Related papers: A program for the full axiom of choice

In program algebra, an algebraic theory of single-pass instruction sequences, three congruences on instruction sequences are paid attention to: instruction sequence congruence, structural congruence, and behavioural congruence. Sound and…

This paper presents PFLP, a library for probabilistic programming in the functional logic programming language Curry. It demonstrates how the concepts of a functional logic programming language support the implementation of a library for…

Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the…

Within the framework of Zermelo-Fraenkel set theory without the Axiom of Choice, we establish equivalents to the assertion "the union of a countable collection of finite sets is countable" in the context of metric spaces, probability…

This paper presents a comprehensive formalization of the von Neumann-Morgenstern (vNM) expected utility theorem using the Lean 4 interactive theorem prover. We implement the classical axioms of preference-completeness, transitivity,…

Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming…

While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…

Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…

The $\lambda\mu$-calculus plays a central role in the theory of programming languages as it extends the Curry-Howard correspondence to classical logic. A major drawback is that it does not satisfy B\"ohm's Theorem and it lacks the…

Given a conditional sentence "P=>Q" (if P then Q) and respective facts, four different types of inferences are observed in human reasoning. Affirming the antecedent (AA) (or modus ponens) reasons Q from P; affirming the consequent (AC)…

We lay out novel foundations for the computer-aided verification of guaranteed bounds on expected outcomes of imperative probabilistic programs featuring (i) general loops, (ii) continuous distributions, and (iii) conditioning. To handle…

This paper exposes a contradiction in the Zermelo-Fraenkel set theory with the axiom of choice (ZFC). While Godel's incompleteness theorems state that a consistent system cannot prove its consistency, they do not eliminate proofs using a…

We give a brief presentation of the capacity theory and show how it derives naturally a measurable selection theorem following the approach of Dellacherie (1972). Then we present the classical method to prove the dynamic programming of…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

We consider a dynamic programming (DP) approach to approximately solving an infinite-horizon constrained Markov decision process (CMDP) problem with a fixed initial-state for the expected total discounted-reward criterion with a…

We address the decision problem for a fragment of real analysis involving differentiable functions with continuous first derivatives. The proposed theory, besides the operators of Tarski's theory of reals, includes predicates for…

When the inverse of an algorithm is well-defined -- that is, when its output can be deterministically transformed into the input producing it -- we say that the algorithm is invertible. While one can describe an invertible algorithm using a…

Chance constrained programming (CCP) refers to a type of optimization problem with uncertain constraints that are satisfied with at least a prescribed probability level. In this work, we study the sample average approximation (SAA) of…

Computers are deterministic dynamical systems (CHAOS 19:033124, 2009). Among other things, that implies that one should be able to use deterministic forecast rules to predict their behavior. That statement is sometimes-but not always-true.…

Almost all modern imperative programming languages include operations for dynamically manipulating the heap, for example by allocating and deallocating objects, and by updating reference fields. In the presence of recursive procedures and…