Nicole Cruz (with Michael Lee)

People draw on event co-occurrences as a foundation for causal and scientific inference, but in which ways can events co-occur? Statistically, one can express a dependency between events A and C as P(C|A) != P(C), but this relation can be further specified in a variety of ways, particularly when A and/or C are themselves conditional events. In the psychology of reasoning, the conditional P(C|A) is often thought to become biconditional when people add the converse, P(A|C), or inverse, P(not-C|not-A), or both, with the effects of these additions largely treated as equivalent. In contrast, from a coherence based logical perspective it makes a difference whether the converse or the inverse is added, and in what way. In particular, the addition can occur by forming the conjunction of two conditionals, or by merely constraining their probabilities to be equal. Here we outline four distinct ways of defining biconditional relationships, illustrating their differences by how they constrain the conclusion probabilities of a set of inference forms. We present a Bayesian latent-mixture model with which the biconditionals can be dissociated from one another, and discuss implications for the interpretation of empirical findings in the field.

Fabrizio Cariani

I identify and develop a solution to the puzzle of anankastic conditionals that is novel in the sense that it has gone largely unnoticed, but also well-worn in that the materials for it have long been available. The solution involves an integration of the classical Kratzerian premise semantics and a default theory of reasons (such as the one presented in Horty, 2012, leveraging several decades of research on default logic). To stress-test the proposal I also investigate how it might be applied to the variety of anankastic-adjacent data discussed by Condoravdi and Lauer (2016). The resulting approach is not just an exceptional fit for the problem of anankastic conditionals, but also an independently promising upgrade on the classical account of modals.

I-Ta Chris Hsieh, National Tsing Hua University, Taiwan

A demonstrative such as that and those may have various uses, be it deictic, anaphoric, or purely descriptive. One of the approaches to demonstratives, namely the Hidden Argument Theory (henceforth, HAT) approach (e.g., King 2001, Blumberg 2020, Nowak 2021, Ahn 2022; a.o.,), is intended to provide a unified account of these uses. In the HAT approach, a demonstrative, unlike a definite article (e.g., the), carries two restrictions; in one recent variant of this approach, namely Ahn (2022, Ling & Phil), the various uses of a demonstrative description are due to the different options to contribute the second restriction, including a deictic demonstration, an index, and a relative clause that adjoins to the demonstrative phrase. In this talk, I examine the interaction between demonstratives and relative clauses and show that current analyses along with the HAT approach could yield some undesirable predictions. Some amendments will be suggested to accurately capture the interpretation of a demonstrative description with a relative clause and at the same time avoid these predictions.

Prerna Nadathur

A range of complement-taking predicates give rise to surprising actuality inferences, in which a modally-embedded complement event is understood non-modally, as taking place in the evaluation world.  I argue that actuality inferences can be explained—and unified across predicate classes—on an approach in which the modality of participating predicates is analyzed in causal terms.  This talk focuses on an illuminating case study: enough and too predicates.

Hacquard (2005) observes that, like the ability modals at the heart of the puzzle (Bhatt 1999), enough/too predicates have aspect-sensitive actuality inferences.  Under imperfective marking, French enough predicates like (1a) are compatible with the non-actualization of their complements; their perfective counterparts (as in 1b) show the complement entailment pattern of implicative verbs like French réussir (‘succeed’, ‘manage’; 2).

Despite the contrast in (1)-(2), I argue that enough/too inferences are—semantically speaking—instances of implicativity.  I build on a causal account of implicative lexical semantics (Nadathur 2016, 2019) to show that enough/too actuality inferences arise just in case the compositional interaction between grammatical aspect, modal flavour, and the enough/too matrix adjective reproduces the semantic structure of an implicative: that is, where the matrix adjective denotes an actionable property which is causally involved in realizing the enough/too complement, and the perfective aspect induces an eventive interpretation of the matrix assertion.   Insofar as the implicative analysis explains the aspect-sensitivity of enough/too inferences, I suggest that it naturally extends to ability modals’ actuality inferences, when coupled with a causal approach to ability.

