THE ∆P PROGRAMMING LANGUAGE: COMBINING IMPERATIVE, LOGICAL, AND PROBABILISTIC CAPABILITIES

Sergey Goncharov, Andrey Nechesov, Sviridenko Dmitry, Dmitry Kondratyev, Igor Anureev, Evgenii Vityaev, Natalia Garanina, Ivan Gorobets, Gulnara Yakhyaeva

Keywords: ΔP language, L = P problem, probabilistic programming, logic-probabilistic reasoning, trusted AI, explainable AI, decision support systems, digital twins, uncertainty quantification, task-based formalization, polynomial completeness, dynamic knowledge bases, IFP conditionals

TL;DR: The paper presents the ∆P programming language, a probabilistic extension of an imperative programming framework designed to support reasoning with both deterministic and probabilistic predicates.

Abstract: Probabilistic reasoning is an essential component of modern intelligent systems, especially in domains where uncertainty, incomplete knowledge, and stochastic processes must be modeled explicitly. This paper presents the ∆P programming language, a probabilistic extension of an imperative programming framework designed to support reasoning with both deterministic and probabilistic predicates. The language combines traditional programming constructs with mechanisms for expressing probabilistic knowledge and uncertainty in program logic. We describe the syntax and core constructs of ∆P, including constants, terms, predicates, declarations, and control statements. In addition, we formalize the operational semantics of the language, providing a precise definition of program execution and probabilistic evaluation. The paper also introduces the internal logical framework used for probabilistic reasoning within programs. A case study and several illustrative examples demonstrate how the proposed language can be used to model and analyze problems involving uncertainty. The presented approach aims to bridge the gap between classical imperative programming and probabilistic reasoning, offering a structured framework for building intelligent systems that require integrated logical and probabilistic computation.

Submission Number: 51