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This document presents a formula selection system for classical first order theorem proving based on the relevance of formulae for the proof of a conjecture. It is based on unifiability of predicates and is also able to use a linguistic approach for the selection. The scope of the technique is the reduction of the set of formulae and the increase of the amount of provable conjectures in a given time. Since the technique generates a subset of the formula set, it can be used as a preprocessor for automated theorem proving. The document contains the conception, implementation and evaluation of both selection concepts. While the one concept generates a search graph over the negation normal forms or Skolem normal forms of the given formulae, the linguistic concept analyses the formulae and determines frequencies of lexemes and uses a tf-idf weighting algorithm to determine the relevance of the formulae. Though the concept is built for first order logic, it is not limited to it. The concept can be used for higher order and modal logik, too, with minimal adoptions. The system was also evaluated at the world championship of automated theorem provers (CADE ATP Systems Competition, CASC-24) in combination with the leanCoP theorem prover and the evaluation of the results of the CASC and the benchmarks with the problems of the CASC of the year 2012 (CASC-J6) show that the concept of the system has positive impact to the performance of automated theorem provers. Also, the benchmarks with two different theorem provers which use different calculi have shown that the selection is independent from the calculus. Moreover, the concept of TEMPLAR has shown to be competitive to some extent with the concept of SinE and even helped one of the theorem provers to solve problems that were not (or slower) solved with SinE selection in the CASC. Finally, the evaluation implies that the combination of the unification based and linguistic selection yields more improved results though no optimisation was done for the problems.
This document presents an axiom selection technique for classic first order theorem proving based on the relevance of axioms for the proof of a conjecture. It is based on unifiability of predicates and does not need statistical information like symbol frequency. The scope of the technique is the reduction of the set of axioms and the increase of the amount of provable conjectures in a given time. Since the technique generates a subset of the axiom set, it can be used as a preprocessor for automated theorem proving. This technical report describes the conception, implementation and evaluation of ARDE. The selection method, which is based on a breadth-first graph search by unifiability of predicates, is a weakened form of the connection calculus and uses specialised variants or unifiability to speed up the selection. The implementation of the concept is evaluated with comparison to the results of the world championship of theorem provers of the year 2012 (CASC J6). It is shown that both the theorem prover leanCoP which uses the connection calculus and E which uses equality reasoning, can benefit from the selection approach. Also, the evaluation shows that the concept is applyable for theorem proving problems with thousands of formulae and that the selection is independent from the calculus used by the theorem prover.
Alles auf Anfang!
(2019)
Im Zuge der Bologna-Reform ist an Hochschulen vieles in Bewegung gekommen. Studium und Lehre sind stärker ins Blickfeld gerückt. Dabei kommt der Studieneingangsphase besondere Bedeutung zu, werden doch hier die Weichen für ein erfolgreiches Studium gestellt. Deshalb ist es verständlich, dass die Hauptanstrengungen der Hochschulen auf den Studieneingang gerichtet sind – ganz nach dem Motto: „Auf den Anfang kommt es an!“. Konsens herrscht dahingehend, dass der Studieneingang neu zu gestalten ist, doch beim „Wie?“ gibt es unterschiedliche Antworten. Zugleich wird immer deutlicher, dass eine wirksame Neugestaltung der Eingangsphase nur mit einer umfassenden Reform des Studiums gelingen kann.
Ziel des vierten Bandes der Potsdamer Beiträge zur Hochschulforschung ist es, eine Zwischenbilanz der Debatte zum Studieneingang zu ziehen. Auf der Basis empirischer Studien werden unterschiedliche Perspektiven auf den Studieneingang eingenommen und Empfehlungen zur Optimierung des Studieneingangs abgeleitet. Die zahlreichen Untersuchungsergebnisse Potsdamer Forschergruppen werden durch weitere nationale sowie internationale Perspektiven ergänzt. Der Band richtet sich an alle, die sich für die Entwicklung an Hochschulen interessieren.
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem prover and especially the functionality of the educational fragment. This currently supports working with terms of the untyped lambda calculus and addresses both undergraduate students and researchers. We show how the tool can be used to support the students' understanding of functional programming and discuss general problems related to the process of building theorem proving software that aims at supporting both research and education.