Related papers: Automated Theorem Proving for Prolog Verification
The application of automatic theorem provers to discharge proof obligations is necessary to apply formal methods in an efficient manner. Tools supporting formal methods, such as Atelier~B, generate proof obligations fully automatically.…
Nondeterminism in scheduling is the cardinal reason for difficulty in proving correctness of concurrent programs. A powerful proof strategy was recently proposed [6] to show the correctness of such programs. The approach captured data-flow…
Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve…
Description Logics (DLs) are a family of languages used for the representation and reasoning on the knowledge of an application domain, in a structured and formal manner. In order to achieve this objective, several provers, such as RACER…
Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed at combining statistical and logical knowledge representation and inference. A key…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…
Using an interactive theorem prover to reason about programs involves a sequence of interactions where the user challenges the theorem prover with conjectures. Invariably, many of the conjectures posed are in fact false, and users often…
Proof engineering is notoriously labor-intensive: proofs that are straightforward on paper often require lengthy scripts in theorem provers. Recent advances in large language models (LLMs) create new opportunities for proof automation:…
Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…
Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to…
We consider the problem of automated reasoning about dynamically manipulated data structures. The state-of-the-art methods are limited to the unfold-and-match (U+M) paradigm, where predicates are transformed via (un)folding operations…
State of the art analyzers in the Logic Programming (LP) paradigm are nowadays mature and sophisticated. They allow inferring a wide variety of global properties including termination, bounds on resource consumption, etc. The aim of this…
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…
This paper introduces ExKLoP, a novel framework designed to evaluate how effectively Large Language Models (LLMs) integrate expert knowledge into logical reasoning systems. This capability is especially valuable in engineering, where expert…
This EPTCS volume collects the post-proceedings of the 10th International Workshop On User Interfaces for Theorem Provers (UITP 2012), held as part of the Conferences on Intelligent Computer Mathematics (CICM 2012) in Bremen on July 11th…
Neural symbolic processing aims to combine the generalization of logical learning approaches and the performance of neural networks. The Neural Theorem Proving (NTP) model by Rocktaschel et al (2017) learns embeddings for concepts and…
Natural language explanations represent a proxy for evaluating explanation-based and multi-step Natural Language Inference (NLI) models. However, assessing the validity of explanations for NLI is challenging as it typically involves the…
The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof…
TLAPS, the TLA+ proof system, is a platform for the development and mechanical verification of TLA+ proofs written in a declarative style requiring little background beyond elementary mathematics. The language supports hierarchical and…