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

Argumentation-Based Contract Monitoring in Uncertain Domains

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Reasoning about Uncertain Information and Conflict Resolution through Trust Revision

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Bootstrapping trust evaluations through stereotypes

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A general framework for consistent logical reasoning in Wigner's friend scenarios: subjective perspectives of agents within a single quantum circuit

It is natural to expect a complete physical theory to have the ability to consistently model agents as physical systems of the theory. In [Nat. Comms. 9, 3711 (2018)], Frauchiger and Renner (FR) claim to show that when agents in quantum theory reason about each other's knowledge in a certain Wigner's friend scenario, they arrive at a logical contradiction. In light of this, Renner often poses the challenge: provide a set of reasoning rules that can be used to program quantum computers that may act as agents, which are (a) logically consistent (b) generalise to arbitrary Wigner's friend scenarios (c) efficiently programmable and (d) consistent with the temporal order of the protocol. Here we develop a general framework where we show that every logical Wigner's friend scenario (LWFS) can be mapped to a single temporally ordered quantum circuit, which allows agents in any LWFS to reason in a way that meets all four criteria of the challenge. Importantly, our framework achieves this general resolution without modifying classical logic or unitary quantum evolution or the Born rule, while allowing agents' perspectives to be fundamentally subjective. We analyse the FR protocol in detail, showing how the apparent paradox is resolved there. We show that apparent logical contradictions in any LWFS only arise when ignoring the choice of Heisenberg cut in scenarios where this choice does matter, and taking this dependence into account will always resolve the apparent paradox. Our results establish that universal applicability of quantum theory does not pose any threat to multi-agent logical reasoning and we discuss the implications of these results for FR's no-go theorem. Moreover, our formalism suggests the possibility of a truly relational and operational description of Wigner's friend scenarios that is consistent with quantum theory as well as probability theory applied to measurement outcomes.Comment: 33 + 14 pages, 10 figure

On the emergent Semantic Web and overlooked issues

The emergent Semantic Web, despite being in its infancy, has already received a lotof attention from academia and industry. This resulted in an abundance of prototype systems and discussion most of which are centred around the underlying infrastructure. However, when we critically review the work done to date we realise that there is little discussion with respect to the vision of the Semantic Web. In particular, there is an observed dearth of discussion on how to deliver knowledge sharing in an environment such as the Semantic Web in effective and efficient manners. There are a lot of overlooked issues, associated with agents and trust to hidden assumptions made with respect to knowledge representation and robust reasoning in a distributed environment. These issues could potentially hinder further development if not considered at the early stages of designing Semantic Web systems. In this perspectives paper, we aim to help engineers and practitioners of the Semantic Web by raising awareness of these issues