A conjunct is another type of adverbial. They differ from disjuncts and adjuncts as they are used to conjoin/connect one part of a sentence to another rather than providing information about the content or manner of a sentence. They are not considered to be essential and sentences still make sense if conjuncts are removed. However, they are useful in connecting sentences and suggesting a relationship between the two.
Both adjuncts and disjuncts are adverbials. Adjuncts are well integrated into the structure of the sentence whereas disjuncts are usually set apart from the rest of the sentence (which is often shown through the use of commas).
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However, there is also a substantial body of work, initiated by Aloni (2002), Simons (2005a), and Alonso-Ovalle (2006), which promotes a different semantic treatment of disjunction, namely as generating sets of alternatives. In particular, when applied to two propositions A and B, disjunction is taken to generate a set of two propositional alternatives, . This treatment has been fruitfully applied to account for a number of phenomena, including disjunctive questions (e.g., Roelofsen & van Gool, 2010; AnderBois, 2011; Biezma & Rawlins, 2012), free choice effects arising from disjunction under modals and in imperatives (e.g., Aloni, 2002, 2007b; Simons, 2005a,b), counterfactuals with disjunctive antecedents (e.g., Alonso-Ovalle, 2006), unconditionals with disjunctive adjuncts (Rawlins, 2013), and sluicing (AnderBois, 2014). However, this alternative account of disjunction lacks the algebraic underpinning that made the traditional account so attractive. This makes it less explanatory: it is motivated by the empirical observations that it is designed to account for, but not by considerations that are independent of these observations.
Now, the standard treatment of disjunction, conjunction, and negation consists in associating each of these connectives with one of the basic algebraic operations: disjunction is taken to express the join operator, conjunction is taken to express the meet operator, and negation is taken to express complementation.
As mentioned above, since these algebraic operations are so basic, it is to be expected that natural languages will generally have lexical items that can be used to express them. And indeed, in virtually all languages words or morphemes have been found that may be taken to fulfil exactly this purpose (see, e.g., Haspelmath, 2007). The algebraic perspective provides an explanation for this finding. Moreover, the account leads us to expect that disjunction, conjunction, and negation are not only applicable to full sentences, but also to expressions of other syntactic categories whose denotations form a suitable algebra, and that in this case they express exactly the same operations. This is again generally found to be the case across languages.
So, just like in truth-conditional semantics, disjunction can be taken to express the join operator, and similarly conjunction and negation can be taken to express the meet operator and complementation, respectively. Thus, while the notion of meaning has been enriched, the essence of the standard treatment of the connectives has been preserved.
Disjunction across languages. No matter whether we construe propositions as sets of possible worlds, as in standard truth-conditional semantics, or as downward closed sets of information states, as in inquisitive semantics, the algebraic perspective on meaning leads us to expect that many natural languages contain words or morphemes that can be used to express the basic algebraic operations on propositions, like the join operator. The inquisitive algebraic perspective on meaning gives rise to a further typological expectation as well. Namely, since the join operator in inquisitive semantics generates multiple alternatives and therefore gives rise to inquisitiveness (unlike the other basic algebraic operations, as witnessed by the examples involving conjunction and negation in Figure 6), it is to be expected that words which are used to express the join operation, i.e., disjunction words, may also function as question words. Interestingly, it has been observed that this is indeed the case in many languages (see, e.g., Jayaseelan, 2008; Cable, 2010; AnderBois, 2011; Slade, 2011; Szabolcsi, 2015). This is illustrated in (7) with Malayalam -oo and Japanese ka: 2ff7e9595c
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