I have seen some researchers classify conditional clauses into the following three types:
content conditionals
epistemic conditionals
speech-act conditionals
For example, the following paper discusses this classification:
From Etymology to Pragmatics; CUP
At the moment, I am not quite sure how to distinguish these three types of conditionals. I would like to ask whether there is a concise way to identify them, especially a simple diagnostic that can help distinguish content conditionals from the other two types.
P.S.
The ultimate purpose of asking this question is to understand which types of conditional clauses can be focused using the “it’s ... that ...” cleft construction. This would allow me to use such a focus structure to negate or question the relationship between the main clause and the conditional clause (i.e., to construct a yes/no question).
It seems that only content conditionals can be focused by the “it’s ... that ...” construction. However, in this question, I am not discussing the issue of focusability. I would like to solve the classification problem first, and only then move on to the issue of focus and cleft constructions.
Below is part of the discussion from the source in the OP - it all seems pretty clear and reasonable at first glance. I don't see a possibility of any sort of syntactic test for distinguishing the three, but the summary at the end of the speech-act conditional section (I've put it in bold) gives a rough tool to distinguish the three.
Content conditionals
Whatever the degree of hypotheticality, the relationship marked by
if-then remains the same: the fulfillment of the protasis, likely or
unlikely, is a sufficient condition for the fulfillment of the
apodosis. In content conjunction, this often means that there is
assumed to be a causal relationship between the two, as in [If Mary
goes, John will go], where the most likely interpretation is probably
that Mary's going (if it occurs) will cause John to decide to go.
Equally, there may be a negative causal relationship involved: for
example, one could take [If Mary goes, John will go] as meaning that
Mary's not going would somehow prevent John's going, although her
going would not be an active cause in making him decide to go too.
[If I were president, I'd sell the White House's Limoges china to
fund bilingual education] is most easily read this way: it is the
speaker's not being president which prevents his/her selling the White
House china, although being president would not cause the sale in
question. In these cases, the fulfillment of the antecedent condition
is rather an enablement than a cause of the consequent; and the
enablement is further viewed as being sufficient to assure the
consequent's fulfillment - i.e, in [If I were president, I'd sell the
White House's Limoges china to fund bilingual education] the will
involved in making the decision is already committed, so no further
positive causality is needed, and enablement suffices. Enablement and
causation are linguistically treated as identical with respect to
conditionals, as they often are elsewhere (see section 4.1 on causal
conjunction). But either a hypothetical enablement or a hypothetical
cause may be a sufficient antecedent for the fulfillment of some
consequent event or condition.
Epistemic conditionals
In the epistemic domain, if-then conjunction expresses the idea that
knowledge of the truth of the hypothetical premise expressed in the
protasis would be a sufficient condition for concluding the truth of
the proposition expressed in the apodosis.
(6) If she's divorced, (then) she's been married.
...
A non-tautological epistemic conditional is expressed in (7):
(7) If John went to that party, (then) he was trying to infuriate Miriam.
In (7) there is no inherent linguistic or logical connection between protasis and apodosis. Presumably the speaker has a general, tacitly assumed data-base; and the addition to that data-base of the truth of "John went to that party" will suffice to allow the conclusion that the proposition "he was
trying to infuriate Miriam" is also true.
Speech-Act Conditionals
It has been recognized for some time that conditional speech acts
exist (see Van der Auwera 1986), and classic examples include cases
like (8)—{10):
(8) If I may say so, that's a crazy idea.
(9) If I haven't already asked you to do so, please sign the guest
book before you go.
(10) If it's not rude to ask, what made you decide to leave IBM?
...
these speech acts "purport" to be conditional, [...] in
fact their actual pragmatic status is somewhat nebulous
...
The way in which conditional speech acts are actually performed, but
present themselves as only conditionally performed, is parallel to the way
in which speech-act uses of or present two alternative speech acts (while
necessarily needing to perform both in order to allow the interlocutor to
"choose" between them). Both appear to rely on the interlocutor's
cooperation in helping keep some jointly agreed-on mental record of what
counts as "really" having been said, and on a convention which puts on
that record only one of two alternative speech acts, and which only
conditionally records a conditional speech act.
...
(11) There are biscuits on the sideboard if you want them.
(12) If you went to the party, was John there?
...
It thus becomes clear that there are a great variety of conditional
speech acts, some more overtly referring to the general felicity conditions
on the relevant class of speech acts, while others refer implicitly to these
general conditions by referring overtly to some more specific felicity
condition on the particular utterance (a sub-case of the general condition).
All speech-act conditionals have in common the fact that they are
appropriately paraphrased by "If [protasis], then let us consider that I
perform this speech act (i.e., the one represented as the apodosis)." This
reading is to be contrasted with both content conditionals (which do not
need paraphrases involving speech acts or logical processes) and with
epistemic conditionals, which are appropriately paraphrased as "If I know
[protasis], then / conclude [apodosis].
