### Citations

1053 |
Isabelle/HOL: A Proof Assistant for Higher-Order Logic
- Nipkow, Paulson, et al.
(Show Context)
Citation Context ...tomatic. Hence this approach was not considered for automated reasoning. Due to a recent approach by G. Sutcliffe and others for such systems, well known higher-order theorem provers such as Isabelle =-=[11]-=-, LEO II [2] and TPS [1] were now integrated into the TPTP Problem Library [13] with already hundreds of higher-order problems [3]. These systems are running fully automated using various search strat... |

995 |
A Formulation of the Simple Theory of Types
- Church
- 1940
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Citation Context ...ibrary. 3 THF0 and Church’s Simple Type Theory The recent higher-order approach in the TPTP problem library implements higher-order logic in the so-called THF0 core by Church’s simple theory of types =-=[6]-=- since this theory is already used as a common basis for a lot of higherorder ATP systems 1 [4]. Church’s simple type theory is based on the simply typed λ-calculus in which functional types are forme... |

356 |
Regular Algebra and Finite Machines.
- Conway
- 1971
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Citation Context ...ritten as a ⊓ b and a + b, resp. Furthermore ⊤ =df S is used to denote the greatest element of S. In particular, the notion of a quantale is equivalent to Conway’s notion of a standard Kleene algebra =-=[7]-=- and a special idempotent semiring. We will have a closer look on the axiomatisation of standard Kleene algebras in the following. According to Conway, a standard Kleene algebra is axiomatically defin... |

159 |
The TPTP Problem Library: CNF Release v1.2.1.
- Sutcliffe, Suttner
- 1998
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Citation Context ... a recent approach by G. Sutcliffe and others for such systems, well known higher-order theorem provers such as Isabelle [11], LEO II [2] and TPS [1] were now integrated into the TPTP Problem Library =-=[13]-=- with already hundreds of higher-order problems [3]. These systems are running fully automated using various search strategies or by interaction with first-order theorem provers for first-order fragme... |

103 |
Quantales and their applications,
- Rosenthal
- 1990
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Citation Context ...orems which we have proved fully automatically using that approach. 2 Quantales In this section we give definitions for quantales. Their axiomatisations are of main interest in this paper.A quantale =-=[12]-=- is a structure (S, ≤, 0, ·, 1) where (S, ≤) is a complete lattice and · is a completely disjunctive inner operation on S, i.e., · distributes over arbitrary suprema. Moreover 0 is the least element o... |

31 |
C.E.: TPS: A hybrid automatic-interactive system for developing proofs.
- Andrews, Brown
- 2006
(Show Context)
Citation Context ...ach was not considered for automated reasoning. Due to a recent approach by G. Sutcliffe and others for such systems, well known higher-order theorem provers such as Isabelle [11], LEO II [2] and TPS =-=[1]-=- were now integrated into the TPTP Problem Library [13] with already hundreds of higher-order problems [3]. These systems are running fully automated using various search strategies or by interaction ... |

29 | Automated reasoning in Kleene algebra.
- Hofner, Struth
- 2007
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Citation Context ...y Kleene algebras and relation algebras have the advantage that they come with a simple first-order equational calculus which directly allows fully automated first-order theorem provers to be applied =-=[9]-=-. Contrarily, axiomatisations of quantales mostly require higher-order encodings. For quite some time it was assumed that theorem provers for higher-order logic need a lot of user interaction and ther... |

16 | Combined Reasoning by Automated Cooperation
- Benzmuller, Sorge, et al.
- 2007
(Show Context)
Citation Context ...t-order logic. Especially set theory is encoded much more naturally in higher-order logic. Moreover Benzmüller et al. stated that theorems are solved more efficiently than using first-order encodings =-=[5]-=-. Even more, we have the benefit that, due to its uniformity, every higher-order theorem prover can now be used that supports the THF0 syntax. 5 Results In this section we present the results from our... |

14 | THF0—The core of the TPTP language for higher-order logic
- Benzmüller, Rabe, et al.
- 2008
(Show Context)
Citation Context ...blem library implements higher-order logic in the so-called THF0 core by Church’s simple theory of types [6] since this theory is already used as a common basis for a lot of higherorder ATP systems 1 =-=[4]-=-. Church’s simple type theory is based on the simply typed λ-calculus in which functional types are formed from basic types. These consists of individuals $i, Boolean values $o and further types using... |

8 | Quantales and temporal logics
- Möller, Höfner, et al.
- 2006
(Show Context)
Citation Context ...ore also quantales are of special interest and can be easily extended to Kleene Algebras. For example, quantales were used to describe the algebraic semantics of the temporal logics CTL*, CTL and LTL =-=[10]-=-. Up to now only Kleene algebras and relation algebras have the advantage that they come with a simple first-order equational calculus which directly allows fully automated first-order theorem provers... |

7 | The LEO-II project
- Benzmüller, Paulson, et al.
- 2007
(Show Context)
Citation Context ...e this approach was not considered for automated reasoning. Due to a recent approach by G. Sutcliffe and others for such systems, well known higher-order theorem provers such as Isabelle [11], LEO II =-=[2]-=- and TPS [1] were now integrated into the TPTP Problem Library [13] with already hundreds of higher-order problems [3]. These systems are running fully automated using various search strategies or by ... |

1 |
Typed Higherorder Form. http://www.cs.miami.edu/∼tptp/TPTP/Proposals/THF.html
- Benzmüller, Rabe, et al.
- 2009
(Show Context)
Citation Context ...ch systems, well known higher-order theorem provers such as Isabelle [11], LEO II [2] and TPS [1] were now integrated into the TPTP Problem Library [13] with already hundreds of higher-order problems =-=[3]-=-. These systems are running fully automated using various search strategies or by interaction with first-order theorem provers for first-order fragments. In this paper we show how quantales can be enc... |

1 |
Database for automated proofs of Kleene algabra. http://www.kleenealgebra.de
- Höfner
(Show Context)
Citation Context ...ing that X, Y have the type α → {true, false} and x has the type α. In the following we only give an extract of the complete input file to demonstrate the encoding. A full version can be found online =-=[8]-=-. We only consider the supremum definition here since it forms the most interesting part of the encoding. 1 thf(sup,type,( 2 sup: ( ( $i > $o ) > $i ) )). This formula defines the type of the supremum... |