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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.
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.
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.
Model-derived relationships between chlorophyll a (Chl-a) and nutrients and temperature have fundamental implications for understanding complex interactions among water quality measures used for lake classification, yet accuracy comparisons of different approaches are scarce. Here, we (1) compared Chl-a model performances across linear and nonlinear statistical approaches; (2) evaluated single and combined effects of nutrients, depth, and temperature as lake surface water temperature (LSWT) or altitude on Chl-a; and (3) investigated the reliability of the best water quality model across 13 lakes from perialpine and central Balkan mountain regions. Chl-a was modelled using in situ water quality data from 157 European lakes; elevation data and LSWT in situ data were complemented by remote sensing measurements. Nonlinear approaches performed better, implying complex relationships between Chl-a and the explanatory variables. Boosted regression trees, as the best performing approach, accommodated interactions among predictor variables. Chl-a-nutrient relationships were characterized by sigmoidal curves, with total phosphorus having the largest explanatory power for our study region. In comparison with LSWT, utilization of altitude, the often-used temperature surrogate, led to different influence directions but similar predictive performances. These results support utilizing altitude in models for Chl-a predictions. Compared to Chl-a observations, Chl-a predictions of the best performing approach for mountain lakes (oligotrophic-eutrophic) led to minor differences in trophic state categorizations. Our findings suggest that both models with LSWT and altitude are appropriate for water quality predictions of lakes in mountain regions and emphasize the importance of incorporating interactions among variables when facing lake management challenges.
The “HPI Future SOC Lab” is a cooperation of the Hasso Plattner Institute (HPI) and industry partners. Its mission is to enable and promote exchange and interaction between the research community and the industry partners.
The HPI Future SOC Lab provides researchers with free of charge access to a complete infrastructure of state of the art hard and software. This infrastructure includes components, which might be too expensive for an ordinary research environment, such as servers with up to 64 cores and 2 TB main memory. The offerings address researchers particularly from but not limited to the areas of computer science and business information systems. Main areas of research include cloud computing, parallelization, and In-Memory technologies.
This technical report presents results of research projects executed in 2018. Selected projects have presented their results on April 17th and November 14th 2017 at the Future SOC Lab Day events.