Related papers: Towards Intuitive Reasoning in Axiomatic Geometry
Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…
In a case study we investigate whether off the shelf higher-order theorem provers and model generators can be employed to automate reasoning in and about quantified multimodal logics. In our experiments we exploit the new TPTP…
We describe an experiment in large-scale autoformalization of algebraic topology in an Interactive Theorem Proving (ITP) environment, where the workload is distributed among multiple LLM-based coding agents. Rather than relying on static…
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…
Geometric embedding methods have shown to be useful for multi-hop reasoning on knowledge graphs by mapping entities and logical operations to geometric regions and geometric transformations, respectively. Geometric embeddings provide direct…
Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the…
Diproche ("Didactical Proof Checking") is an automatic system for supporting the acquistion of elementary proving skills in the initial phase of university education in mathematics. A key feature of Diproche - which is designed by the…
Although there are several systems that successfully generate construction steps for ruler and compass construction problems, none of them provides readable synthetic correctness proofs for generated constructions. In the present work, we…
In this article we discuss how abstraction boundaries can help tame complexity in mathematical research, with the help of an interactive theorem prover. While many of the ideas we present here have been used implicitly by mathematicians for…
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…
Recent work on activation and latent steering has demonstrated that modifying internal representations can effectively guide large language models (LLMs) toward improved reasoning and efficiency without additional training. However, most…
Powerful sentence encoders trained for multiple languages are on the rise. These systems are capable of embedding a wide range of linguistic properties into vector representations. While explicit probing tasks can be used to verify the…
Isabelle/PIDE has emerged over more than 10 years as the standard Prover IDE for interactive theorem proving in Isabelle. The well-established Archive of Formal Proofs (AFP) testifies the success of such applications of formalized…
Multi-trait automated essay scoring (AES) systems provide a fine-grained evaluation of an essay's diverse aspects. While they excel in scoring, prior systems fail to explain why specific trait scores are assigned. This lack of transparency…
Answer Set Programming (ASP) is a prominent problem-modeling and solving framework, whose solutions are called answer sets. Epistemic logic programs (ELP) extend ASP to reason about all or some answer sets. Solutions to an ELP can be seen…
The rapid growth of AI-generated imagery has blurred the boundary between real and synthetic content, raising practical concerns for digital integrity. Vision-language models (VLMs) can provide natural language explanations, but standard…
Modern vision-based world models can represent observations as compact yet expressive latent manifolds, but fast goal-oriented planning in these spaces remains challenging. This raises a central question: when does a learned representation…
We introduce and discuss, through a computational algebraic geometry approach, the automatic reasoning handling of propositions that are simultaneously true and false over some relevant collections of instances. A rigorous, algorithmic…
Epistemic protocol specifications allow programs, for settings in which multiple agents act with incomplete information, to be described in terms of how actions are related to what the agents know. They are a variant of the knowledge-based…
The broader goal of this research, on the one hand, is to obtain the State of the Art in Automated Test Production (ATP), to find the open questions and related problems and to track the progress of researchers in the field, and on the…