Motivations

At their core, syntactic and semantic theories are (at least) explanations of judgments about strings–i.e. elements of the set \(\Sigma^* = \bigcup_{i=0}^\infty \Sigma^i\) for some vocabulary \(\Sigma\).¹ One kind of judgment we are often concerned with is acceptability (see Schütze 2016 and references therein): introspective judgments of strings’ well-formedness relative to a language, context of use, etc. For example, in a context where a host is asking a guest what they would like in addition to coffee, (1) is clearly well-formed (or acceptable), while (2) is clearly not (Ross 1967; see Sprouse and Villata 2021 and references therein).

1. What would you like with your coffee?
2. What would you like and your coffee?

Another kind of judgment we are often concerned with–particularly in semantic theory–is about inferential relationships between strings (see Davis and Gillon 2004, Ch. 4 and references therein). For example, in a context where someone uses (3) and their addressee both trusts the user and doesn’t know that (4), the addressee will tend to infer that (4)–i.e. the content of the subordinate clause in (3) (see White 2019 and references therein).

3. Jo loved that Mo left.
4. Mo left.

One important property we want syntactic and semantic theories to have is observational adequacy (Chomsky 1964): for any string \(s \in \Sigma^*\), we can predict how acceptable someone who knows the language will find \(s\) relative to a particular context; and for any pair of strings \(s, s' \in \Sigma^*\) that person judges acceptable, we can predict whether that person judges \(s'\) to be inferable from \(s\) and vice versa–again, relative to a particular context.²

In addition to observational adequacy, we tend to want theories that are parsimonious. A common way of moving forward in this respect is to posit methods for mapping vocabulary elements and strings to a more or less constrained set of abstractions for use in predicting the relationship between a string and judgments of its acceptability or inferential relationships to other strings.³

These abstractions may take a wide variety of forms:

1. They may be discrete, continuous, or some hybrid of the two.
2. They may be interrelated–e.g. by some type of ordering.
3. They may be more or less richly structured–e.g. they may be strings, trees, etc. constructed from a set of abstractions that themselves might have any combination of the properties (i) and (ii).

This course covers techniques both for learning such abstractions (or representations) from experimental and/or corpus data–with a focus on acceptability and inference judgment data–and for quantitatively assessing the observational adequacy and parsimony of some set of assumptions about the nature of those representations.

This approach is motivated by the mutually supportive goals of enabling syntacticians and semanticists to:

1. develop and use models that accord with their representational assumptions in order to assist in constructing quantitatively grounded analyses under those assumptions.
2. compare different sorts of representational assumptions in a formally explicit, quantitatively grounded way.

My aim in this course is to give you the conceptual and practical tools to understand (what I take to be) the theoretically relevant portions of the computational modeling literature and to provide you with a jumping off point from which to begin your research journey into it. You should not expect the course to provide you with a comprehensive overview of the literature in a particular area–even the areas that we will use as case studies. For example, I am not going to cover all the ways that researchers have modeled island effects. Rather, I will demonstrate how to incrementally develop hypothesis-driven models that can help us answer particular theoretical questions.

References

Berwick, Robert C., Paul Pietroski, Beracah Yankama, and Noam Chomsky. 2011. “Poverty of the Stimulus Revisited.” Cognitive Science 35 (7): 1207–42. https://doi.org/10.1111/j.1551-6709.2011.01189.x.

Chomsky, Noam. 1964. “Current Issues in Linguistic Theory.” Edited by J. Fodor and J. Katz. The Structure of Language. New York: Prentice Hall.

Davis, Steven, and Brendan S Gillon. 2004. Semantics: A Reader. New York: Oxford University Press.

Higginbotham, James. 1985. “On Semantics.” Linguistic Inquiry 16 (4): 547–93.

Ross, John Robert. 1967. “Constraints on Variables in Syntax.” PhD thesis, Massachusetts Institute of Technology.

Schütze, Carson T. 2016. The Empirical Base of Linguistics. Classics in Linguistics 2. Berlin: Language Science Press. https://doi.org/10.17169/langsci.b89.101.

Sprouse, Jon, and Sandra Villata. 2021. “Island Effects.” In The Cambridge Handbook of Experimental Syntax, edited by Grant Goodall, 227–57. Cambridge Handbooks in Language and Linguistics. Cambridge University Press. https://doi.org/10.1017/9781108569620.010.

White, Aaron Steven. 2019. “Lexically Triggered Veridicality Inferences.” In Handbook of Pragmatics, 22:115–48. John Benjamins Publishing Company. https://doi.org/10.1075/hop.22.lex4.

Footnotes

1. Depending on your persuasion, the vocabulary \(\Sigma\) might be a set of words; or it might be a set of morphemes. Nothing’s going to hinge on this distinction in this course.

2. We may furthermore want explanations that handle inference judgements between strings that are judged to be degraded in some sense (Higginbotham 1985; Berwick et al. 2011).

3. Definition of a set of vocabulary elements and segmentation of a string into those elements is already a highly nontrivial form of abstraction. This course will generally presuppose that the correct segmentations are given.