Proof-theoretic methods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi is proved, and (...) used to conclude that the considered logical systems are PSPACE-complete. (shrink)

In this paper I focus on a recently discussed phenomenon illustrated by sentences containing predicates of taste: the phenomenon of " perspectival plurality " , whereby sentences containing two or more predicates of taste have readings according to which each predicate pertains to a different perspective. This phenomenon has been shown to be problematic for (at least certain versions of) relativism. My main aim is to further the discussion by showing that the phenomenon extends to other perspectival expressions than predicates (...) of taste and by proposing a general solution to the problem raised by it on behalf of the relativist. The core claim of the solution (" multiple indexing ") is that utterances of sentences containing perspectival expressions should be evaluated with respect to (possibly infinite) sequences of perspective parameters. (shrink)

In his highly engaging book, Speech and Morality, Terence Cuneo advances a transcendental argument for moral realism from the fact that we speak. After summarizing the major moves in the book, I argue that its master argument is not as friendly to non-naturalist versions of moral realism as Cuneo advertises and relies on a diet of insufficient types of speech acts. I also argue that expressivists have compelling replies to each of Cuneo's objections individually, but taken together, Cuneo's objections provide (...) the resources for issuing a new and interesting challenge to expressivists. (shrink)

Based on a crowdsourced truth value judgment experiment, we provide empirical evidence challenging two classical views in semantics, and we develop a novel account of counterfactuals that combines ideas from inquisitive semantics and causal reasoning. First, we show that two truth-conditionally equivalent clauses can make different semantic contributions when embedded in a counterfactual antecedent. Assuming compositionality, this means that the meaning of these clauses is not fully determined by their truth conditions. This finding has a clear explanation in inquisitive semantics: (...) truth-conditionally equivalent clauses may be associated with different propositional alternatives, each of which counts as a separate counterfactual assumption. Second, we show that our results contradict the common idea that the interpretation of a counterfactual involves minimizing change with respect to the actual state of affairs. We propose to replace the idea of minimal change by a distinction between foreground and background for a given counterfactual assumption: the background is held fixed in the counterfactual situation, while the foreground can be varied without any minimality constraint. (shrink)

What is the communicative value of negative polarity? That is, why do so many languages maintain a stock of special indefinites that occur only in a proper subset of the contexts in which ordinary indefinites can appear? Previous answers include: marking the validity of downward inferences; marking the invalidity of veridical inferences; or triggering strengthening implications. My starting point for exploring a new answer is the fact that an NPI must always take narrow scope with respect to its licensing context. (...) In contrast, ordinary indefinites are notorious for taking wide scope. So whatever other functions NPIs may have, they at least serve as an utterly reliable signal that an indefinite is taking narrow scope. As also proposed in recent work of Kusumoto and Tancredi, I will show that NPIs are only licensed in contexts in which the wide scope construal of an indefinite fails to entail the narrow scope. In other words, weak NPIs occur only in contexts in which taking narrow scope matters for interpretation. Thus one part of the explanation for the ubiquity and robust stability of negative polarity is that it signals scope relations. (shrink)

There is a prominent line of work in natural language semantics, rooted in the work of Hamblin, in which the meaning of a sentence is not taken to be a single proposition, but rather a set of propositions—a set of alternatives. This allows for a more fine-grained view on meaning, which has led to improved analyses of a wide range of linguistic phenomena. However, this approach also faces a number of problems. We focus here on two of these, in our (...) view the most fundamental ones. The first has to do with how meanings are composed, i.e., with the type-theoretic operations of function application and abstraction; the second has to do with how meanings are compared, i.e., the notion of entailment. Our aim is to reconcile what we take to be the essence of Hamblin’s proposal with the more orthodox type-theoretic framework rooted in the work of Montague in such a way that both the explanatory utility of the former and the solid formal foundations of the latter are preserved. Our proposal builds on insights from recent work on inquisitive semantics, and it also contributes to the further development of this framework by specifying how the inquisitive meaning of a sentence may be built up compositionally. (shrink)

An action is a pair of sets, C and S, and a function \. Rothschild and Yalcin gave a simple axiomatic characterization of those actions arising from set intersection, i.e. for which the elements of C and S can be identified with sets in such a way that elements of S act on elements of C by intersection. We introduce and axiomatically characterize two natural classes of actions which arise from set intersection and union. In the first class, the \-actions, (...) each element of S is identified with a pair of sets \\), which act on a set c by intersection with \ and union with \. In the second class, the \-biactions, each element of S is labeled as an intersection or a union, and acts accordingly on C. We give intuitive examples of these actions, one involving conversations and another a university’s changing student body. The examples give some motivation for considering these actions, and also help give intuitive readings of the axioms. The class of \-actions is closely related to a class of single-sorted algebras, which was previously treated by Margolis et al., albeit in another guise, and we note this connection. Along the way, we make some useful, though very general, observations about axiomatization and representation problems for classes of algebras. (shrink)

This light piece reflects on analogies between two often disjoint streams of research: the logical semantics and pragmatics of natural language and dynamic logics of general information-driven agency. The two areas show significant overlap in themes and tools, and yet, the focus seems subtly different in each, defying a simple comparison. We discuss some unusual questions that emerge when the two are put side by side, without any pretense at covering the whole literature or at reaching definitive conclusions.

I propose a new semantics for intuitionistic logic, which is a cross between the construction-oriented semantics of Brouwer-Heyting-Kolmogorov and the condition-oriented semantics of Kripke. The new semantics shows how there might be a common semantical underpinning for intuitionistic and classical logic and how intuitionistic logic might thereby be tied to a realist conception of the relationship between language and the world.