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See detailComputational Metaphysics
Benzmüller, Christoph UL; Wisniewski, Max; Steen, Alexander UL

Report (2015)

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See detailEfficient Data Structures for Automated Theorem Proving in Expressive Higher-Order Logics
Steen, Alexander UL

Bachelor/master dissertation (2014)

Church's Simple Theory of Types (STT), also referred to as classical higher-order logik, is an elegant and expressive formal system built on top of the simply typed λ-calculus. Its mechanisms of explicit ... [more ▼]

Church's Simple Theory of Types (STT), also referred to as classical higher-order logik, is an elegant and expressive formal system built on top of the simply typed λ-calculus. Its mechanisms of explicit binding and quantification over arbitrary sets and functions allow the representation of complex mathematical concepts and formulae in a concise and unambiguous manner. Higher-order automated theorem proving (ATP) has recently made major progress and several sophisticated ATP systems for higher-order logic have been developed, including Satallax, Osabelle/HOL and LEO-II. Still, higher-order theorem proving is not as mature as its first-order counterpart, and robust implementation techniques for efficient data structures are scarce. In this thesis, a higher-order term representation based upon the polymorphically typed λ-calculus is presented. This term representation employs spine notation, explicit substitutions and perfect term sharing for efficient term traversal, fast β-normalization and reuse of already constructed terms, respectively. An evaluation of the term representation is performed on the basis of a heterogeneous benchmark set. It shows that while the presented term data structure performs quite well in general, the normalization results indicate that a context dependent choice of reduction strategies is beneficial. A term indexing data structure for fast term retrieval based on various low-level criteria is presented and discussed. It supports symbol-based term retrieval, indexing of terms via structural properties, and subterm indexing. [less ▲]

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See detailThe Leo-III Project
Wisniewski, Max; Steen, Alexander UL; Benzmüller, Christoph UL

in Bolotov, Alexander; Kerber, Manfred (Eds.) Proceedings of the Joint Automated Reasoning Workshop and Deduktionstreffen: As part of the Vienna Summer of Logic – IJCAR 23-24 July 2014 (2014)

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See detailGeneration and State-Space Reduction of Program Graphs for Non-deterministic Programs
Steen, Alexander UL

Bachelor/master dissertation (2013)

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