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

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

The Expressive Power of Modal Dependence Logic

We study the expressive power of various modal logics with team semantics. We show that exactly the properties of teams that are downward closed and closed under team k-bisimulation, for some finite k, are definable in modal logic extended with intuitionistic disjunction. Furthermore, we show that the expressive power of modal logic with intuitionistic disjunction and extended modal dependence logic coincide. Finally we establish that any translation from extended modal dependence logic into modal logic with intuitionistic disjunction increases the size of some formulas exponentially.Comment: 19 page

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

Ignorance Implicatures and Non-doxastic Attitude Verbs

This paper is about conjunctions and disjunctions in the scope of non-doxastic atti- tude verbs. These constructions generate a certain type of ignorance implicature. I argue that the best way to account for these implicatures is by appealing to a notion of contex- tual redundancy (Schlenker, 2008; Fox, 2008; Mayr and Romoli, 2016). This pragmatic approach to ignorance implicatures is contrasted with a semantic account of disjunctions under `wonder' that appeals to exhaustication (Roelofsen and Uegaki, 2016). I argue that exhaustication-based theories cannot handle embedded conjunctions, so a pragmatic account of ignorance implicatures is superior

Complexity of validity for propositional dependence logics

We study the validity problem for propositional dependence logic, modal dependence logic and extended modal dependence logic. We show that the validity problem for propositional dependence logic is NEXPTIME-complete. In addition, we establish that the corresponding problem for modal dependence logic and extended modal dependence logic is NEXPTIME-hard and in NEXPTIME^NP.Comment: In Proceedings GandALF 2014, arXiv:1408.556

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