Critical analysis of the Carmo-Jones system of Contrary-to-Duty obligations

We offer a technical analysis of the contrary to duty system proposed in Carmo-Jones. We offer analysis/simplification/repair of their system and compare it with our own related system

Number-neutral bare plurals and the multiplicity implicature

Bare plurals (dogs) behave in ways that quantified plurals (some dogs) do not. For instance, while the sentence John owns dogs implies that John owns more than one dog, its negation John does not own dogs does not mean "John does not own more than one dog", but rather "John does not own a dog". A second puzzling behavior is known as the dependent plural reading; when in the scope of another plural, the 'more than one' meaning of the plural is not distributed over, but the existential force of the plural is. For example, My friends attend good schools requires that each of my friends attend one good school, not more, while at the same time being inappropriate if all my friends attend the same school. This paper shows that both these phenomena, and others, arise from the same cause. Namely, the plural noun itself does not assert 'more than one', but rather the plural denotes a predicate that is number neutral (unspecified for cardinality). The 'more than one' meaning arises as an scalar implicature, relying on the scalar relationship between the bare plural and its singular alternative, and calculated in a sub-sentential domain; namely, before existential closure of the event variable. Finally, implications of this analysis will be discussed for the analysis of the quantified noun phrases that interact with bare plurals, such as indefinite numeral DPs (three boys), and singular universals (every boy)

Cumulative constraint interaction and the equalizer of OT and HG

We show that, in general, Optimality Theory (OT) grammars containing a restricted family of locally-conjoined constraints (Smolensky 2006) make the same typological predictions as corresponding Harmonic Grammar (HG) grammars. We provide an intuition for the generalization using a simple constrast and neutralization typology, as well as a formal proof. This demonstration adds structure to claims about the (non)equivalence of HG and OT with local conjunction (Legendre et al. 2006, Pater 2016) and provides a tool for understanding how different sets of constraints lead to the same typological predictions in HG and OT

Independence and abstract multiplication

We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems