Related papers: Mechanization of Separation in Generic Extensions
In this paper, we propose the use of interactive theorem proving for explainable machine learning. After presenting our proposition, we illustrate it on the dedicated application of explaining security attacks using the Isabelle…
In this paper we exploit the structural properties of standard and non-standard models of set theory to produce models of set theory admitting automorphisms that are well-behaved along an initial segment of their ordinals. $\mathrm{NFU}$ is…
We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions.…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
In the case of systems composed of identical particles, a typical instance in quantum statistical mechanics, the standard approach to separability and entanglement ought to be reformulated and rephrased in terms of correlations between…
We present three natural combinatorial properties for class forcing notions, which imply the forcing theorem to hold. We then show that all known sufficent conditions for the forcing theorem (except for the forcing theorem itself),…
Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities.…
We show how to express intuitionistic Zermelo set theory in deduction modulo (i.e. by replacing its axioms by rewrite rules) in such a way that the corresponding notion of proof enjoys the normalization property. To do so, we first rephrase…
We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three…
An algebraic framework in which to study infinite sums is proposed, complementing and augmenting the usual topological tools. The framework subsumes numerous examples in the literature. It is developed using many varied examples, with a…
According to the principle of compositional generalization, the meaning of a complex expression can be understood as a function of the meaning of its parts and of how they are combined. This principle is crucial for human language…
Forking is a central notion of model theory, generalizing linear independence in vector spaces and algebraic independence in fields. We develop the theory of forking in abstract, category-theoretic terms, for reasons both practical (we…
We study the effective versions of several notions related to incompleteness, undecidability and inseparability along the lines of Pour-El's insights. Firstly, we strengthen Pour-El's theorem on the equivalence between effective essential…
When reasoning about formal objects whose structures involve binding, it is often necessary to analyze expressions relative to a context that associates types, values, and other related attributes with variables that appear free in the…
Forcing axioms are generalizations of Baire category principles that allow one to intersect more dense open sets and to do so in a wider variety of circumstances. In this paper we introduce two new forcing axioms related to posets which…
In many expert and everyday reasoning contexts it is very useful to reason on the basis of defeasible assumptions. For instance, if the information at hand is incomplete we often use plausible assumptions, or if the information is…
We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When…
The separation between two theorems in reverse mathematics is usually done by constructing a Turing ideal satisfying a theorem P and avoiding the solutions to a fixed instance of a theorem Q. Lerman, Solomon and Towsner introduced a forcing…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
Category theory is famous for its innovative way of thinking of concepts by their descriptions, in particular by establishing universal properties. Concepts that can be characterized in a universal way receive a certain quality seal, which…