Results 1  10
of
13
A Generic Modular Data Structure for Proof Attempts Alternating on Ideas and Granularity
 Proceedings of MKM’05, volume 3863 of LNAI, IUB
, 2006
"... Abstract. A practically useful mathematical assistant system requires the sophisticated combination of interaction and automation. Central in such a system is the proof data structure, which has to maintain the current proof state and which has to allow the flexible interplay of various components i ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
Abstract. A practically useful mathematical assistant system requires the sophisticated combination of interaction and automation. Central in such a system is the proof data structure, which has to maintain the current proof state and which has to allow the flexible interplay of various components including the human user. We describe a parameterized proof data structure for the management of proofs, which includes our experience with the development of two proof assistants. It supports and bridges the gap between abstract level proof explanation and lowlevel proof verification. The proof data structure enables, in particular, the flexible handling of lemmas, the maintenance of different proof alternatives, and the representation of different granularities of proof attempts. 1
A proofcentric approach to mathematical assistants
 Journal of Applied Logic: Special Issue on Mathematics Assistance Systems
, 2005
"... We present an approach to mathematical assistants which uses readable, executable proof scripts as the central language for interaction. We examine an implementation that combines the Isar language, the Isabelle theorem prover and the IsaPlanner proof planner. We argue that this synergy provides a f ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We present an approach to mathematical assistants which uses readable, executable proof scripts as the central language for interaction. We examine an implementation that combines the Isar language, the Isabelle theorem prover and the IsaPlanner proof planner. We argue that this synergy provides a flexible environment for the exploration, certification, and presentation of mathematical proof.
System description: LEO – a resolution based higherorder theorem prover
 IN PROC. OF LPAR05 WORKSHOP: EMPIRICALLY SUCCESSFULL AUTOMATED REASONING IN HIGHERORDER LOGIC (ESHOL), MONTEGO
, 2005
"... We present Leo, a resolution based theorem prover for classical higherorder logic. It can be employed as both an fully automated theorem prover and an interactive theorem prover. Leo has been implemented as part of the Ωmega environment [23] and has been integrated with the Ωmega proof assistant. ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
We present Leo, a resolution based theorem prover for classical higherorder logic. It can be employed as both an fully automated theorem prover and an interactive theorem prover. Leo has been implemented as part of the Ωmega environment [23] and has been integrated with the Ωmega proof assistant. Higherorder resolution proofs developed with Leo can be displayed and communicated to the user via Ωmega’s graphical user interface Loui. The Leo system has recently been successfully coupled with a firstorder resolution theorem prover (Bliksem).
ΩMEGA: Computer supported mathematics
 IN: PROCEEDINGS OF THE 27TH GERMAN CONFERENCE ON ARTIFICIAL INTELLIGENCE (KI 2004)
, 2004
"... The year 2004 marks the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number” (with Martin Davis’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated dedu ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
The year 2004 marks the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number” (with Martin Davis’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated deduction used machine oriented calculi to find the proof for a theorem by automatic means, the Automath project of N.G. de Bruijn – more modest in its aims with respect to automation – showed in the late 1960s and early 70s that a complete mathematical textbook could be coded and proofchecked by a computer. Classical theorem proving procedures of today are based on ingenious search techniques to find a proof for a given theorem in very large search spaces – often in the range of several billion clauses. But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited. The shift
Disproving False Conjectures
 Proceedings of the 10 th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, volume 2850 of LNAI
, 2003
"... For automatic theorem provers it is as important to disprove false conjectures as it is to prove true ones, especially if it is not known ahead of time if a formula is derivable inside a particular inference system. ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
For automatic theorem provers it is as important to disprove false conjectures as it is to prove true ones, especially if it is not known ahead of time if a formula is derivable inside a particular inference system.
A Basic Extended Simple Type Theory
, 2001
"... This paper presents an extended version of Church's simple type theory called Basic Extended Simple Type Theory (bestt). By adding type variables and support for reasoning with tuples, lists, and sets to simple type theory, it is intended to be a practical logic for formalized mathematics. 1 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
This paper presents an extended version of Church's simple type theory called Basic Extended Simple Type Theory (bestt). By adding type variables and support for reasoning with tuples, lists, and sets to simple type theory, it is intended to be a practical logic for formalized mathematics. 1
A Lost Proof
 IN TPHOLS: WORK IN PROGRESS PAPERS
, 2001
"... We reinvestigate a proof example presented by George Boolos which perspicuously illustrates Gödel’s argument for the potentially drastic increase of prooflengths in formal systems when carrying through the argument at too low a level. More concretely, restricting the order of the logic in which t ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We reinvestigate a proof example presented by George Boolos which perspicuously illustrates Gödel’s argument for the potentially drastic increase of prooflengths in formal systems when carrying through the argument at too low a level. More concretely, restricting the order of the logic in which the proof is carried through to the order of the logic in which the problem is formulated in the first place can result in unmanageable long proofs, although there are short proofs in a logic of higher order. Our motivation in this paper is of practical nature and its aim is to sketch the implications of this example to current technology in automated theorem proving, to point to related questions about the foundational character of type theory (without explicit comprehension axioms) for mathematics, and to work out some challenging aspects with regard to the automation of this proof – which, as we belief, nicely illustrates the discrepancy between the creativity and intuition required in mathematics and the limitations of state of the art theorem provers.
Summary Report, Spring 2002
"... This paper was accepted and I plan to present the work at the conference in July ..."
Abstract
 Add to MetaCart
This paper was accepted and I plan to present the work at the conference in July