Automated theorem proving - theory and practice
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Theory Exploration with Theorema
Automated theorem proving is a well established subject in computer science. The advances made in the algorithmic techniques for automated theorem proving are impressive, see the survey paper [Loveland 1996]. Also, automated theorem proving has found various important applications in computer science. For example, Robinson’s resolution proving method launched a whole new programming paradigm, n...
متن کاملQualitative Theorem Proving in Linear Constraints
We know, from the classical work of Tarski on real closed elds, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take pla...
متن کاملAutomated Theorem Proving in Loop Theory
In this paper we compare the performance of various automated theorem provers on nearly all of the theorems in loop theory known to have been obtained with the assistance of automated theorem provers. Our analysis yields some surprising results, e.g., the theorem prover most often used by loop theorists doesn’t necessarily yield the best performance.
متن کاملSolving Geometric Construction Problems Supported by Theorem Proving
Over the last sixty years, a number of methods for automated theorem proving in geometry, especially Euclidean geometry, have been developed. Almost all of them focus on universally quantified theorems. On the other hand, there are only few studies about logical approaches of geometric constructions. Consequently, automated proving of ∀∃ theorems, that correspond to geometric construction probl...
متن کاملComputer Theorem Proving for Verifiable Solving of Geometric Construction Problems
Over the last sixty years, a number of methods for automated theorem proving in geometry, especially Euclidean geometry, have been developed. Almost all of them focus on universally quantified theorems. On the other hand, there are only few studies about logical approaches to geometric constructions. Consequently, automated proving of ∀∃ theorems, that correspond to geometric construction probl...
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تاریخ انتشار 2001