Related papers: Realizability algebras: a program to well order R
It is well understood that classification algorithms, for example, for deciding on loan applications, cannot be evaluated for fairness without taking context into account. We examine what can be learned from a fairness oracle equipped with…
We initiate the mathematical study of replicability as an algorithmic property in the context of reinforcement learning (RL). We focus on the fundamental setting of discounted tabular MDPs with access to a generative model. Inspired by…
We give a novel and effective criterion for algebraicity of rational normal analytic surfaces constructed from resolving the singularity of an irreducible curve-germ on $CP^2$ and contracting the strict transform of a given line and all but…
Reinforcement learning and classical planning are typically seen as two distinct problems, with differing formulations necessitating different solutions. Yet, when humans are given a task, regardless of the way it is specified, they can…
Elimination theory has many applications, in particular, it describes explicitly an image of a complex line under rational transformation and determines the number of common zeroes of two polynomials in one variable. We generalize classical…
We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
Realizability for knowledge representation formalisms studies the following question: given a semantics and a set of interpretations, is there a knowledge base whose semantics coincides exactly with the given interpretation set? We…
Classical planning aims to find a sequence of actions, a plan, that maps a starting state into one of the goal states. If a trajectory appears to be leading to the goal, should we prioritise exploring it? Seminal work in goal recognition…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
In arXiv:0905.1675, Nik Weaver proposed a novel intuitionistic formal theory of third-order arithmetic as a formalisation of his philosophical position known as mathematical conceptualism. In this paper, we will construct a realisability…
Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the…
Given a single (differential-algebraic) input-output equation, we present a method for finding different representations of the associated system in the form of rational realizations; these are dynamical systems with rational right-hand…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
We use the theory of bialgebras to provide the algebraic background for state space realization theorems for input-output maps of control systems. This allows us to consider from a common viewpoint classical results about formal state space…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
PECR is a formal system designed to explore the properties of computability of programs on a real-world computer. As such PECR incorporates the finite resources of the machine upon which a program is to be executed. The main features of the…
We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…
We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. In this paper we focus on the…