9,720 research outputs found
Game-based notions of locality over finite models
Locality notions in logic say that the truth value of a formula can be determined locally, by looking at the isomorphism type of a small neighborhood of its free variables. Such notions have proved to be useful in many applications. They all, however, refer to isomorphism of neighborhoods, which most local logics cannot test for. A more relaxed notion of locality says that the truth value of a formula is determined by what the logic itself can say about that small neighborhood. Or, since most logics are characterized by games, the truth value of a formula is determined by the type, with respect to a game, of that small neighborhood
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
A Characterization Theorem for a Modal Description Logic
Modal description logics feature modalities that capture dependence of
knowledge on parameters such as time, place, or the information state of
agents. E.g., the logic S5-ALC combines the standard description logic ALC with
an S5-modality that can be understood as an epistemic operator or as
representing (undirected) change. This logic embeds into a corresponding modal
first-order logic S5-FOL. We prove a modal characterization theorem for this
embedding, in analogy to results by van Benthem and Rosen relating ALC to
standard first-order logic: We show that S5-ALC with only local roles is, both
over finite and over unrestricted models, precisely the bisimulation invariant
fragment of S5-FOL, thus giving an exact description of the expressive power of
S5-ALC with only local roles
Bell nonlocality
Bell's 1964 theorem, which states that the predictions of quantum theory
cannot be accounted for by any local theory, represents one of the most
profound developments in the foundations of physics. In the last two decades,
Bell's theorem has been a central theme of research from a variety of
perspectives, mainly motivated by quantum information science, where the
nonlocality of quantum theory underpins many of the advantages afforded by a
quantum processing of information. The focus of this review is to a large
extent oriented by these later developments. We review the main concepts and
tools which have been developed to describe and study the nonlocality of
quantum theory, and which have raised this topic to the status of a full
sub-field of quantum information science.Comment: 65 pages, 7 figures. Final versio
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