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To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
This tutorial provides an introduction to CPAchecker for users. CPAchecker is a flexible and configurable framework for software verification and testing. The framework provides many abstract domains, such as BDDs, explicit values,…
ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented…
With recent progress in the field of Explainable Artificial Intelligence (XAI) and increasing use in practice, the need for an evaluation of different XAI methods and their explanation quality in practical usage scenarios arises. For this…
Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…
Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…
Modular arithmetic is widely used in crytography and symbolic computation. This paper presents a vectorized Montgomery algorithm for modular multiplication, the key to fast modular arithmetic, that fully utilizes the SIMD instructions. We…
Viruses utilize various means to circumvent the immune detection in the biological systems. Several mathematical models have been investigated for the description of viral dynamics in the biological system of human and various other…
I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…
In the midst of widespread misinformation and disinformation through social media and the proliferation of AI-generated texts, it has become increasingly difficult for people to validate and trust information they encounter. Many…
We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…
The likelihood of an automated reasoning program being of substantial assistance for a wide spectrum of applications rests with the nature of the options and parameters it offers on which to base needed strategies and methodologies. This…
We have developed a web-based pedagogical proof assistant, the Proof Tree Builder, that lets you apply rules upwards from the initial goal in sequent calculus and Hoare logic for a simple imperative language. We equipped our tool with a…
The most promising recent methods for AI reasoning require applying variants of reinforcement learning (RL) either on rolled out trajectories from the LLMs, even for the step-wise rewards, or large quantities of human-annotated trajectory…
In argumentative writing, writers must brainstorm hierarchical writing goals, ensure the persuasiveness of their arguments, and revise and organize their plans through drafting. Recent advances in large language models (LLMs) have made…
To understand diverse natural language commands, virtual assistants today are trained with numerous labor-intensive, manually annotated sentences. This paper presents a methodology and the Genie toolkit that can handle new compound commands…
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
A system that could reliably identify and sum up the most important points of a conversation would be valuable in a wide variety of real-world contexts, from business meetings to medical consultations to customer service calls. Recent…