The Dynamics of Group Knowledge and Belief

5th International Workshop On Philosophy and Logic of Social Reality. 15-17 November 2019.Hokkaido University, Sapporo, Japa

A Topos Perspective on State-Vector Reduction

A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all $M$-sets, where $M$ is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way. However, the formalism also suggests a new way of constructing a `neo-realist' interpretation of quantum theory in which the truth values of propositions are determined by the actions of the monoid of strings of finite projection operators. By these means, a novel topos perspective is gained on the concept of state-vector reduction

A topos perspective on the Kochen-Specker theorem: II. Conceptual Aspects, and Classical Analogues:

In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; and in part mathematical---the valuation arises naturally in the topos theory of presheaves. This paper discusses the conceptual aspects of this proposal. We also undertake two other tasks. First, we explain how the proposed valuations could arise much more generally than just in quantum physics; in particular, they arise as naturally in classical physics. Second, we give another motivation for such valuations (that applies equally to classical and quantum physics). This arises from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition.Comment: Small changes and correction

Mightyl: A compositional translation from mitl to timed automata

Metric Interval Temporal Logic (MITL) was first proposed in the early 1990s as a specification formalism for real-time systems. Apart from its appealing intuitive syntax, there are also theoretical evidences that make MITL a prime real-time counterpart of Linear Temporal Logic (LTL). Unfortunately, the tool support for MITL verification is still lacking to this day. In this paper, we propose a new construction from MITL to timed automata via very-weak one-clock alternating timed automata. Our construction subsumes the well-known construction from LTL to Büchi automata by Gastin and Oddoux and yet has the additional benefits of being compositional and integrating easily with existing tools. We implement the construction in our new tool MightyL and report on experiments using Uppaal and LTSmin as back-ends

Classical Yang-Baxter equation from beta-supergravity

Yang-Baxter deformations of superstring sigma-models have recently inspired a supergravity solution generating technique. Using the open/closed string map and a Killing bi-vector as a deformation parameter, new solutions can be built, such that the (generalised) supergravity field equations were conjectured to always reduce to the classical Yang-Baxter equation (CYBE). In this work we provide a proof of this conjecture, using a systematic approach based on the so-called $\beta$-supergravity, which is a dynamical theory for the field $\beta^{mn}$ instead of the NSNS 2-form $b_{mn}$.Comment: 19 pages; v2: references updated; v3: published versio