Inquisitive bisimulation

Inquisitive 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. We characterise inquisitive modal logic, as well as its multi-agent epistemic S5-like variant, as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures. These results crucially require non-classical methods in studying bisimulation and first-order expressiveness over non-elementary classes of structures, irrespective of whether we aim for characterisations in the sense of classical or of finite model theory

Bisimulation in Inquisitive Modal Logic

Inquisitive 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, and characterise inquisitive modal logic as the bisimulation invariant fragments of first-order logic over various classes of two-sorted relational structures. These results crucially require non-classical methods in studying bisimulations and first-order expressiveness over non-elementary classes.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Implicatures of modified numerals: quantity or quality?

We propose a new analysis of modified numerals that allows us to: (i) predict ignorance with respect to the prejacent of at least (and thereby avoid to Bernard Schwarz's recent criticism of Coppock and Brochhagen 2013), (ii) get a three-way contrast between superlative modifiers, comparative modifiers, and numerals, without appeal to a two-sided analysis of numerals, and (iii) avoid the prediction that at least should produce quantity implciatures when only is not a grammatical alternative. With it, we reconcile Westera and Brasoveanu's (2014) findings with the achievements of the Coppock and Brochhagen account, bring that work in line with recent theorizing in inquisitive semantics using downward-closed possibilities, and show that inquisitive sincerity can interact with Horn-based quantity in a non-trivial way, something that may be fruitful to consider in other domains as well.https://4f669968-a-62cb3a1a-s-sites.googlegroups.com/site/sinnundbedeutung21/proceedings-preprints/modified-numerals-sub-2016-final.pdf?attachauth=ANoY7cp1Q88YF1lYnJLBxpbbMXxIReQLbjxbyfwsP3Dv0qStClh5zYCtiMY7oAffAskO4UIYw6zMQdQsLC51Szi9TVOkc2R-u24FpZ2Kxynell_DpHjqNGsvjzr4pn_sCZW_Zh7IuhuPtq1BvO_Qhr3GD0edCikCRvmXyduRelK7rMAl5SiQoQA4owH7XZgPb2UzcSrB-usqdQ5lUe6d4wevpSEM1M8AqgtmWwDMWfkSeWZ6iF5T_aAPRuLWJg5ate1CWzhwRqsS_gXl8hWNNKvB3-KRsLfRtw==&attredirects=0Published versio

Breaking de Morgan's law in counterfactual antecedents

The main goal of this paper is to investigate the relation between the meaning of a sentence and its truth conditions. We report on a comprehension experiment on counterfactual conditionals, based on a context in which a light is controlled by two switches. Our main finding is that the truth-conditionally equivalent clauses (i) "switch A or switch B is down" and (ii) "switch A and switch B are not both up" make different semantic contributions when embedded in a conditional antecedent. Assuming compositionality, this means that (i) and (ii) differ in meaning, which implies that the meaning of a sentential clause cannot be identified with its truth conditions. We show that our data have a clear explanation in inquisitive semantics: in a conditional antecedent, (i) introduces two distinct assumptions, while (ii) introduces only one. Independently of the complications stemming from disjunctive antecedents, our results also challenge analyses of counterfactuals in terms of minimal change from the actual state of affairs: we show that such analyses cannot account for our findings, regardless of what changes are considered minimal

The dynamic logic of stating and asking

Inquisitive dynamic epistemic logic (IDEL) extends standard public announcement logic incorporating ideas from inquisitive semantics. In IDEL, the standard public announcement action can be extended to a more general public utterance action, which may involve a statement or a question. While uttering a statement has the effect of a standard announcement, uttering a question typically leads to new issues being raised. In this paper, we investigate the logic of this general public utterance action. We find striking commonalities, and some differences, with standard public announcement logic. We show that dynamic modalities admit a set of reduction axioms, which allow us to turn any formula of IDEL into an equivalent formula of static inquisitive epistemic logic. This leads us to establish several complete axiomatizations of IDEL, corresponding to known axiomatizations of public announcement logic

Probabilities of conditionals: updating Adams

The 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 supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. We address two common objections to Adams' view: that the relevant probabilities are 'probabilities only in name', and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them

Question Meaning = Resolution Conditions

Traditional approaches to the semantics of questions analyze questions indirectly, via the notion of an answer. In recent work on inquisitive semantics, a different perspective is taken: the meaning of a question is equated with its resolution conditions, just like the meaning of a statement is traditionally equated with its truth-conditions. In this paper I argue that this proposal improves on previous approaches, combining the formal elegance and explanatory power of Groenendijk and Stokhof’s partition theory with the greater generality afforded by answer-set theories

Lifting conditionals to inquisitive semantics

This paper describes how any theory which assigns propositions to conditional sentences can be lifted to the setting of inquisitive semantics, where antecedents and consequents may be associated with multiple propositions. We show that the lifted account improves on the original account in two ways: first, it leads to a better analysis of disjunctive antecedents, which are treated as introducing multiple assumptions; second, it extends the original account to cover two further classes of conditional constructions, namely, unconditionals and conditional questions.

Inquisitive Semantics

There is an age-old tradition in linguistics and philosophy to identify the meaning of a entence with its truth-conditions. This can be explained by the fact that linguistic and philosophical investigations are usually carried out in a logical framework that was originally designed to characterize valid reasoning. Indeed, in order to determine whether an argument is valid, it suffices to know the truth-conditions of the premises and conclusion. However, argumentation is neither the sole, nor the primary function of language. One task that language more widely and ordinarily fulfils is to enable the exchange of information between conversational participants. Inquisitive semantics is a new logical framework for the analysis of this fundamental usage of language. Information exchange can be seen as a process of raising and resolving issues. Inquisitive semantics provides a new formal notion of issues, which makes it possible to model various concepts that are crucial for the analysis of linguistic information exchange in a more refined and more principled way than has been possible in previous frameworks. This book provides a detailed exposition of inquisitive semantics, and demonstrates its benefits with a range of applications in the semantic analysis of questions, coordination, modals, conditionals, and intonation