In this paper we propose a semantic analysis of Lewis' counterfactuals. By exploiting the structural properties of the recently introduced boolean algebras of conditionals, we show that counterfactuals can be expressed as formal combinations of a conditional object and a normal necessity modal operator. Specifically, we introduce a class of algebras that serve as modal expansions of boolean algebras of conditionals, together with their dual relational structures. Moreover, we show that Lewis' semantics based on sphere models can be reconstructed in (...) this framework. As a consequence, we establish the soundness and completeness of a slightly stronger variant of Lewis' logic for counterfactuals with respect to our algebraic models. In the second part of the paper, we present a novel approach to the probability of counterfactuals showing that it aligns with the uncertainty degree assigned by a belief function, as per Dempster-Shafer theory, to its associated conditional formula. Furthermore, we characterize the probability of a counterfactual in terms of Gärdenfors' imaging rule for the probabilistic update. (shrink)

In this paper we argue for a unified semantics for hypothetical conditionals, hc s, e.g. _if it rains, we’ll cancel the picnic_, and biscuit conditionals, bc s, e.g., _if you are hungry, there are biscuits on the sideboard_. We side with recent literature in proposing that differences in the interpretation are related to (in)dependence between antecedent and consequent, but we move beyond current accounts in spelling out a characterization of independence that is actually predictive. We further establish a systematic link (...) between _if_-constructions and discourse structure, providing a dynamic update model that integrates the QUD, and thus the intentional discourse-structure. We argue that in bc s the antecedent sets up the question that is addressed by the consequent, and show that rescuing (Gricean) relevance in face of independence gives rise to implicatures corresponding to the different flavors associated with bc s. Crucially, we argue, this is the same mechanism responsible for our understanding that in the hc above, for example, it is the rain that will cause the cancellation of the picnic. Along the way we notice how the phenomena observed in _if_-constructions are also replicated in other quantificational structures. Ultimately, there is not much that is biscuit-specific. Their interpretation is the result of a conspiracy among semantics, dynamic update and intentional discourse-structure. (shrink)

Causal Modeling Semantics (CMS, e.g., Galles and Pearl 1998; Pearl 2000; Halpern 2000) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual (A ∨ B) > C at a causal model M as a weighted (...) average of the probability of C in those submodels that truthmake A∨ B (Briggs 2012; Fine 2016, 2017). The weights of the submodels are given by the inverse distance to the original model M, based on a distance metric proposed by Eva, Stern, and Hartmann (2019). Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined. (shrink)

This paper provides an update semantics for counterfactual conditionals. It does so by giving a dynamic twist to the ‘Premise Semantics’ for counterfactuals developed in Veltman (1976) and Kratzer (1981). It also offers an alternative solution to the problems with naive Premise Semantics discussed by Angelika Kratzer in ‘Lumps of Thought’ (Kratzer, 1989). Such an alternative is called for given the triviality results presented in Kanazawa et al. (2005, this issue).

The exclusive component of unembedded disjunctions is standardly derived as a conversational implicature by assuming that or forms a lexical scale with and. It is well known, however, that this assumption does not suffice to determine the required scalar competitors of disjunctions with more than two atomic disjuncts (McCawley, Everything that linguists have always wanted to know about logic* (But were ashamed to ask). Chicago University Press, Chicago, 1993, p. 324; Simons, “Or”: Issues in the semantics and pragmatics of disjunction. (...) Ph.D. thesis, Cornell University, Ithaca, NY, 1998). To solve this, Sauerland (Linguist Philos 27(3): 367–391, 2004) assumes that or forms a lexical scale with two otherwise unattested silent connectives ( ${\mathbb{L}}$ and ${\mathbb{R}}$ ) that retrieve the left and right terms of a disjunction. A number of recent works have proposed an Alternative Semantics for indefinites and disjunction to account for their interaction with modals and other propositional operators (Kratzer and Shimoyama, In: Otsu Y (ed) The Proceedings of the Third Tokyo Conference on Psycholinguistics. Hituzi Syobo, Tokyo, pp. 1–25, 2002; Aloni, In: Weisgerber M (ed) Proceedings of the Conference “SuB7—Sinn und Bedeutung”. Arbeitspapier Nr. 114. Konstanz, pp. 28–37, 2003; Simons, Nat Lang Semantics 13: 271–316, 2005; Alonso-Ovalle, Disjunction in alternative semantics. Ph.D. thesis, University of Massachusetts, Amherst, MA, 2006). We note that the McCawley–Simons problem does not arise in an Alternative Semantics, if we assume that the set of pragmatic competitors to a disjunction is the closure under intersection of the set of propositions that it denotes. An adaptation of the strengthening mechanism presented in Fox (In: Sauerland U, Stateva P (eds) Presupposition and implicature in compositional semantics. MacMillan, Palgrave, pp. 71–120, 2007) allows for the derivation of the exclusive component of disjunctions with more than two atomic disjuncts without having to rely on the ${\mathbb{L}}$ and ${\mathbb{R}}$ operators. The proposal extends to the case of disjunctions with logically dependent disjuncts. (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)

