee?
It keeps me awake.

conclusions (IC) which was deduced from (16b, c),(16d, e) and (16f, g), respectively. They arecontextual implications. They are deduced asfollows:(16b) + (16c) → (16d)(16d) + (16e) → (16f)⇔ (16b) + (16c) + (16e) → (16f)(16f) + (16g) → (16h)⇔ (16b) + (16c) + (16e) + (16g) → (16h)The confirmation value of (16d), (16f) and (16h) arecalculated respectively as follows:CV( IC d ) = CV( E b ) × CV( IPc )= 0.9 × 0.8= 0.72CV( IC f ) = CV( IC d ) × CV( IPe )= 0.72 × 0.8= 0.576
CV( IC h ) = CV( IC f ) × CV( IPg )= 0.576 × 0.8= 0.4608

Suppose that Y must get up early for next day's
morning work. X retrieves and deduces thefollowing assumptions.
(16) a.
b.
c.

d.
e.

f.
g.

h.

Y must get up early next morning. (1.0)
Coffee keeps Y awake after dinner. (0.9)
If coffee keeps Y awake awhile after
dinner, then Y would not be able to go to
bed early tonight.
(0.8)
Y would not be able to go to bed early
tonight.
If Y would not be able to go to bed early
tonight, then Y would not be able to get up
early next morning.
(0.8)
Y would not be able to get up early nextmorning.
If Y would not be able to get up early nextmorning, then Y should not drink a cup ofcoffee.
(0.8)
Y should not drink a cup of coffee.

Values in parentheses are confirmation values wesuppose. (16a) is a fact about Y. (16b) is the
explicature (E) which was derived by saturation andfree enrichment. (16c, e, g) are implicated premises(IP). (16d), (16f) and (16h) are implicatedwhere Eb is (16b), IPc is (16c), ICd is (16d), IPe is(16e), ICf is (16f), IPg is (16g) and ICh is (16h).
Suppose that X is aware of (17). They are direct
responses to X's question.
(17) a.
b.

Y would like a cup of coffee.
Y would not like a cup of coffee.

(0.5)
(0.5)

(16h) is most similar to (17b) among (16d, f, h).
Hence, the confirmation value of (16h) isrecalculated as follows:CV( IC h ) =CV( IC f ) × CV( IPg ) + 1

2
0.576 × 0.8 + 1=
2= 0.7304(16d), (16f) and (16h) are contextual implication.
Hence, each cognitive effect is as follows:CE( IC f ) = 0.576
CE( IC h ) = 0.7304
Next we calculate the processing effort. Here
we assume that the dialogue (15) is begun by X'sutterance. That is, the X's utterance is 1st utterance
in the conversation. Therefore, we disregard mα
which is included in definition of cost(ai). That is,cost(ai) = β/(n+1). Additionally, we assume that all
premises (16b, c, e, g) were retrieved with same
frequency. In β/(n+1), n and β denote frequency andarbitrary constant respectively. In this example
β/(n+1) is constant because n is same value for all
premises. Hence the value of PE is the number of
retrieved premises.
In order to deduce (16d), (16b, c) were retrieved.
Hence, the processing effort of (16d) is as follows:2β
PE( IC d ) =n +1
Similarly, in order to deduce (16f) and (16f), (16b, c,e) and (16b, c, e, g) were respectively retrieved.
Hence, processing efforts of (16d) and (16h) are as
follows:3βn +1
4βPE(IC h ) =n +1
PE(IC f ) =Fig. 1 shows the degree of the cognitive effect andprocessing effort. Both CE and PE of (16d) are better
than those of (16f). Thus, (16d) dominates (16f). PEof (16d) is better than that of (16h). However, CE of(16h) is better than that of (16d). Thus, (16d) and(16h) are Pareto-optimal solutions. They are
implicatures with the maximal relevance.
5
Conclusion
In this paper, we presented a method to model the
relevance of implicatures. First, we defined a processof deriving implicatures. And we formalized thecognitive effect and the processing effort, andapplied them to multi-objective optimization. The
validity of our method was exemplified.
In future work, we will observe various cases

Processing effort

CE( IC d ) = 0.72
(16h)
(16f)
(16d)

Cognitive effectFig. 1 Result.

about implications, experiment and evaluate ourmethod. Additionally, we intend to experiment witha method which combined this paper with [6].

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