Abstract This paper examines two approaches to presuppositions: one viewing them as inferences projecting from sentences under negation and other logical operators, and another defining them as admittance conditions of utterances. Neither approach fully accounts for the “proviso problem”, which arises when a sentence’s presuppositional inferences are logically stronger than its necessary admittance conditions. To address this challenge, we propose a calculus of a trivalent logic that formally distinguishes between admittance and projection, extending Karttunen’s dynamic, logical form-based analysis. The resulting framework enables a simple pragmatic strategy: presuppositional conclusions are accommodated unless overridden by a contextually likelier admittance condition. We provide evidence that this approach is empirically superior to methods that address the proviso problem using pragmatic strengthening.

Abstract I develop a framework for the compositional semantics of focus association that differs minimally from Rooth (Nat Lang Semant 1:75–116, 1992) in letting focus-sensitive operators optionally pass up evaluated focus alternatives. My proposal is informed by prior work on various complex constructions involving multiple alternative-sensitive operators and alternative sources—including multiple association with a single focus, multiple overlapping associations with separate foci, focus intervention effects in wh-questions, and focus association with wh-phrases—all of which I show can be accurately modeled in my framework. The framework allows us to maintain the idea due to Beck (Nat Lang Semant 14:1–56, 2006) that alternatives computed for the semantics of questions (Hamblin in Found Lang 10:41–53, 1973, a.o.) and of focus (Rooth in Association with focus, University of Massachusetts, Amherst, 1985, a.o.) are formally the same objects, defusing the argument in Li and Law (Linguist Philos 39:201–245, 2016) against such unification.

This paper presents the first formal event semantic analysis of two prominent types of serial verb construction (SVC) in Igbo (Benue-Congo), namely multi-event and sequential SVCs. Both SVC types are composed of two or more transitive verbs and appear to be similar on the surface, but they differ with respect to the property of internal argument sharing (Baker 1989). Based on the different formal semantic mechanisms proposed for complex event formation in the literature, we develop a catalogue of diagnostics for identifying the semantic mechanisms at play in different SVC configurations, both within and across languages. Applying the diagnostics to multi-event and sequential SVCs in Igbo, we show that the two SVC types come with different semantic properties, which correlate with the syntactic property of [+/−] object sharing. Whereas SVCs without OBJ-sharing denote conjunctions of proposition-denoting extended verbal projections, OBJ-sharing SVCs involve a tighter event construal, conceptualised as a complex process event or macro-event (Stewart in The serial verb construction parameter. McGill, New York, 1998; Pietroski in Causing Actions. Oxford University Press, Oxford, 2000; Events and Semantic Architecture. Oxford University Press, Oxford, 2005; Williams in Arguments in syntax and semantics. Cambridge University Press, Cambridge, 2015a; Bohnemeyer et al. in Language 83(3):495–532, 2007). We propose a formal analysis of OBJ-sharing sequential SVCs as denoting complex events with quantificational substructure.

The literature on demonstratives mostly focuses on DPs (demonstrative pronouns and determiners), which denote in the entity domain. However, demonstratives can also belong to other categories and denote in the domains of manners (she acted like this/like that/thus), locations (she was here/there), degrees (she was yay tall), amounts (Russian: ona vypila stolʲko vody ‘she drank that_much water’), qualities (Russian: ona uže pila takoe vino ‘she drank that_kind_of wine’), and even times (she arrived then). The problem I address is twofold. How can we define a unified semantics for these expressions that incorporates a single concept of demonstration, yet allows denotations to vary across domains? And how can we make sense of demonstrative feature values such as proximal or distal in domains that have no spatial component, such as degrees or manners? I argue that the solution comes from a generalized application of the familiar phenomenon of deferred reference: all demonstrative reference outside the entity and (possibly) spatial domains is deferred.

The dominant model of linguistic communication in current philosophy of language, semantics and formal pragmatics is centered around the idea that communication involves interlocutors coordinating with respect to a single body of information, the common ground. This body of information is understood to serve two central roles: it is the target of speech acts, and constitutes the information available to interlocutors for planning and interpreting utterances. In this paper, I provide a series of examples which show that, contra the dominant model, the information available to interlocutors cannot be modeled as common ground information. The examples involve interpreters making use of background information which cannot become common ground either because the interpreter refuses to accept it, or because the communicative situation is what Harris (2020) calls publicity averse. I consider and disarm a variety of responses that might be offered on behalf of the common ground view, including alternative construals of acceptance and of publicity. I demonstrate that a model of communication in which interlocutors maintain separate representations of their own and their interlocutors' information states easily accommodates these cases, taking as an example the model due to Heller and Brown-Schmidt (2023). I end the paper with the observation that my conclusions do not pose any threat to formal models of dynamic semantics/pragmatics, as these can be, and in some cases already are, interpreted as modelling the evolution of individual information states