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We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
We give an overview and conceptual discussion of some of our results on contextuality and non-locality. We focus in particular on connections with the work of Itamar Pitowsky on correlation polytopes, Bell inequalities, and Boole's…
Contextuality has long been associated with topological properties. In this work, such a relationship is elevated to identification in the broader framework of generalized contextuality. We employ the usual identification of states,…
Entanglement is an useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and is not locally possible. We focus on orthogonal states, which can…
We present a bisimulation relation for neighbourhood spaces, a generalisation of topological spaces. We show that this notion, path preserving bisimulation, preserves formulas of the spatial logic SLCS. We then use this preservation result…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
In quantum mechanics, nonlocality (a violation of a Bell inequality) is intimately linked to complementarity, by which we mean that consistently assigning values to different observables at the same time is not possible. Nonlocality can…
Based on a clear ontology of material individuals, we analyze in detail the factual semantics of quantum theory, and argue that the basic mathematical formalism of quantum theory is just okay with (a certain form of ) realism and that it is…
Generalized topological spaces are not necessarily closed under finite intersections. Moreover, the whole universe does not need to be open. We use modified version of this framework to establish certain models for non-normal modal logics.…
Despite the wide use of explainability techniques to attempt to understand the behavior of Artificial Intelligence (AI), the generated explanations may not always be reliable. An explanation can appear plausible to humans but fail to…
The classical conformality is one of the possible candidates for explaining the gauge hierarchy of the Standard Model. We show that it is naturally obtained from the Coleman's theory on baby universe.
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
We observe that there is an example of an automorphism group of a model of an omega-stable theory---in fact, the prime model of an uncountably-categorical theory---that is not locally (OB), answering a question of C. Rosendal.
A 1964 paper by John Bell gave the first demonstration that quantum mechanics is incompatible with local hidden variables. There is an ongoing and vigorous debate on whether he relied on an assumption of determinism, or instead, as he later…
We derive the N=1 supersymmetric extension for a class of weakly nonlocal four dimensional gravitational theories.The construction is explicitly done in the superspace and the tree-level perturbative unitarity is explicitly proved both in…
Quantum nonlocality and contextuality are two phenomena stemming from nonclassical correlations. Whereas the former requires entanglement that is consumed in the measurement process the latter can occur for any state if one chooses a proper…
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…