Quantified Multimodal Logics in Simple Type Theory
- Christoph Benzmüller, Lawrence Charles Paulson
- Computer ScienceLogica Universalis
- 14 May 2009
The embedding supports the application of off-the-shelf higher-order theorem provers for reasoning within and about quantified multimodal logics and provides a starting point for further logic embeddings and their combinations in simple type theory.
LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description)
- Christoph Benzmüller, Lawrence Charles Paulson, Frank Theiss, Arnaud Fietzke
- Computer ScienceInternational Joint Conference on Automated…
- 12 August 2008
The improved performance of LEO-II, especially in comparison to its predecessor LEO, is due to several novel features including the exploitation of term sharing and term indexing techniques, support for primitive equality reasoning, and improved heuristics at the calculus level.
Automating Gödel's Ontological Proof of God's Existence with Higher-order Automated Theorem Provers
- Christoph Benzmüller, B. W. Paleo
- PhilosophyEuropean Conference on Artificial Intelligence
- 18 August 2014
The background theory of the work presented here offers a novel perspective towards a computational theoretical philosophy in Kurt Godel's ontological argument for God's existence.
System Description: LEO - A Higher-Order Theorem Prover
- Christoph Benzmüller, M. Kohlhase
- Computer ScienceCADE
- 5 July 1998
Leo uses a higher-order Logic based upon Church's simply typed λ-calculus, so that the comprehension axioms are implicitly handled by αβη-equality, and extensionality principles are build in into Leo’s unification, and hence do not have to be axiomatized in order to achieve Henkin completeness.
Universal (meta-)logical reasoning: Recent successes
- Christoph Benzmüller
- Philosophy, Computer ScienceScience of Computer Programming
- 1 March 2019
The Higher-Order Prover Leo-III
- A. Steen, Christoph Benzmüller
- Computer ScienceInternational Joint Conference on Automated…
- 8 February 2018
The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented and natively supports almost every normal higher- order modal logic.
THF0 - The Core of the TPTP Language for Higher-Order Logic
- Christoph Benzmüller, Florian Rabe, G. Sutcliffe
- Computer ScienceInternational Joint Conference on Automated…
- 12 August 2008
The core of the TPTP language for higher-order logic --- THF0, based on Church's simple type theory, is introduced, a syntactically conservative extension of the untyped first-order TPTP Language.
Higher-order semantics and extensionality
- Christoph Benzmüller, C. Brown, M. Kohlhase
- Computer ScienceJournal of Symbolic Logic (JSL)
- 1 December 2004
A methodology of abstract consistency methods is developed by providing the necessary model existence theorems needed to analyze completeness of (machine-oriented) higher-order calculi with respect to these model classes.
Automated Reasoning in Higher-Order Logic using the TPTP THF Infrastructure
- G. Sutcliffe, Christoph Benzmüller
- Computer ScienceJournal of Formalized Reasoning
- 14 April 2010
Key developments have been the specification of the THF language, the addition of higher-order problems to theTPTP, the development of the TPTP THF infrastructure, several ATP systems for higher- order logic, and the use of higher -order ATP in a range of domains.
Proof Development with OMEGA
- J. Siekmann, Christoph Benzmüller, J. Zimmer
- MathematicsCADE
- 27 July 2002
The Ωmega proof development system [2] is the core of several related and well integrated research projects of the Ωmega research group.
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