Related papers: A structure theorem for generalized-noncontextual …
The definition of 'classical state', and how it was used in earlier work to prove a decomposition theorem internally in the language of State Property Systems, presupposes as an additional datum an orthocomplementation on the property…
Despite the empirical success of foundation models, we do not have a systematic characterization of the representations that these models learn. In this paper, we establish the contexture theory. It shows that a large class of…
The infrastructure upon which the functioning of society depends is composed of complex ecosystems of systems. Consequently, we must reason about the properties of such ecosystems, which requires that we construct models of them. There are…
We discuss the role of propositions, truth, context and observers in scientific theories. We introduce the concept of generalized proposition and use it to define an algorithm for the classification of any scientific theory. The algorithm…
In this paper, we present a probabilistic adaptation of an Assume/Guarantee contract formalism. For the sake of generality, we assume that the extended state machines used in the contracts and implementations define sets of runs on a given…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
Objects or structures that are regular take uniform dimensions. Based on the concepts of regular models, our previous research work has developed a system of a regular ontology that models learning structures in a multiagent system for…
Recently a new impulse has been given to the experimental investigation of contextuality. In this paper we show that for a widely used definition of contextuality there can be no decisive experiment on the existence of contextuality. To…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
A quantum process encodes the causal structure that relates quantum operations performed in local laboratories. The process matrix formalism includes as special cases quantum mechanics on a fixed background space-time, but also allows for…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
We fill a gap in the study of contextuality by extending the sheaf-theoretic framework for non-locality by Abramsky and Brandenburger to deal with operational scenarios in the presence of arbitrary definite causal orders.
Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes. To overcome these difficulties, economists have introduced an interesting distinction between 'risk' and 'ambiguity'…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
The Principle of Complementarity of Probabilities based on of noncommutative probability is introduced.
Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must be placed on algorithmic procedures for obtaining numerical results subject to the experimental verifiability. For, a physical science is…
In the concluding remarks of Ontological Promiscuity Hobbs (1985) made what we believe to be a very insightful observation: given that semantics is an attempt at specifying the relation between language and the world, if "one can assume a…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally…
When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…