Related papers: Definitional Quantifiers Realise Semantic Reasonin…
We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a…
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…
Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We…
Concept Induction refers to the problem of creating complex Description Logic class descriptions (i.e., TBox axioms) from instance examples (i.e., ABox data). In this paper we look particularly at the case where both a set of positive and 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…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…
Language models (LMs) can solve tasks such as answering questions about tables or images by writing programs. However, using primitive functions often leads to verbose and error-prone programs, and higher-level functions require expert…
Our goal is a modern approach to answering questions via systematic reasoning where answers are supported by human interpretable proof trees grounded in an NL corpus of authoritative facts. Such a system would help alleviate the challenges…
Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…
Large language models (LLMs) have recently demonstrated impressive performance on complex, multi-step reasoning tasks, especially when post-trained with outcome-rewarded reinforcement learning Guo et al. 2025. However, it has been observed…
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…
Mission-time Linear Temporal Logic (MLTL) is rapidly increasing in popularity as a specification logic, e.g., for runtime verification and model checking, driving a need for a trustworthy tool base for analyzing MLTL. In this work, we…
We present StepFun-Prover Preview, a large language model designed for formal theorem proving through tool-integrated reasoning. Using a reinforcement learning pipeline that incorporates tool-based interactions, StepFun-Prover can achieve…
Bhat et al. developed an inductive compiler that computes density functions for probability spaces described by programs in a simple probabilistic functional language. In this work, we implement such a compiler for a modified version of…
As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…
Explainable AI (XAI) in high-stakes domains should help stakeholders trust and verify system outputs. Yet Chain-of-Thought methods reason before concluding, and logical gaps or hallucinations can yield conclusions that do not reliably align…
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…