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LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description)
TLDR
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. Expand
Automating Gödel's Ontological Proof of God's Existence with Higher-order Automated Theorem Provers
TLDR
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. Expand
Quantified Multimodal Logics in Simple Type Theory
TLDR
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. Expand
System Description: LEO - A Higher-Order Theorem Prover
TLDR
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. Expand
The Higher-Order Prover Leo-III
TLDR
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. Expand
Automated Reasoning in Higher-Order Logic using the TPTP THF Infrastructure
TLDR
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. Expand
The Higher-Order Prover Leo-II
TLDR
It is crucial that Leo-II returns proof information in a standardised syntax, so that these proofs can eventually be transformed and verified within proof assistants. Expand
Proof Development with OMEGA
The Ωmega proof development system [2] is the core of several related and well integrated research projects of the Ωmega research group.
THF0 - The Core of the TPTP Language for Higher-Order Logic
TLDR
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. Expand
Proof development with ΩMEGA
TLDR
An overview of the architecture of the OMEGA system is presented and some of its novel features are sketched, including methods to develop proofs at a knowledge-based level. Expand
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