相关论文: Advanced Proof Viewing in ProofTool

This paper explores the connection between two central results in the proof theory of classical logic: Gentzen's cut-elimination for the sequent calculus and Herbrands "fundamental theorem". Starting from Miller's expansion-tree-proofs, a…

Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…

Graph Spectral Clustering methods (GSC) allow representing clusters of diverse shapes, densities, etc. However, the results of such algorithms, when applied e.g. to text documents, are hard to explain to the user, especially due to…

The popular bag of words assumption represents a document as a histogram of word occurrences. While computationally efficient, such a representation is unable to maintain any sequential information. We present a continuous and…

This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the…

Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata…

This paper introduces a refinement of the sequent calculus approach called cirquent calculus. While in Gentzen-style proof trees sibling (or cousin, etc.) sequents are disjoint sequences of formulas, in cirquent calculus they are permitted…

Network clustering requires making many decisions manually, such as the number of groups and a statistical model to be used. Even after filtering using an information criterion or regularizing with a nonparametric framework, we are commonly…

We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a…

This paper introduces ProofCloud, a proof retrieval engine for verified proofs in higher order logic. It provides a fast proof searching service for mathematicians and computer scientists for the reuse of proofs and proof packages. In…

Complex sequential decision-making planning problems, covering infinite states' space have been shown to be solvable by AlphaZero type of algorithms. Such an approach that trains a neural model while simulating projection of futures with a…

Connection calculi allow for very compact implementations of goal-directed proof search. We give an overview of our work related to connection tableaux calculi: First, we show optimised functional implementations of clausal and nonclausal…

We present a sequent-style proof system for provability logic GL that admits so-called circular proofs. For these proofs, the graph underlying a proof is not a finite tree but is allowed to contain cycles. As an application, we establish…

We consider the problem of formalizing the familiar notion of widening in abstract interpretation in higher-order logic. It turns out that many axioms of widening (e.g. widening sequences are ascending) are not useful for proving…

Fact checking is a challenging task because verifying the truthfulness of a claim requires reasoning about multiple retrievable evidence. In this work, we present a method suitable for reasoning about the semantic-level structure of…

Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…

Graphs are often used to model relationships between entities. The identification and visualization of clusters in graphs enable insight discovery in many application areas, such as life sciences and social sciences. Force-directed graph…

The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…

We apply the foundational proof certificate (FPC) framework to the problem of designing high-level outlines of proofs. The FPC framework provides a means to formally define and check a wide range of proof evidence. A focused proof system is…

Although we have seen a proliferation of algorithms for recommending visualizations, these algorithms are rarely compared with one another, making it difficult to ascertain which algorithm is best for a given visual analysis scenario.…