In Mapudungun, the suffix -fu- typically indicates the unsuccessful realization of either an event or its expected consequences. As is the case for frustrative morphemes in several unrelated languages, when applied to a stative VP, the interpretation tends to be linked to non-continuation. Interestingly, in addition to these core readings, -fu- also occurs in conditionals conveying counterfactuality, and in a large subclass of deontic and bouletic constructions, such as the ones that express weak necessity and unattainable desires. Following recent developments in the study of both frustratives and conditionals, this article shows how a modal analysis of -fu- can integrate these different readings into a unified account.

Questions concerning the proof-theoretic strength of classical versus nonclassical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First-Degree Entailment—a logic recently studied by Hannes Leitgeb under the label HYPE. We show in particular that, by formulating the theory PKF over HYPE, one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart KF. Moreover, we establish that also its schematic extension—in the sense of Feferman—is as strong as the schematic extension of KF, thus matching the strength of predicative analysis.

A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presented. The analysis is a form of ‘global’ expressivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic (negation, disjunction, etc.) and so allows the conditional to embed in arbitrarily complex sentences (thus avoiding the Frege–Geach problem). The expressivist framework is semantically characterized in a restrictor semantics due to Vann McGee, and is completely axiomatized in a logic dubbed ICL (‘Indicative Conditional Logic’). The expressivist framework extends the AGM (after Alchourron, Gärdenfors, Makinson) framework for belief revision and so provides a categorical (‘yes’–‘no’) epistemology for conditionals that complements McGee’s probabilistic framework while drawing on the same semantics. The result is an account of the semantics and acceptability conditions of the indicative conditional that fits well with the linguistic data (as pooled by linguists and from psychological experiments) while integrating both expressivist and semanticist perspectives.

This article explores conditionals expressing that the antecedent makes a difference for the consequent. A ‘relevantised’ version of the Ramsey Test for conditionals is employed in the context of the classical theory of belief revision. The idea of this test is that the antecedent is relevant to the consequent in the following sense: a conditional is accepted just in case (i) the consequent is accepted if the belief state is revised by the antecedent and (ii) the consequent fails to be accepted if the belief state is revised by the antecedent’s negation. The connective thus defined violates almost all of the traditional principles of conditional logic, but it obeys an interesting logic of its own. The article also gives the logic of an alternative version, the ‘Dependent Ramsey Test,’ according to which a conditional is accepted just in case (i) the consequent is accepted if the belief state is revised by the antecedent and (ii) the consequent is rejected (e.g., its negation is accepted) if the belief state is revised by the antecedent’s negation. This conditional is closely related to David Lewis’s counterfactual analysis of causation.

This paper addresses the controversy between Koeneman & Zeijlstra (K&Z) (2014) and Heycock & Sundquist (2017) concerning the viability of K&Z’s strong version of the Rich Agreement Hypothesis in the light of apparent counterexamples from the diachrony of Danish. It makes the general point that establishing whether or not cases of putative V-to-I movement in subordinate clauses can be reanalyzed as V-to-C, i.e. as embedded Verb Second (EV2), depends on the EV2-type of a language. The empirical discussion concerns appositive relatives and conditional protases, with V-to-C in the former being in principle compatible with ‘narrow’ nEV2 as displayed by Modern Mainland Scandinavian languages, and V-to-C in the latter with Old Norse-style ‘broad’ bEV2. It is concluded that the critical stages of Danish need to be scrutinized more closely before the above dispute can be settled.

Standard conditionals $\varphi > \psi$, by which I roughly mean variably strict conditionals à la Stalnaker and Lewis, are trivially true for impossible antecedents. This article investigates three modifications in a doxastic setting. For the neutral conditional, all impossible-antecedent conditionals are false, for the doxastic conditional they are only true if the consequent is absolutely necessary, and for the metaphysical conditional only if the consequent is ‘model-implied’ by the antecedent. I motivate these conditionals logically, and also doxastically by properties of conditional belief and belief revision. For this I show that the Lewisian hierarchy of conditional logics can be reproduced within ranking semantics, provided we slightly stretch the notion of a ranking function. Given this, acceptance of a conditional can be interpreted as a conditional belief. The epistemic and the neutral conditional deviate from Lewis’ weakest system $V$, in that ID ($\varphi > \varphi$) or even CN ($\varphi > \top$) are dropped, and new axioms appear. The logic of the metaphysical conditional is completely axiomatised by $V$ to which we add the known Kripke axioms T5 for the outer modality. Related completeness results for variations of the ranking semantics are obtained as corollaries.

