Related papers: Object-Oriented Theorem Proving (OOTP): First Thou…
Approximation Fixpoint Theory (AFT) is a powerful theory covering various semantics of non-monotonic reasoning formalisms in knowledge representation such as Logic Programming and Answer Set Programming. Many semantics of such non-monotonic…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
For the right application, the use of programming paradigms such as functional or logic programming can enormously increase productivity in software development. But these powerful paradigms are tied to exotic programming languages, while…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
Automated theorem proving (ATP) has been a classical problem in artificial intelligence since its inception, yet it remains challenging due to its vast state and action space. Large language models (LLMs) have recently emerged as a…
We develop an inductive proof-technique to generate imperative programs for pointer data structures from behavioural specifications expressed in the Answer Set Programming (ASP) formalism. ASP is a non-monotonic logic based formalism that…
The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of…
Using formal tools in computer science to describe games is an interesting problem. We give games, exactly two person games, an axiomatic foundation based on the process algebra ACP (Algebra of Communicating Process). A fresh operator…
Programming is an integral part of computer science discipline. Every day the programming environment is not only rapidly growing but also changing and languages are constantly evolving. Learning of object-oriented paradigm is compulsory in…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
Context Oriented Programming (COP) concerns the ability of programs to adapt to changes in their running environment. A number of programming languages endowed with COP constructs and features have been developed. However, some foundational…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
The universal object oriented languages made programming more simple and efficient. In the article is considered possibilities of using similar methods in computer algebra. A clear and powerful universal language is useful if particular…
A simple dynamically-typed, (purely) object-oriented language is defined. A structural operational semantics as well as a Hoare-style program logic for reasoning about programs in the language in multiple notions of correctness are given.…
Task-oriented parsing (TOP) aims to convert natural language into machine-readable representations of specific tasks, such as setting an alarm. A popular approach to TOP is to apply seq2seq models to generate linearized parse trees. A more…
Multi-token prediction (MTP) has been proposed as an auxiliary objective to improve next-token prediction (NTP) in language model training but shows inconsistent improvements, underperforming in standard NLP benchmarks. We found MTP's exact…
G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers. The following has been done (and in this order): A detailed natural deduction…
The deep neural networks are known to be vulnerable to well-designed adversarial attacks. The most successful defense technique based on adversarial training (AT) can achieve optimal robustness against particular attacks but cannot…
Abstract reasoning, the ability to reason from the abstract essence of a problem, serves as a key to generalization in human reasoning. However, eliciting language models to perform reasoning with abstraction remains unexplored. This paper…