Related papers: Forcing as a computational process
Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
This paper describes a neural semantic parser that maps natural language utterances onto logical forms which can be executed against a task-specific environment, such as a knowledge base or a database, to produce a response. The parser…
A forcing extension may create new isomorphisms between two models of a first order theory. Certain model theoretic constraints on the theory and other constraints on the forcing can prevent this pathology. A countable first order theory is…
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at…
Computer programs are often factored into pure components -- simple, total functions from inputs to outputs -- and components that may have side effects -- errors, changes to memory, parallel threads, abortion of the current loop, etc. We…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
We deal with an iteration theorem of forcing notion with a kind of countable support of nice enough forcing notion which is proper aleph_2-c.c. forcing notions. We then look at some special cases (Q_D 's preceded by random forcing).
We characterize when a subfactor $N\subseteq M$ is oracle computable relative to a presentation of the ambient factor $M$ in terms of computability of the Jones basic construction, in terms of computable Pismner-Popa bases, and in terms of…
We initiate the effective metric structure theory of Keisler randomizations. We show that a classical countable structure $\mathcal{M}$ has a decidable presentation if and only if its Borel randomization $\mathcal{M}^{[0,1)}$ has a…
This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular…
Several families of continual learning techniques have been proposed to alleviate catastrophic interference in deep neural network training on non-stationary data. However, a comprehensive comparison and analysis of limitations remains…
An often used model for quantum theory is to associate to every physical system a C*-algebra. From a physical point of view it is unclear why operator algebras would form a good description of nature. In this paper, we find a set of…
We present a simple numerical scheme for perturbation theory (PT) calculations of large-scale structure. Solving the evolution equations for perturbations numerically, we construct the PT kernels as building blocks of statistical…
The Functional Machine Calculus (FMC) was recently introduced as a generalization of the lambda-calculus to include higher-order global state, probabilistic and non-deterministic choice, and input and output, while retaining confluence. The…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…
We generalize the Umbral Calculus of G-C. Rota by studying not only sequences of polynomials and inverse power series, or even the logarithms studied in, but instead we study sequences of formal expressions involving the iterated logarithms…
Chung, Graham and Wilson defined a set of graphs $\mathcal{H}$ to be forcing, if any sequence of graphs $\{G_n\}_{n \geq 0}$ with $|G_n| = n$ must be quasirandom, whenever $hom(H, G_n)= (p^{|E(H)|}+o(1))n^{|V(H)|}$ for every $H \in…
Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…