The development of grammatical markers has been described from several theoretical perspectives over the last decade: Grammaticalization Theory (Hopper & Traugott 2003, Heine, Claudi & Hünnemeyer (1991), the Minimalist Program (Roberts & Roussou 2003, van Gelderen 2004), and Lexical-Functional Grammar (Vincent 2001), see also the overview in (Börjars & Vincent 2010). It has recently been addressed in Construction Grammar, where it is argued that a shift towards a constructional perspective on change may yield new insights into the workings of grammaticalization (Bergs & Diewald 2008, Hoffmann & Trousdale 2013, Traugott & Trousdale 2013). This paper should be taken as a contribution to a constructional view on grammaticalization. It is about the rise of the concessive subordinator fast(än) in the history of Swedish occurring in a construction or clause type called universal concessive conditional (Haspelmath & Köning 1998), in Swedish generaliserande bisats (SAG 1999). The Swedish fast, etymologically (and still productively) as an adjective in the meaning ‘steady’, ‘robust’ is used as an intensifier, ‘very’, ‘much’, in early Modern Swedish, eventually established as a concessive marker ‘even if’, ‘although’ in the 18th century. The conventionalization of a concessive inference is highly interesting and may be traced back to specific constructions in the 16th and 17th centuries. On the basis of an extensive corpus study, I analyze the critical contexts and discuss the development as constructional change rather than lexical change, arguing that a remapping between form and function takes place in concessive conditional constructions due to processes of inferencing and mismatch.

We report the results of two experiments investigating conditional inferences from conditional unless assertions, such as Juan is not in León unless Nuria is in Madrid. Experiments 1 and 2 check Fillenbaum's hypothesis about the semantic similarity of unless with if not and only if assertions; both also examine inferential endorsements (Experiment 1) and endorsements and latencies (Experiment 2) of the four logically equivalent conditional formulations: if A then B, if not-B then not-A, A only if B and not-A unless B. The results of these experiments show the similarity of unless and only if, confirming that the representation of both conditionals from the outset probably include two possibilities directionally oriented from B to A; results also confirm the especial difficulty of unless assertions. The implications of the results are discussed in the context of recent psychological and linguistic theories of the meaning of unless.

We report research investigating the role of mental models in deduction. The first study deals with conjunctive inferences (from one conjunction and two conditional premises) and disjunctive inferences (from one disjunction and the same two conditionals). The second study examines reasoning from multiple conditionals such as: If e then b; If a then b; If b then c; What follows between a and c? The third study addresses reasoning from different sorts of conditional assertions, including conditionals based on if then, only if, and unless. The paper also presents research on figural effects in syllogistic reasoning, on the effects of structure and believability in reasoning from double conditionals, and on reasoning from factual, counterfactual, and semifactual conditionals. The findings of these studies support the model theory, pose some difficulties for rule theories, and show the influence on reasoning of the linguistic structure and the semantic content of problems.

We report the results of an experiment investigating conditional inferences from conditional assertions such as ‘Juan won't go to León unless Nuria goes to Madrid’ and ‘Either Nuria goes to Madrid or Juan won't go to León’. This experiment addresses Dancygier's claims about the semantics of ‘unless’ by examining inferential endorsements of ‘not-A unless B’ and ‘Either B or not-A’ in the canonical order, presenting the categorical premise after the conditional assertions, and in the inverse order, presenting the categorical premise before the conditional assertions. The results of the experiment confirm that the representation of ‘unless’ includes two possibilities, although as Dancygier holds one of the possibilities may not be complete. The implications of the results are discussed in the context of the strategic nature of conditional reasoning and recent convergent theories of linguistic processing.

How do people make deductions? The orthodox view in psychology is that they use formal rules of inference like those of a “natural deduction” system. Deduction argues that their logical competence depends, not on formal rules, but on mental models. They construct models of the situation described by the premises, using their linguistic knowledge and their general knowledge. They try to formulate a conclusion based on these models that maintains semantic information, that expresses it parsimoniously, and that makes explicit something not directly stated by any premise. They then test the validity of the conclusion by searching for alternative models that might refute the conclusion. The theory also resolves long-standing puzzles about reasoning, including how nonmonotonic reasoning occurs in daily life. The book reports experiments on all the main domains of deduction, including inferences based on prepositional connectives such as “if” and “or,” inferences based on relations such as “in the same place as,” inferences based on quantifiers such as “none,” “any,” and “only,” and metalogical inferences based on assertions about the true and the false. Where the two theories make opposite predictions, the results confirm the model theory and run counter to the formal rule theories. Without exception, all of the experiments corroborate the two main predictions of the model theory: inferences requiring only one model are easier than those requiring multiple models, and erroneous conclusions are usually the result of constructing only one of the possible models of the premises.