Related papers: Proof Generation from Delta-Decisions

Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…

Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…

We present a method of generating first-order logic statements whose complexity can be controlled along multiple dimensions. We use this method to automatically create several datasets consisting of questions asking for the truth or falsity…

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…

Counterfactual reasoning, a hallmark of intelligence, consists of three steps: inferring latent variables from observations (abduction), constructing alternatives (interventions), and predicting their outcomes (prediction). This skill is…

The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…

Verification proofs encode complete program behavior, yet we discard them after checking correctness. We present compiling by proving, a paradigm that transforms these proofs into optimized execution rules. By constructing All-Path…

Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…

Automated testing tools typically create test cases that are different from what human testers create. This often makes the tools less effective, the created tests harder to understand, and thus results in tools providing less support to…

We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…

Assisting LLMs with code generation improved their performance on mathematical reasoning tasks. However, the evaluation of code-assisted LLMs is generally restricted to execution correctness, lacking a rigorous evaluation of their generated…

Argument systems are based on the idea that one can construct arguments for propositions; i.e., structured reasons justifying the belief in a proposition. Using defeasible rules, arguments need not be valid in all circumstances, therefore,…

LLMs can be unpredictable, as even slight alterations to the prompt can cause the output to change in unexpected ways. Thus, the ability of models to accurately explain their behavior is critical, especially in high-stakes settings. One…

We present verification methods for logic programs with delay declarations. The verified properties are termination and freedom from errors related to built-ins. Concerning termination, we present two approaches. The first approach tries to…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

Verification methods based on SAT, SMT, and Theorem Proving often rely on proofs of unsatisfiability as a powerful tool to extract information in order to reduce the overall effort. For example a proof may be traversed to identify a minimal…

Recent work has shown that Large Language Models (LLMs) are not only a suitable tool for code generation but also capable of generating annotation-based code specifications. Scaling these methodologies may allow us to deduce provable…

One problem to solve in the context of information fusion, decision-making, and other artificial intelligence challenges is to compute justified beliefs based on evidence. In real-life examples, this evidence may be inconsistent,…