Cian Dorr and Matthew Mandelkern (NYU)

In the course of proving a tenability result about the probabilities of conditionals, van Fraassen (1976) introduced a semantics for conditionals based on sequences of worlds, representing a particularly simple special case of ordering semantics for conditionals. According to sequence semantics, ‘If p, then q’ is true at a sequence just in case either q is true at the first truncation of the sequence where p is true, or there is no truncation where p is true. This approach has become increasingly popular in recent years. However, its logic has never been explored. We axiomatize the logic of sequence semantics, showing that it is the result of adding two new axioms to Stalnaker’s logic C2: one which is prima facie attractive, and one which is complex and difficult to assess. We also show that when sequence models are generalized to allow transfinite sequences, the result is the logic that adds only the first (more attractive) axiom to C2.

Maria Aloni

People often reason contrary to the prescriptions of classical logic. In the talk I will discuss some cases of divergence between everyday and logical-mathematical reasoning and propose that they are a consequence of a tendency in human cognition to neglect models which verify sentences by virtue of an empty configuration [neglect-zero tendency, Aloni 2022]. I will then introduce a bilateral state-based modal logic (BSML) which formally represents the neglect-zero tendency and can be used to rigorously study its impact on reasoning and interpretation. After discussing some of the applications, I will compare BSML with related systems (truthmaker semantics, possibility semantics, and inquisitive semantics) via translations into Modal Information Logic [van Benthem 2019].

Maria Aloni. Logic and conversation: The case of free choice, Semantics and Pragmatics, vol 15 (2022)
Johan van Benthem. Implicit and Explicit Stances in Logic, Journal of Philosophical Logic, vol 48, pages 571–601 (2019)

Elitzur Bar-Asher Siegal

This talk introduces a systematic way of analyzing the semantics of causative linguistic expressions, and of how natural languages express causal relationships. For this purpose, I will employ the Structural Equation Modeling (SEM) framework and demonstrate how this method offers a rigorous model-theoretic approach to examining the distinct semantics of causal expressions. This paper introduces formal logical definitions of different types of conditions using SEM networks, and illustrates how this proposal, along with its formal tools, can help to clarify the asymmetric entailment relationship among different causative constructions.

Yimei Xiang

Wh-questions with the modal verb can admit both mention-some (MS) and mention-all (MA) answers. This paper argues that we should treat MS as a grammatical phenomenon, primarily determined by the grammar of the wh-interrogative. I assume that MS and MA answers can be modeled using the same definition of answerhood (Fox 2013) and attribute the MS/MA ambiguity to structural variations within the question nucleus. The variations are: (i) the scope ambiguity of the higher-order wh-trace, and (ii) the absence/presence of an anti-exhaustification operator. However, treating MS answers as complete answers in this way contradicts the widely adopted analysis of uniqueness effects in questions of Dayal 1996, according to which the uniqueness effects of singular which-phrases arise from an exhaustivity presupposition, namely that a question must have a unique exhaustive true answer. To solve this dilemma, I propose that question interpretations presuppose ‘Relativized Exhaustivity’: roughly, the exhaustivity in questions is evaluated relative to the accessible worlds as opposed to the anchor/utterance world. Relativized Exhaustivity preserves the merits of Dayal’s exhaustivity presupposition while permitting MS; moreover, it explains the local-uniqueness effects in modalized singular wh-questions.

The speaker also has a relevant manuscript on Lingbuzz: https://ling.auf.net/lingbuzz/005322

Sarah Murray

Across languages, sentences are marked for sentence type, or sentential mood, e.g., declarative and interrogative. These sentence types are associated with speech acts: assertions and questions, respectively. However, sentential mood does not determine the force of an utterance of a sentence. We argue that the semantic contribution of sentential mood is a relation that constrains utterance force. This relation takes a proposition as an argument and uses it to affect a component of the context. The semantic constraint together with additional pragmatic factors produce utterance force.

This logic for speech acts involves a semantics for the three main sentence types found cross-linguistically (declarative, interrogative, imperative) as well as a distinction between speaker commitment and discourse reference. In addition to a semantics for sentential mood, this approach provides a framework for a range of phenomena, including evidentials, parentheticals, hedges, and “speech act modifiers”. We conclude by discussing the Linguistic Modification Thesis, the idea that linguistic material can only influence utterance force by influencing sentential force.

This talk is based on joint work with William Starr