1,721,002 research outputs found
Indicative conditionals and graded information
Full text linkI propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: “if p then q” is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of spheres. Worlds in the inner sphere are considered possible; worlds outside of it are ruled out, but to different degrees. In this way, even when a state supports “not p”, it is still possible to suppose p consistently. I argue that this account does better than its predecessors with respect to a set of desiderata concerning inferences with conditionals. In particular, it captures three important facts: (i) that a conditional is logically independent from its antecedent; (ii) that a sequence of antecedents behaves like a single conjunctive antecedent (the import-export equivalence); and (iii) that conditionals restrict the quantification domain of epistemic modals. I also discuss two ways to construe the role of a premise, and propose a generalized notion of entailment that keeps the two apart
The restrictor view, without covert modals
Full text linkThe view that if-clauses function semantically as restrictors is widely regarded as the only candidate for a fully general account of conditionals. The standard implementation of this view assumes that, where no operator to be restricted is in sight, if-clauses restrict covert epistemic modals. Stipulating such modals, however, lacks independent motivation and leads to wrong empirical predictions. In this paper I provide a theory of conditionals on which if-clauses are uniformly interpreted as restrictors, but no covert modals are postulated. Epistemic if-clauses, like those in bare conditionals, restrict an information state parameter which is used to interpret an expressive layer of the language. I show that this theory yields an attractive account of bare and overtly modalized conditionals and solves various empirical problems for the standard view, while dispensing with its less plausible assumption
Restriction without quantification: embedding and probability for indicative conditionals
Full text linkMany modern theories of indicative conditionals treat them as restricted epistemic necessity modals. This view, however, faces two problems. First, indicative
conditionals do not behave like necessity modals in embedded contexts, e.g., under ‘might’ and ‘probably’: in these contexts, conditionals do not contribute a
universal quantification over epistemic possibilities. Second, when we assess the probability of a conditional, we do not assess how likely it is that the consequent is epistemically necessary given the antecedent. I propose a semantics which solves
both problems, while still accounting for the data that motivated the necessity modal view. The account is based on the idea that the semantics of conditionals
involves only a restriction of the relevant epistemic state, and no quantification over epistemic possibilities. The relevant quantification is contributed by an at-
titude parameter in the semantics, which is shifted by epistemic modals. If the conditional is asserted, the designated attitude is acceptance, which contributes
a universal quantification, producing the effect of a restricted necessity modal
Inquisitive bisimulation
Full text linkInquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states, and characterise inquisitive modal logic as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures
Intuitionistic conditional logics
No full textBuilding on recent work by Yale Weiss, we study conditional logics in the intuitionistic setting. We consider a number of semantic conditions which give rise, among others, to intuitionistic counterparts of Lewis’s logic VC and Stalnaker’s C2. We show how to obtain a sound and complete axiomatization of each logic arising from a combination of these conditions. On the way, we remark how, in the intuitionistic setting, certain classically equivalent principles of conditional logic come apart, and how certain logical connections between different principles no longer hold
Coherence in inquisitive first-order logic
Full text linkInquisitive first-order logic, InqBQ, is a conservative extension of classical first-order logic with questions. Formulas of InqBQ are interpreted with respect to information states---essentially, sets of relational structures over a common domain. It is unknown whether entailment in InqBQ is compact, and whether validities are recursively enumerable. In this paper, we study the semantic property of finite coherence: a formula of InqBQ is finitely coherent if in order to determine whether it is satisfied by a state, it suffices to check substates of a fixed finite size. We show that finite coherence has interesting implications. Most strikingly, entailment towards finitely coherent conclusions is compact. We identify a broad syntactic fragment of the language, the rex fragment, where all formulas are finitely coherent. We give a natural deduction system which is complete for InqBQ- entailments with rex conclusions, showing in particular that rex validities are recursively enumerable. On the way to this result, we study approximations of InqBQ obtained by restricting to information states of a fixed cardinality. We axiomatize the finite approximations and show that, in contrast to the situation in the propositional setting, InqBQ does not coincide with the limit of its finite approximations, settling a question posed by Sano
Probabilities of conditionals: updating Adams
Full text linkThe problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities of conditionals violate standard probability theory. This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of ..
Games and cardinalities in inquisitive first-order logic
Full text linkInquisitive first-order logic, InqBQ, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrcnfeucht-Frai'ssc game for InqBQ and show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what statements and questions can be expressed in InqBQ about the number of individuals satisfying a given predicate. As special cases, we show that several variants of the question how many individuals satisfy a(x) are not expressible in InqBQ, both in the general case and in restriction to finite models
Modalities in the realm of questions: axiomatizing inquisitive epistemic logic
Full text linkBuilding on ideas from inquisitive semantics, the recently proposed framework of in-quisitive epistemic logic (IEL) provides the tools to model and reason about scenarios in which agents do not only have information, but also entertain issues. This frame-work has been shown to allow for a generalization to issues of important notions, such as common knowledge and public announcements, and it has been argued to form a suitable basis for the analysis of information exchange as an interactive process of raising and resolving issues. From an abstract point of view, the system is interesting, in that it implies extending the logical operations, including the modalities, beyond the truth-conditional realm, in such a way that they can embed not only standard declarative formulas, but also interrogatives. The present paper investigates the logic of IEL, building up to a completeness result. It is shown that the standard logical features of the logical constants extend smoothly beyond the truth-conditional realm, except for double negation, which is the hallmark of truth-conditionality. In partic-ular, while the modalities of IEL operate in a crucially richer semantic space than Kripke modalities do, they retain entirely standard logical features
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