To take one example, discourse saliency is a factor which plays a key role in the structural theory. For example, Fox & Katzir (2011) argue that constituents made salient in the discourse can be treated as if they were no more complex than a constituent in the assertion. This can explain why (6) – due to Matsumoto (1995) – implies that yesterday it was not a little bit more than warm. (6) Yesterday it was warm, today it was a little bit more than warm. The appeal to salience leads to predictions that are important to verify, yet introspective judgements are reported to be delicate. In particular, Fox & Katzir (2011) argue that a salient constituent can create a situation where it can compete with a lexical alternative and so create symmetry, leading to no overall implicature. Thus the claim is that (7) does not imply that Alice did not do just some of her homework yesterday; The reason for the absence of this inference would be the presence of the lexically generated symmetric alternative (all), which cannot be ignored. (7) is compared to (8), for which there would be no symmetric alternatives, given the presence of the universal deontic modals, and which would instead involve an inference that yesterday Alice didn’t have to do all of her homework and she didn’t have to do just some of the homework. (7) Yesterday, Alice did some of her homework. Today, she did just some of her homework. (8) Yesterday, Alice had to do some of her homework. Today, she has to do just some of her homework. Examples such as (7) versus (8) are important evidence for the structural theory’s argument that symmetry is determined by structural factors alone and cannot be broken by contextual salience. However, introspective judgments about them and related data points are very delicate, particularly as (7) is generally judged to be infelicitous with respect to (8) (and none of the approaches to alternatives offer an explanation of its infelicity). It is possible that conversational expectations related to explicitness have an impact in these cases. And it is also possible that this data point brings in other factors that have been unearthed in the Scalar Diversity literature – mentioned below. We think that it is therefore crucial that data point like (7) vs (8) are investigated experimentally, so that the role of discourse saliency, in contrast with other factors, is brought out clearly and better understood. As another example, direction of discourse inference seems to also play a role into a theory of alternatives. To illustrate one instance, consider the following example from Trinh and Haida (2016). Suppose someone says (9): (9) John ran and didn’t smoke. Bill ran. This utterance can have an implication that Bill smoked, presumably arising from the negation of the alternative Bill ran and didn’t smoke, made salient in the context. How to obtain this alternative, without at the same time not having to consider its less complex, symmetric counterpart (Bill ran and smoked) is entirely non-trivial and constitutes another important challenge for theories of alternatives (Trinh and Haida 2016, Breheny et al 2017 for discussion). Here, we also focus on another aspect of the problem. Consider a minimally different utterance: (10) John ran but didn’t lift weights. Bill ran. As observed by Trinh & Haida 2016, (10) does not seem to have an SI that Bill lifted weights. This pair of examples suggest that the direction of contextual implications of the predicates “not smoke” and “not lift weights” matter for selection of alternatives. That is, “not smoke” implies the same kind of health benefits as “run”, while “not lift weights” and “run” potentially contrast in health benefits. Regarding (9), Trinh & Haida (2016) show that to simply posit an ad hoc scale (<run and not smoke, run>) for (9), building on a proposal by Klinedinst 2004, makes incorrect predictions when a competing alternative run and smoke is considerably less complex. While we can agree with Trinh & Haida that it is insufficient to suppose simply an ad hoc scale is created by context for (9), the contrast with (10) remains unaccounted for in their proposal. And indeed, it seems, natural, that parallelism of discourse implication may add benefit (or reduce cost) of alternatives, compared with contrasting implications. A factor of this kind may then trade off with others such as complexity and informativeness and that could be the source of contrasts like (9) vs (10). An important aim of our project is to explore whether factors that encompass `parallelism of implications’ vs `contrast’ between alternatives play indeed a role for cases like the above. If correct, this would give us a more complete picture of the factors underlying the different cases of the symmetry problem. In addition, as discussed in Breheny et al. (2017), Trinh & Haida’s proposal for a modified structural account of examples like (8) does not adequately cover similar cases of this type. For one, it does not handle minimally different examples without conjunction, suggesting that a different way of re-thinking the structural approach is necessary. Similarly, the RSA approach, as it stands, does not even handle the basic case in (9), thus it also requires modifications to reach empirical adequacy with data points like those. In addition, as discussed in Spector 2017, this approach makes a series of specific predictions which also require experimental testing. Finally, another case discussed in Breheny, Klinedinst, Romoli & Sudo (2017) involves adjectives and their possible inferences. In particular, some negative adjectives appear to give rise to scalar inferences, (11), while others do not, (12). (Note that contrasts between cases like full and transparent show that scale structure does not fully predict the strength of the scalar inference (Gotzner et al 2018), as both of these adjectives are associated with upper (and lower) bounded scales (Kennedy & McNally, 2005)). (11) a. The cup is not full ~> the cup is not empty b. A tie is not required ~> A tie is allowed c. Mary’s promotion is not certain ~> Mary’s promotion is possible (12) a. John is not tall ~/~> John is not small b. This neighborhood is not safe ~/~> This neighborhood is not dangerous c. The glass is not transparent ~/~> The glass is not opaque These cases are problematic for all approaches to alternatives. They, however, also involve delicate comparative judgments about subtle inferences. Therefore careful experimental investigation of this area is necessary as a further step in understanding the empirical landscape related to the symmetry problem. In sum, the symmetry problem remains an important challenge for theories of alternatives and in turn theories of scalar implicatures. An as soon as we move away from the basic case of “some”, none of the approaches available in the literature appear able to account for all the various data points involving symmetry. Further, the divergent predictions of such approaches have not been for the most part experimentally tested. We aim to make progress in this area by providing experimental evidence to bear on those predictions and compare, develop and modify the different theories on the basis of those results. In particular, the objectives of the project are outlined below: Objectives: (a) To establish large-scale database of facts to be explained, in order that theoretical discussion is less reliant on subtle introspective judgements. (b) To Identify which factors may be relevant to determining alternatives and their weighting, using off-line judgement and on-line methods. (c) To evaluate different theoretical approaches to alternatives (such as the structural theory and Bayesian/probabilistic frameworks) in terms of their ability to accommodate several factors (cost/structural complexity, informativity, etc.) and appropriately modify/develop such approaches on the basis of the collected experimental data.