Related papers: Object-Oriented Theorem Proving (OOTP): First Thou…

Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…

Object-Oriented Programming (OOP) has become a crucial paradigm for managing the growing complexity of modern software systems, particularly in fields like machine learning, deep learning, large language models (LLM), and data analytics.…

Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve…

We find ourselves in the midst of an explosion in artificial intelligence research, particularly with large language models (LLMs). These models have diverse applications spanning finance, commonsense knowledge graphs, medicine, and visual…

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…

Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…

This article expands our work in [Ca16]. By its reliance on Turing computability, the classical theory of effectivity, along with effective reducibility and Weihrauch reducibility, is only applicable to objects that are either countable or…

State-machine based notations are ubiquitous in the description of component systems, particularly in the robotic domain. To ensure these systems are safe and predictable, formal verification techniques are important, and can be…

Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.…

Object oriented constraint programs (OOCPs) emerge as a leading evolution of constraint programming and artificial intelligence, first applied to a range of industrial applications called configuration problems. The rich variety of…

Pattern-Oriented Analysis and Design (POAD) is the practice of building complex software by applying proven designs to specific problem domains. Although a great deal of research and practice has been devoted to formalizing existing design…

Context. TypeState-Oriented Programming (TSOP) is a paradigm intended to help developers in the implementation and use of mutable objects whose public interface depends on their private state. Under this paradigm, well-typed programs are…

Automated theorem provers (ATPs) can disprove conjectures by saturating a set of clauses, but the resulting saturated sets are opaque certificates. In the unit equational fragment, a saturated set can in fact be read as a convergent rewrite…

A one-time program (OTP) works as follows: Alice provides Bob with the implementation of some function. Bob can have the function evaluated exclusively on a single input of his choosing. Once executed, the program will fail to evaluate on…

Dependent Object Types (DOT) is intended to be a core calculus for modelling Scala. Its distinguishing feature is abstract type members, fields in objects that hold types rather than values. Proving soundness of DOT has been surprisingly…

Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…

Answer Set Programming (ASP) is a powerful declarative programming paradigm commonly used for solving challenging search and optimization problems. The modeling languages of ASP are supported by sophisticated solving algorithms (solvers)…

The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…

While next-token prediction (NTP) has been the standard objective for training language models, it often struggles to capture global structure in reasoning tasks. Multi-token prediction (MTP) has recently emerged as a promising alternative,…

Despite the strong reasoning capabilities of large language models (LLMs), optimizing the execution efficiency of tensor programs remains challenging due to the need for precise, composable transformation decisions. Recent LLM-guided…