Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

How To Efficiently Implement An OSHL-Based Automatic Theorem Prover

Ordered Semantic Hyper-linking (OSHL) is a general-purpose instance-based first-order automated theorem proving algorithm. Although OSHL has many useful properties, previous implementations of OSHL were not very efficient. The implementation of such a theorem prover differs from other more traditional programs in that a lot of its subroutines are more mathematical than procedural. The low performance of previous implementations prevents us from evaluating how the proof strategy used in OSHL matches up against other theorem proving strategies. This dissertation addresses this problem on three levels. First, an abstract, generalized version genOSHL is defined which captures the essential features of OSHL and for which the soundness and completeness are proved. This gives genOSHL the flexibility to be tweaked while still preserving soundness and completeness. A type inference algorithm is introduced which allows genOSHL to possibly reduce its search space while still preserving the soundness and completeness. Second, incOSHL, a specialized version of genOSHL, which differs from the original OSHL algorithm, is defined by specializing genOSHL. Its soundness of completeness follows from that of genOSHL. Third, an embedded programming language called STACK EL, which allows managing program states and their dependencies on global mutable data, is designed and implemented. STACK EL allows our prover to generate instances incrementally. We also study the performance of our incremental theorem prover that implements incOSHL.Doctor of Philosoph

Proceedings

The CADE ATP System Computer (CASC) evaluates the performance of sound, fully automatic, classical first-order logic, ATP systems. The evaluation is in terms of the number of problems solved, the number of acceptable proofs and models produced, and the average runtime for problems solved, in the context of a bounded number of eligible problems chosen from the TPTP problem library, and a specified time limit for each solution attempt. The 3rd IJCAR ATP System Competition (CASC-J3) was held on 18th August 2006. The design of the competition and it’s rules, and information regarding the competing systems, are provided in this report.