Related papers: Automated Theorem Proving for Prolog Verification
Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe…
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…
Automatically generated code is gaining traction recently, owing to the prevalence of Large Language Models (LLMs). Further, the AlphaProof initiative has demonstrated the possibility of using AI for general mathematical reasoning.…
Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…
The Diproche system, an automated proof checker for natural language proofs specifically adapted to the context of exercises for beginner's students similar to the Naproche system by Koepke, Schr\"oder, Cramer and others, uses a…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…
Automated Theorem Proving (ATP) is an established branch of Artificial Intelligence. The purpose of ATP is to design a system which can automatically figure out an algorithm either to prove or disprove a mathematical claim, on the basis of…
Ladder Logics is a programming language standardized in IEC 61131-3 and widely used for programming industrial Programmable Logic Controllers (PLC). A PLC program consists of inputs (whose values are given at runtime by factory sensors),…
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…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
{log} (read 'setlog') was born as a Constraint Logic Programming (CLP) language where sets and binary relations are first-class citizens, thus fostering set programming. Internally, {log} is a constraint satisfiability solver implementing…
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…
To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…
This work explores the application of deep learning, a machine learning technique that uses deep neural networks (DNN) in its core, to an automated theorem proving (ATP) problem. To this end, we construct a statistical model which…
We give a process for verifying numerical programs against their functional specifications. Our implementation is capable of automatically verifying programs against tight error bounds featuring common elementary functions. We demonstrate…
Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…
Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise…
Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers…
Termination is an important and well-studied property for logic programs. However, almost all approaches for automated termination analysis focus on definite logic programs, whereas real-world Prolog programs typically use the cut operator.…