Advanced Proof Viewing in ProofTool

Sequent calculus is widely used for formalizing proofs. However, due to the proliferation of data, understanding the proofs of even simple mathematical arguments soon becomes impossible. Graphical user interfaces help in this matter, but since they normally utilize Gentzen's original notation, some of the problems persist. In this paper, we introduce a number of criteria for proof visualization which we have found out to be crucial for analyzing proofs. We then evaluate recent developments in tree visualization with regard to these criteria and propose the Sunburst Tree layout as a complement to the traditional tree structure. This layout constructs inferences as concentric circle arcs around the root inference, allowing the user to focus on the proof's structural content. Finally, we describe its integration into ProofTool and explain how it interacts with the Gentzen layout.Comment: In Proceedings UITP 2014, arXiv:1410.785

Enumerating All Maximal Clique-Partitions of an Undirected Graph

We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by assigning the vertices shared among maximal cliques, to belong to only one clique. This simple algorithm has the following drawbacks: (1) the search space is very large; (2) it finds some clique-partitions which are not maximal; and (3) some clique-partitions are found more than once. We propose two criteria to avoid these drawbacks. The outcome is an algorithm that explores a much smaller search space and guarantees that every maximal clique-partition is computed only once. The algorithm can be used in problems such as anti-unification with proximity relations or in resource allocation tasks when one looks for several alternative ways to allocate resources.Comment: In Proceedings FROM 2023, arXiv:2309.1295

Reasoning Methods in Semantic Web

Semantic Web is a collection of different technologies, where most of them is already standardized. The main purpose of these technologies is to describe semantic content of the web, i.e. their meaning and sense, in the format understood by computers. As a consequence, computer programs will be able to use more (human) knowledge to do assigned tasks. In this paper we overview the ontology and logic layers of the semantic web stack. Although ontology languages are standardized by W3C, there are still many problems remaining, which are related to reasoning over the ontologies. On the logic layer of the semantic web stack are considered unranked languages, where function and predicate symbols do not have a fixed arity. Such languages can naturally model XML documents and operations on them. In this paper we present survey of reasoning methods over such unranked languages

PROOFTOOL: a GUI for the GAPT Framework

This paper introduces PROOFTOOL, the graphical user interface for the General Architecture for Proof Theory (GAPT) framework. Its features are described with a focus not only on the visualization but also on the analysis and transformation of proofs and related tree-like structures, and its implementation is explained. Finally, PROOFTOOL is compared with three other graphical interfaces for proofs