In conversation, listeners often arrive at meanings for sentences that go beyond their literal interpretation. This enriched, pragmatic meaning can be the result of the listener considering what sentences the speaker could have used but did not, i.e. alternative utterances. For example, given the context in (1), the listener might consider the alternative in (1b) when hearing (1a). Given that this alternative was not used, the stronger, pragmatic interpretation the listener might arrive at is (1c), often referred to as the exhaustive reading.

Traditionally, the strong, exhaustive reading in (1c) is not taken to be part of the literal meaning of (1a). That is, the proposition that‘Yolanda did not like the eggs’ is not entailed by (1a). This is easy to see when considering a minimally different context where it is common knowledge that Yolanda only had spinach for lunch. In that context, an inference that she did not like the eggs does not arise for (1a). However, given the context in (1) and assuming that the speaker is as informative as possible (cf. Quantity maxim, Grice, 1989), the listener can infer (1c) from (1a): since (1b) would have been more informative but was not used by the speaker, they must have meant to convey that (1b) is not true. The result of this reasoning process is the pragmatically stronger, exhaustive meaning in (1c), which consists of the literal meaning in (1a), plus the inference that (1b) is false. This inferred non-literal meaning component is a type of quantity-based conversational implica ture.

There is an ongoing debate in the theoretical and experimental literature regarding the exact nature of the strengthening mechanism behind quantity-based conversational implicatures (referred to as quantity implicatures in what follows) see in particularBreheny et al., 2006, Chierchia, 2013, Chierchia et al., 2012, Franke, 2011, Geurts, 2010, Grodner et al., 2010, Huang and Snedeker, 2009, Magri, 2009, Spector, 2016.1 A central issue in this debate is whether different kinds of alternatives influence pragmatic strengthening, and how (Bott and Chemla, 2016, Breheny et al., 2013, Fox and Katzir, 2011, Horn, 1972, Levinson, 2000, Rees and Bott, 2018, Waldon and Degen, 2020).

Two sources of alternatives for quantity implicatures have been identified in the literature: the lexicon and the context. Example (1) above illustrates a case where alternatives are provided by the context of utterance. But lexically determined alternatives also appear to play an important role in the derivation of quantity implicatures, and were in fact at the origin of theoretical and experimental investigations into the phenomenon. For example, since the disjunction ‘or’ forms a lexical scale with the logically stronger ‘and,’ (2b) is a salient alternative to (2a), even in the absence of a rich context (Horn, 1972). Consequently, the disjunctive sentence in (2a) competes with the lexically derived alternative in (2b). The stronger reading in (2c) emerges, often referred to as the exclusive reading of disjunction.

Quantity implicatures involving lexical alternatives have been shown to be far less context dependent. They have therefore been subsumed under the term generalized conversational implicatures (Levinson, 2000). That is, (2c) is a salient reading of (2a) even without specifying a context of utterance as we did for (1). Due to this dependence of the latter form of quantity implicature on a particular context it has been referred to as particularized conversational implicature in the literature.

The two types of implicatures share a high-level description in terms of reasoning about a speaker’s communicative intentions as a function of statements they conspicuously did not make. Yet, the underlying mechanisms for accessing and excluding alternatives, that is the relevant sentences that the speaker did not utter, may be distinct. Specifically, whereas one requires lexical access (what alternatives is the sentence lexically associated with?), the other requires a context search (what alternatives are salient in the context?). This article addresses the question whether these two cases can or should be treated uniformly. To do so, we report on two studies testing whether the strengthening mechanism involved in particularized and generalized conversational implicatures influence each other. To look more into the nature of the alternatives involved, we included more complex cases involving conjunction within a complex disjunction as in (3a). The sentence has two readings beyond its literal meaning: a relatively weak one in (3b), and a much stronger reading in (3c).

The simple exclusive inference in (3b) is well-known, and can be derived by any theory that derives exclusive interpretations for simple disjunctions, including a naive theory that simply states that natural-language ‘or’ is ambiguous between an inclusive interpretation and an exclusive one, the latter amounting to the logician’s Xor (a or b but not both). The implicature in (3c) seems perhaps more exotic, but it has been observed in the literature on the basis of introspective judgments (Spector, 2007), and studied in some detail in the context of reasoning problems (Koralus and Mascarenhas, 2013, Mascarenhas, 2014, Picat, 2019, Sablé-Meyer and Mascarenhas, 2021).

Importantly, unlike the cases in (2c) or in (3b), the strengthening in (3c) cannot be derived by simply taking it that English ‘or’ sometimes behaves like the logician’s Xor. Take a schematic representation of (3a), for ease of exposition: [a and b] or c. A simple Xor analysis of ‘or’ in this schema yields [a and b and not c] or [c and not [a and b]]. But notice that (3c) is much stronger than this, it corresponds to the schema [a and b and not c] or [c and not a and not b].

Thus, the inference in (3c) works as a rather refined test case of what strategies humans use when deriving implicatures of this sort. Our experimental investigation into the two processes illustrated in (1) and (2) involved a paradigm of training-with-feedback, where we trained participants on sentences with ‘or’ and manipulated the contexts of utterance. We gave them feedback meant to push them toward literal or strengthened interpretations of those sentences. Testing participants on the inference in (3c) allowed us to check precisely what participants were trained for: a particular strategy for dealing with the word ‘or’, which could not plausibly be generalized to derive the strong meaning in (3c), or more abstract mechanisms for constructing and excluding alternatives proposed in the theoretical literature, which would be able to generate the strong interpretation in (3c). Specifically, the implicature in (3c) requires an exhaustification analysis, essentially the view that there exist unpronounced occurrences of an operator much like English ‘only’ at play in these sentences. Continuing with the schematic meaning for simplicity of discussion, this amounts to ‘only [a and b] or only c.’2 The unpronounced exhaustive operator only is sensitive to contextual alternatives by design, so that this schema can be paraphrased more intuitively as ‘either a and b and nothing else that is relevant, or c and nothing else that is relevant.’ The relevant propositions here are a, b, and c, so this reduces to ‘either a and b but not c, or c but not a and not b.’ Complex disjunctions as in (3c) are thus an extremely telling test case for determining what underlying mechanisms are shared by implicatures involving different alternative types.

Armed with these two methodological ingredients — a new paradigm based on training and a new test case in the form of complex disjunctions — we conducted two experiments meant to shed light on the differences and similarities between the two kinds of alternatives and two kinds of mechanisms discussed in the literature. Our Experiment 1 established that, after training which encouraged (or discouraged) the computation of implicatures associated with simple disjunctions, participants were significantly more likely (respectively less likely) to compute implicatures at a later testing phase which crucially involved the novel complex disjunctions. Experiment 2 replicated these results, and demonstrated additionally that our training methodology can be made to work across different kinds of implicatures, as long as certain conditions of salience obtain for the alternatives of the kind not directly trained on. We conclude that our methodology successfully trained participants in complex, abstract strategies for pragmatic enrichment, as demonstrated by their ready extension to complex disjunctions. More tentatively, we submit that our results are most compatible with the view that different mechanisms are at play in the access and construction of contextual and lexical alternatives.