18,397 research outputs found
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
Structural completeness in propositional logics of dependence
In this paper we prove that three of the main propositional logics of
dependence (including propositional dependence logic and inquisitive logic),
none of which is structural, are structurally complete with respect to a class
of substitutions under which the logics are closed. We obtain an analogues
result with respect to stable substitutions, for the negative variants of some
well-known intermediate logics, which are intermediate theories that are
closely related to inquisitive logic
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
Undefinability in Inquisitive Logic with Tensor
Logics based on team semantics, such as inquisitive logic and dependence logic, are not closed under uniform substitution. This leads to an interesting separation between expressive power and definability: it may be that an operator O can be added to a language without a gain in expressive power, yet O is not definable in that language. For instance, even though propositional inquisitive logic and propositional dependence logic have the same expressive power, inquisitive disjunction and implication are not definable in propositional dependence logic. A question that has been open for some time in this area is whether the tensor disjunction used in propositional dependence logic is definable in inquisitive logic. We settle this question in the negative. In fact, we show that extending the logical repertoire of inquisitive logic by means of tensor disjunction leads to an independent set of connectives; that is, no connective in the resulting logic is definable in terms of the others.Peer reviewe
Uniform Definability in Propositional Dependence Logic
Both propositional dependence logic and inquisitive logic are expressively
complete. As a consequence, every formula with intuitionistic disjunction or
intuitionistic implication can be translated equivalently into a formula in the
language of propositional dependence logic without these two connectives. We
show that although such a (non-compositional) translation exists, neither
intuitionistic disjunction nor intuitionistic implication is uniformly
definable in propositional dependence logic
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
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
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