In the account provided by K. Bach & R.M. Harnish, the term 'illocutionary act is used and defined, following an idea P.F. Strawson had issued in "Intention and Convention in Speech Act", in two completely different ways, and for two completely different kinds of action. Firstly, they define the 'communicative illocutionary act', which they also mostly aim at when using the term 'illocutionary act' (without qualification). Secondly, they introduce the notion of a 'conventional illocutionary act'.
(I) The 'communicative illocutionary act', or just 'illocutionary act', is either attempted
(linguistic) communication, or an act of achieved (linguistic) communication (Bach & Harnish do not clear up which exactly). To have a communicative intention, according to them, is to be
equated with meaning something in the sense of Grice's 'speaker meaning', and with having a (certain kind of) reflexive intention: an R-intention, whose fulfilment consists in its recognition, as
well as with the expressing of an attitude. (1979, xiv-v).
(II) The conventional illocutionary act is an institutional act. "Whereas a communicative [illocutionary] intention is fulfilled by means of recognition of that intention, a conventional intention is fulfilled by means of satisfying a convention", they (1979, 108) explain. The term "convention" is meant to express a particular technical notion:
Convention: A (in C) is a convention for D-ing in G if and only if:
i. it is MB-ed in G that whenever a member of G does A in C, he is D-ing, and
ii. A in C .counts as D-ing only because it is MB-ed in G to count as such. (1979, 109)
That "conventional illocutionary acts" are institutional acts makes them correspond partially to Austin's 'Illocutionary Acts'. Yet while Austin's 'Illocutionary Acts" additionally
involve the 'securing of uptake', Bach & Harnish omit this feature (they never discuss why). A "conventional illocutionary act" in the sense they define is really just an institutional act.
Indeed, there is reason to believe that on Bach & Harnish’s account, if a given kind of act does essentially involve communicative intentions then this act
does not count as a ‘conventional IA’: "Conventional illocutionary acts are not essentially communicative and do not require R-intentions", they (1979, 117) say.
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Bach, K. & R.M. Harnish (1979), Linguistic Communication and Speech Acts. Cambridge, Mass. / London: MIT Press.