Related papers: Primal implication as encryption

Research on Symbolic Probabilistic Inference (SPI) [2, 3] has provided an algorithm for resolving general queries in Bayesian networks. SPI applies the concept of dependency directed backward search to probabilistic inference, and is…

There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…

Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its…

Let \phi be a first order formula and M be a countable model. \phi^M denotes the set of all assignments that satisfy \phi in M. Let M, N be countable models. A formula \phi distinguishes these models if |\phi^M|\neq |\phi^N|. We show that…

We present an illative system I_s of classical higher-order logic with subtyping and basic inductive types. The system I_s allows for direct definitions of partial and general recursive functions, and provides means for handling functions…

Let $\varphi\colon\Gamma\to G$ be a homomorphism of groups. In this paper we introduce the notion of a subnormal map (the inclusion of a subnormal subgroup into a group being a basic prototype). We then consider factorizations…

We show that the principal types of the closed terms of the affine fragment of $\lambda$-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry…

Indifferentiability is a popular cryptographic paradigm for analyzing the security of ideal objects -- both in a classical as well as in a quantum world. It is typically stated in the form of a composable and simulation-based definition,…

Quantum cryptography leverages many unique features of quantum information in order to construct cryptographic primitives that are oftentimes impossible classically. In this work, we build on the no-cloning principle of quantum mechanics…

This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of…

Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of…

We show that the classical interpretations of Tarski's inductive definitions actually allow us to define the satisfaction and truth of the quantified formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers…

In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…

Are certain cognitive biases mathematically inevitable consequences of sequential information processing? We prove that primacy effects, anchoring, and order-dependence are architecturally necessary in autoregressive language models due to…

We argue that progress toward AGI is theory limited rather than data or scale limited. Building on the critical rationalism of Popper and Deutsch, we challenge the Platonic Representation Hypothesis. Observationally equivalent worlds can…

A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic…

We establish a connection between two results in the literature on probabilistic semantics: a formulation of De Finetti's theorem in the language of category theory due to Jacobs and Staton, and the generic construction of the free…

We are interested in the problem of translating between two representations of closure systems, namely implicational bases and meet-irreducible elements. Albeit its importance, the problem is open. Motivated by this problem, we introduce…

Proofs (sequent calculus, natural deduction) and imperative algorithms (pseudocodes) are two well-known coexisting concepts. Then what is their relationship? Our answer is that \[ imperative\ algorithms\ =\ proofs\ with\ cuts \] This…

We study the notion of conservative translation between logics introduced by Feitosa and D'Ottaviano. We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set…