Related papers: Tinker, tailor, solver, proof
There has been a recent surge in transformer-based architectures for learning on graphs, mainly motivated by attention as an effective learning mechanism and the desire to supersede handcrafted operators characteristic of message passing…
We explore the power of interactive proofs with a distributed verifier. In this setting, the verifier consists of $n$ nodes and a graph $G$ that defines their communication pattern. The prover is a single entity that communicates with all…
This paper applies t-SNE, a visualisation technique familiar from Deep Neural Network research to argumentation graphs by applying it to the output of graph embeddings generated using several different methods. It shows that such a…
Inductive theorem provers often diverge. This paper describes a simple critic, a computer program which monitors the construction of inductive proofs attempting to identify diverging proof attempts. Divergence is recognized by means of a…
Deciding which sub-tool to use for a given proof state requires expertise specific to each ITP. To mitigate this problem, we present PaMpeR, a Proof Method Recommendation system for Isabelle/HOL. Given a proof state, PaMpeR recommends proof…
Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified…
Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise…
This paper studies recommender systems with knowledge graphs, which can effectively address the problems of data sparsity and cold start. Recently, a variety of methods have been developed for this problem, which generally try to learn…
A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data.…
Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…
The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not…
Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…
This paper presents Holbert: a work-in-progress pedagogical proof assistant and online textbook platform, aimed at the educational use-case, specifically for the teaching of programming language theory. Holbert allows proof exercises and…
Network administration is an inherently complex task, in particular with regard to security. Using the Isabelle interactive proof assistant, we develop two automated, formally verified tools which help uncovering and preventing bugs in…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
In education there exists a tension between two modes of learning: traditional lecture-based instruction and more tinkering-based creative learning. In this paper, we outline our efforts as two Ph.D. students (who are skilled in…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
On signed social networks, balanced and unbalanced triangles are a critical motif due to their role as the foundations of Structural Balance Theory. The uses for these motifs have been extensively explored in networks with known edge signs,…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
Graphs, such as social networks, word co-occurrence networks, and communication networks, occur naturally in various real-world applications. Analyzing them yields insight into the structure of society, language, and different patterns of…