2,421 research outputs found
Inadequacy of Modal Logic in Quantum Settings
We test the principles of classical modal logic in fully quantum settings.
Modal logic models our reasoning in multi-agent problems, and allows us to
solve puzzles like the muddy children paradox. The Frauchiger-Renner thought
experiment highlighted fundamental problems in applying classical reasoning
when quantum agents are involved; we take it as a guiding example to test the
axioms of classical modal logic. In doing so, we find a problem in the original
formulation of the Frauchiger-Renner theorem: a missing assumption about
unitarity of evolution is necessary to derive a contradiction and prove the
theorem. Adding this assumption clarifies how different interpretations of
quantum theory fit in, i.e., which properties they violate. Finally, we show
how most of the axioms of classical modal logic break down in quantum settings,
and attempt to generalize them. Namely, we introduce constructions of trust and
context, which highlight the importance of an exact structure of trust
relations between agents. We propose a challenge to the community: to find
conditions for the validity of trust relations, strong enough to exorcise the
paradox and weak enough to still recover classical logic.Comment: In Proceedings QPL 2018, arXiv:1901.0947
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
Aximo: automated axiomatic reasoning for information update
Aximo is a software written in C++ that verifies epistemic properties of dynamic scenarios in multi-agent systems. The underlying logic of our tool is based on the algebraic axiomatics of Dynamic Epistemic Logic. We also present a new theoretical result: the worst case complexity of the verification problem of Aximo
Geometric Aspects of Multiagent Systems
Recent advances in Multiagent Systems (MAS) and Epistemic Logic within
Distributed Systems Theory, have used various combinatorial structures that
model both the geometry of the systems and the Kripke model structure of models
for the logic. Examining one of the simpler versions of these models,
interpreted systems, and the related Kripke semantics of the logic (an
epistemic logic with -agents), the similarities with the geometric /
homotopy theoretic structure of groupoid atlases is striking. These latter
objects arise in problems within algebraic K-theory, an area of algebra linked
to the study of decomposition and normal form theorems in linear algebra. They
have a natural well structured notion of path and constructions of path
objects, etc., that yield a rich homotopy theory.Comment: 14 pages, 1 eps figure, prepared for GETCO200
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