We show that Gabbay’s nonmonotonic consequence relations c an be reduced to a new family of relations, called entrenchment relations. Entrenchment relations provide a direct generalization of epistemic entrenchment and expectation ordering introduced by G ̈ardenfors and Makinson for the study of belief revision and expectation inference, respectively.

This paper deals with the truth conditions of conditional sentences. It focuses on a particular class of problematic examples for semantic theories for these sentences. I will argue that the examples show the need to refer to dynamic, in particular causal laws in an approach to their truth conditions. More particularly, I will claim that we need a causal notion of consequence. The proposal subsequently made uses a representation of causal dependencies as proposed in Pearl (2000) to formalize a causal (...) notion of consequence. This notion inserted in premise semantics for counterfactuals in the style of Veltman (1976) and Kratzer (1979) will provide a new interpretation rule for conditionals. I will illustrate how this approach overcomes problems of previous proposals and end with some remarks on remaining questions. (shrink)

Counterfactuals are typically thought--given the force of Sobel sequences--to be variably strict conditionals. I go the other way. Sobel sequences and (what I call) Hegel sequences push us to a strict conditional analysis of counterfactuals: counterfactuals amount to some necessity modal scoped over a plain material conditional, just which modal being a function of context. To make this worth saying I need to say just how counterfactuals and context interact. No easy feat, but I have something to say on the (...) matter. (shrink)

“Counterfactual” readings of might/could have were previously analyzed using metaphysical modal bases. This paper presents examples and scenarios where the assumptions of such a branching-time semantics are not met, because there are facts at the base world that preclude the complement of the modal becoming true. Additional arguments show that counterfactual readings are context dependent. These data motivate a semantics using a circumstantial (or factual) modal base, which refers to context-dependent facts about a world and time. The analysis is formulated (...) in a version of premise semantics for modality. (shrink)

We carry out the Karttunen-Stalnaker pragmatic account of presupposition projection within a state-of-the art version of dynamic epistemic logic. It turns out that the basic projection facts can all be derived from a Gricean maxim ‘be informative’. This sheds light on a recent controversy on the appropriateness of dynamic semantics as a tool for analysing presupposition.

A sentence A is epistemically less entrenched in a belief state K than a sentence B if and only if a person in belief state K who is forced to give up either A or B will give up A and hold on to B. This is the fundamental idea of epistemic entrenchment as introduced by Gärdenfors (1988) and elaborated by Gärdenfors and Makinson (1988). Another distinguishing feature of relations of epistemic entrenchment is that they permit particularly simple and elegant (...) construction recipes for minimal changes of belief states. These relations, however, are required to satisfy rather demanding conditions. In the present paper we liberalize the concept of epistemic entrenchment by removing connectivity, minimality and maximality conditions. Correspondingly, we achieve a liberalization of the concept of rational belief change that does no longer presuppose the postulates of success and rational monotony. We show that the central results of Gärdenfors and Makinson are preserved in our more flexible setting. Moreover, the generalized concept of epistemic entrenchment turns out to be applicable also to relational and iterated belief changes. (shrink)