We will call logical context this part of the shared knowledge which is necessary (for us and also for the people involved in the conversation) to determine the relevance of what is uttered. This concept of logical context could be thought to be non-operational. How can we decide what in the shared knowledge should or should not be part of the logical context, when this context is not made explicit by the speakers? Fortunately a procedure exists which gives an experimental way to bring it out. In case of conversational breakdown, the first speaker makes spontaneously some elements of the logical context of her/his intervention explicit. It is thus quite simple to provoke such a breakdown in order to get elements of the logical context : simply say "So what?", "Why do you want to know?", "Why do you say this?", or "What are you getting at" (your difficulty has to appear clearly motivated, or else answers may be different, involving aggression or humor). This procedure may occur naturally, or may even be performed as a thought experiment. Let us see a few spontaneous examples.
[ex_Mercedes]
context: On the highway from Paris to Germany. Big Mercedes are common. B does not notice that the Mercedes just passing had a Hungarian license number. At the time, when Hungary was a communist country, individuals were supposed to be not rich.
A1- T'as vu la Mercedes ?
B1- Hé bé quoi ?
A2- Tu savais que les hongrois, ils avaient des voitures comme a ?
A1- Did you see the Mercedes?
B1- So what?
A2- Did you know that Hungarians had such cars?
Elements given in A2 (Hungarians were not supposed to own big cars) allows to isolate the logical context from shared knowledge unambiguously:
Hungarian( X ) => not rich( X )
[owns( X, Car ) & big( Car )] => rich( X )
In the next excerpt, we observe an ironic reply as a consequence of a misunderstanding about the context, which will be made more explicit by the first speaker.
[ex_antenna]
context: 1987 near Paris; parabolic TV antennas are very rare on private houses, while every house has its "comb" antenna.
A1- Tu sais, j'ai vu une antenne sur une maison de la rue des Roissys
B1- Dis donc, quel événement!
A2- mais non, une antenne comme... une antenne parabolique
A1- you know, I've seen an antenna on a house of the Roissys street
B1- gee, what an event!
A2- but no, an antenna like, a parabolic antenna
Something interesting happens here : there are two contexts, "A saw a 'comb' aerial in the neighborhood", and "A saw a parabolic antenna in the neighborhood", but only the second one makes A1 relevant while the first one, which is what B perceived, provokes the ironic reply B1. The relevance of A1 comes clearly from the fact that seeing a parabolic antenna in the neighborhood is a priori very improbable (while it is not the case for usual antennas). It seems that pure logical formalism is unable to represent the meaning of A1-A2. That is why we introduce a new modality, IMPR, which denotes a highly improbable fact. So we get something like:
[ parabolic_antenna(X) & neighbourhood(X) ] => IMPR
Here ( p => IMPR ) simply means that p is a priori highly improbable. The variable X denotes any object, since the assessment of the a priori probability holds for any object and not only for the specific object A saw. We saw another example of spontaneous breakdown in [ex_lunch, p.6]. In this excerpt A did make the logical context (Christmas special lunch) explicit, but this was not recorded. Here again, we need a special modality to represent a crucial element of the logical context :
[ chrismas_lunch ] => DES
( p => DES ) means that p is a priori desirable. We just saw examples of logical contexts, and we saw that this context may be made explicit after a breakdown. Sometimes the logical context is spontaneously made explicit by the first speaker before other participants ask for it. We could observe this phenomenon in [ex_Goffman, p.6], where the logical representation of A6 was exactly an instantiation of the logical context of A1 (with X instantiated to A).
It is worth noticing the epistemological importance of such breakdowns. We see clearly from our examples that these breakdowns were not caused by any trouble at the semantic level : the meaning of the preceding utterance was not ambiguous. In [ex_lunch] for instance, B had perfectly understood the meaning of the question, but refused to answer. As we will see, the trouble was essentially logical. It is also amazing that no pragmatic theory is able to predict such breakdowns. Sperber and Wilson [1986] try to define the conditions for relevance, but in a way which is not convenient here since none of the examples we gave is detected as non relevant. The addressee can easily infer new propositions from " I've seen an antenna ", or " I came by train ". (S)he could have simply answered the questions " Did you see the Mercedes " or " Did you have a good lunch " from which they also could make many inferences. Unfortunately, the observation (and also our intuition) indicates that these utterances were not relevant in the situation in which they occurred, and Sperber and Wilson fail at predicting this phenomenon. The definition of logical relevance that we will give here successfully predicts logical breakdowns.