Variations on a Theme: A Bibliography on Approaches to Theorem Proving Inspired From Satchmo

This articles is a structured bibliography on theorem provers, approaches to theorem proving, and theorem proving applications inspired from Satchmo, the model generation theorem prover developed in the mid 80es of the 20th century at ECRC, the European Computer- Industry Research Centre. Note that the bibliography given in this article is not exhaustive

Hypertableau Reasoning for Description Logics

We present a novel reasoning calculus for the description logic SHOIQ^+---a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableau-based reasoning calculi used in state-of-the-art reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions---a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over state-of-the-art reasoners on several well-known ontologies

Parallelizing Description Logic Reasoning

Description Logic has become one of the primary knowledge representation and reasoning methodologies during the last twenty years. A lot of areas are benefiting from description logic based technologies. Description logic reasoning algorithms and a number of optimization techniques for them play an important role and have been intensively researched. However, few of them have been systematically investigated in a concurrency context in spite of multi-processor computing facilities growing up. Meanwhile, semantic web, an application domain of description logic, is producing vast knowledge data on the Internet, which needs to be dealt with by using scalable solutions. This situation requires description logic reasoners to be endowed with reasoning scalability. This research introduced concurrent computing in two aspects: classification, and tableau-based description logic reasoning. Classification is a core description logic reasoning service. Over more than two decades many research efforts have been devoted to optimizing classification. Those classification optimization algorithms have shown their pragmatic effectiveness for sequential processing. However, as concurrent computing becomes widely available, new classification algorithms that are well suited to parallelization need to be developed. This need is further supported by the observation that most available OWL reasoners, which are usually based on tableau reasoning, can only utilize a single processor. Such an inadequacy often leads users working in ontology development to frustration, especially if their ontologies are complex and require long processing times. Classification service finds out all named concept subsumption relationships entailed in a knowledge base. Each subsumption test enrolls two concepts and is independent of the others. At most n^2 subsumption tests are needed for a knowledge base which contains n concepts. As the first contribution of this research, we developed an algorithm and a corresponding architecture showing that reasoning scalability can be gained by using concurrent computing. Further, this research investigated how concurrent computing can increase performance of tableau-based description logic reasoning algorithms. Tableau-based description logic reasoning decides a problem by constructing an AND-OR tree. Before this research, some research has shown the effectiveness of parallelizing processing disjunction branches of a tableau expansion tree. Our research has shown how reasoning scalability can be gained by processing conjunction branches of a tableau expansion tree. In addition, this research developed an algorithm, merge classification, that uses a divide and conquer strategy for parallelizing classification. This method applies concurrent computing to the more efficient classification algorithm, top-search & bottom-search, which has been adopted as a standard procedure for classification. Reasoning scalability can be observed in a number of real world cases by using this algorithm

Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic

This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL , in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book