In the next two weeks, **Giorgio Magri** will give a series of four informal presentations about learnability in OT. The times and locations are listed below, and a description of the topics follows. (Meetings 1 and 3 will be special meetings of 24.981 and 24.964, respectively)

**Topic 1: Idempotency, chain shifts, and learnability**

Time: Monday 4/11 11am-1pm

Place: 32-D461

Reading: https://sites.google.com/site/magrigrg/home/idempotency

A grammar is idempotent if it yields no chain shifts. I will give a ”reasoned” overview of the OT literature on chain shifts. The idea is that idempotency holds if all the faithfulness constraints satisfy a certain idempotency faithfulness condition(IFC). You can study formally which faithfulness constraints satisfy the IFC and which do not. Once you have your list of faithfulness constraints that do not satisfy the IFC, you can synopsize the various accounts for chain shifts in OT based on which faithfulness constraint they pick from that list. This little bit of theory of idempotency/chain shifts might have some implications for learnability. From a learnability perspective, a chain shift (a->e->i) is not necessarily problematic, as long as it is ”benign”, in the sense that the typology explored by the learner contains another grammar which is idempotent (no chain shifts) and makes the same phonotactic distinctions ([a] illicit; [e, i] licit). The obvious reason is that a phonotactic learner can simply assume he is learning the latter grammar instead of the former. These considerations lead to the following question: is it true that all chain shifts are benign? I don’t know. Yet, I have some ideas on how to use the results of the theory of idempotency to try to establish that. Existing inventories of chain shifts (like the one compiled by Moreton) might provide the empirical basis to address the question. Dinnsen also has a long list of child case studies with chain shifts that might be interesting to look at.

**Topic 2: Idempotency, the triangular inequality, and McCarthy’s (2003) categoricity conjecture**

Time: Tuesday 4/12 3-5pm

Place: 24-115 (**** Note special place)

Reading: https://sites.google.com/site/magrigrg/home/idempotenceoutputdrivenness

The IFC mentioned above is a fairly abstract and weird-looking condition on the faithfulness constraints. I will suggest that it admits nonetheless a very intuitive interpretation. Here is the idea. Faithfulness constraints intuitively measure the ”phonological distance” between URs and SRs. Thus, it makes sense to ask whether they satisfy axiomatic properties of the notion of distance. One such property is the ”triangular inequality”, which says that the distance between A and C is smaller than the distance between A and B plus the distance between B and C. I will argue that the IFC turns out to be equivalent to the requirement that faithfulness constraints satisfy the triangular inequality (properly readapted). In other words, OT idempotency holds when the faithfulness constraints have good ”metric properties”. Crucially, I can establish this equivalence for faithfulness constraints which satisfy a slightly stronger version of McCarthy’s (2003) categoricity generalization. Is it true that the faithfulness constraints which are relevant for natural language phonology satisfy this stronger categoricity generalization? I don’t know. But the ones I have started to look at seem as they do. The connection between the IFC and the triangular inequality is strengthen in the case of HG, because in that case it holds for any faithfulness constraint, not only for the categorical ones.

**Topic 3: Tesar’s characterization of opacity based on output-drivenness**

Time: Wednesday 4/13 1-3pm

Place: 32-D461

Tesar (2013) develops an extremely difficult theory of his notion of output-drivenness. Intuitively, this notion is meant to capture opaque interactions (or at least a subset thereof) without resorting to rules, namely in a way which is consistent with constraint-based frameworks. I will present a reconstruction of (a slight generalization of) Tesar’s theory of output-drivenness which (I personally submit) is quite simpler than his original formulation. This reconstruction builds on the results on the faithfulness triangular inequality anticipated above. What is the actual relationship between Tesar’s notion of output-drivenness and opacity? I don’t know—and Tesar does not seem to really care about that after all (that is indeed not what his book is really about). I would be very interested in going through a list of opaque cases (like the list in Baković’s paper) and see how they fare from the classifying perspective of output-drivenness. The task is not trivial, because (as we will see), the definition of output-drivenness has a free parameter which needs to be ”set by the user”. Furthermore, I think that this little project might potentially turn out to be quite interesting for the following reason. We know that opacity is hard to get in OT and it has indeed motivated all kind of advanced technology. Tesar has a fresh approach to it. He cares about learnability, not opacity. He starts from the assumption that opacity is bad for learnability and thus he wants to put opacity aside. This means that he needs to develop constraint conditions which ensure that the grammars in the corresponding typology are output-driven and thus display no opacity. Since opacity is hard to get, you might expect that Tesar has an easy job in characterizing constraint sets which forbid opacity. That turns out not to be the case: Tesar’s task turns out to be very difficult—-even though he makes a number of additional simplifying assumptions (one-to-one correspondence relations, only three faithfulness constraints, etcetera). Thus, it looks like opacity in OT is at the same time hard to get and hard to avoid!! I wonder whether understanding this surprising tension might lead to any new insights on opacity in OT.

**Topic 4: The Merchant/Tesar theory of inconsistency detection for learning underlying forms**

Time: Thurs 4/21 3-5pm

Place: 32-D461