General
Assume a complex proposition of the form ‘S↴, although ↴S’. ↴S is the concessive proposition. All such complex propositions share the following properties:
- A conditional ‘if ↴S, notS↴’ (q → ¬p) is presupposed.
- ↴Sis taken for granted.
- S↴is asserted.
The presupposition #1 is normally grounded in a causal relation between S↴ and ↴S. Consider, for instance, a concessive construction such as .
| . | Although I exerted myself, I flunked the exam. | 
Such a sentence involves the presupposition ‘if I exert myself, I should pass the exam,’ which it contradicts. The presupposition is understood to be based on a causal relation between exerting oneself and passing exams. In this respect, concessive constructions are semantically based on causal constructions. By the combination of conditions #2 and #3, the speaker denies the conditional (thus trying to cancel it from the universe of discourse).
Subtypes of concessive relations are generated by the following alternatives:
- As for the above condition #2, the proposition ↴Sof the subordinate clause may either be factive or be assumed hypothetically.
- As for the above condition #1, the conditional relation between S↴and↴Smay hinge on some degree to which↴Sis the case.
Accordingly, the following subsections are devoted to factive vs. conditional concessives and to indifferent concessives.
Conditional and factive concessives
In a conditional concessive (), the subordinate proposition (↴S) is explicitly assumed rather than presupposed.  is an example.
| . | Even if I exert myself, I will flunk the exam. | 
The conditional concessive combines two independent features:
- It explicitly assumes the protasis ↴S. It is, consequently, a conditional.
- It presupposes the implication q → ¬pand contradicts it. It is, consequently, a concessive.
For this reason, the construction is called both conditional concessive and concessive conditional in the literature and in the present script. The concessive conditional is also treated as a subtype of the conditional.
In a factive concessive (), the speaker takes the reality of ↴S for granted. ↴S seems to be asserted rather than presupposed.1 The clause representing ↴S thus defined is a (factive) concessive clause. In English, most factive concessive clauses are introduced by (al)though.2
Just as the conditional concessive bears the said paradigmatic relation to a conditional, contradicting it, so a factive concessive bears a paradigmatic, viz. a contradictory, relation to a causal clause: It presupposes the relation '↴S causes ¬p' and contradicts it. Thus,  presupposes the causal relation ‘because I exerted myself, I did not flunk the exam’ and contradicts it.
Indifferent concessives
In a variety of the concessive relation, ↴S involves variation on some parameter and the presupposed conditional concerns a certain value on this parameter which would prevent the realization of S↴. Such an indifferent concessive relation may be coded by an indifferent (relative) clause of the kind of .
| . | However much I exerted myself, I always flunked the exams. | 
The two binary subdivisions of concessive relations are logically independent and cross-classify. is an indifferent conditional concessive.
| . | However much I may exert myself, I will flunk the exams. | 
1 The negation test on presupposition status is not easily applied to a sentence such as .
2 The English conjunction although nicely illustrates the necessity of distinguishing between the onomasiological and the semasiological approach: All factive concessive clauses may be introduced by although; but not every clause introduced by although is a factive concessive clause. In the sentence “Dowty ... proposes ... a different decomposition system from the one presented here, although this system has many features in common with Dowty's proposal.” (Van Valin & La Polla 1997:655), no concessive relation between the two propositions is involved, since the second proposition is not meant to be an obstacle to the first one. This use of although appears to involve a kind of corrective contrast.