Related papers: Realizing realizability results with classical con…
We combine several folklore observations to provide a working framework for iterating constructions which contradict the axiom of choice. We use this to define a model in which any kind of structural failure must fail with a proper class of…
Following the work of Lloyd Shapley on the Shapley value, and tangentially the work of Guillermo Owen, we offer an alternative non-probabilistic formulation of part of the work of Robert J. Weber in his 1978 paper "Probabilistic values for…
In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the…
We investigate learnability of possibilistic theories from entailments in light of Angluin's exact learning model. We consider cases in which only membership, only equivalence, and both kinds of queries can be posed by the learner. We then…
We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$…
We study how linear orders can be employed to realise choice functions for which the set of potential choices is restricted, i.e., the possible choice is not possible among the full powerset of all alternatives. In such restricted settings,…
Potentialism is the view that objects are successively generated in an incompletable process. A strict version of the view adds that truths are successively determined. Strict potentialism can be analyzed using two modalities: one for the…
The transition from the quantum to the classical world is not yet understood. Here we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except in some specific basis. But we have no…
Taking symmetric extensions can be considered as a generalisation of forcing, which produces a richer multiverse of models with and without the axiom of choice. We can study the structure of this multiverse using modal logic. In particular,…
The polynomial hierarchy has been widely studied in classical complexity theory. In this paper, we will generalize some commonly known results about the polynomial hierarchy to a version of the hierarchy extended to promise problems. This…
We introduce a systematic method to solve a type of Cartan's realization problem. Our method builds upon a new theory of Lie algebroids and Lie groupoids with structure group and connection. This approach allows to find local as well as…
The Complex Langevin (CL) method to simulate `complex probabilities', ideally produces expectation values for the observables that converge to a limit equal to the expectation values obtained with the original complex `probability' measure.…
Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of…
In this paper we examine the commutativity of ideal extensions. We introduce methods of constructing such extensions, in particular we construct a noncommutative ring T which contains a central and idempotent ideal I such that T/I is a…
In this paper we present a semantics for a linear algebraic lambda-calculus based on realizability. This semantics characterizes a notion of unitarity in the system, answering a long standing issue. We derive from the semantics a set of…
In this paper we extend Savage's theory of decision-making under uncertainty from a classical environment into a non-classical one. We formulate the corresponding axioms and provide representation theorems for qualitative measures and…
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object", "everything can possibly exist, unless it yields contradiction", "the ideal elements correctly determine…
We introduce a novel choice dataset, called joint choice, in which options and menus are multidimensional. In this general setting, we define a notion of choice separability, which requires that selections from some dimensions are never…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
It is an old idea to replace averages of observables with respect to a complex weight by expectation values with respect to a genuine probability measure on complexified space. This is precisely what one would like to get from complex…