NDLI: An Improvement of Herbrand's Theorem and Its Application to Model Generation Theorem Proving

Content Provider	Springer Nature Link
Author	Chao, Yu Yan He, Li Feng Nakamura, Tsuyoshi Shi, Zheng Hao Suzuki, Kenji Itoh, Hideri
Copyright Year	2007
Abstract	This paper presents an improvement of Herbrand’s theorem. We propose a method for specifying a sub-universe of the Herbrand universe of a clause set $ {\mathcal{S}} $ for each argument of predicate symbols and function symbols in $ {\mathcal{S}} $ . We prove that a clause set $ {\mathcal{S}} $ is unsatisfiable if and only if there is a finite unsatisfiable set of ground instances of clauses of $ {\mathcal{S}} $ that are derived by only instantiating each variable, which appears as an argument of predicate symbols or function symbols, in $ {\mathcal{S}} $ over its corresponding argument's sub-universe of the Herbrand universe of $ {\mathcal{S}} $ . Because such sub-universes are usually smaller (sometimes considerably) than the Herbrand universe of $ {\mathcal{S}} $ , the number of ground instances may decrease considerably in many cases. We present an algorithm for automatically deriving the sub-universes for arguments in a given clause set, and show the correctness of our improvement. Moreover, we introduce an application of our approach to model generation theorem proving for non-range-restricted problems, show the range-restriction transformation algorithm based on our improvement and provide examples on benchmark problems to demonstrate the power of our approach.
Starting Page	541
Ending Page	553
Page Count	13
File Format	PDF
ISSN	10009000
Journal	Journal of Computer Science and Technology
Volume Number	22
Issue Number	4
e-ISSN	18604749
Language	English
Publisher	Springer US
Publisher Date	2007-09-13
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Herbrand’s theorem Herbrand universe model generation theorem proving SATCHMO really non-propositinal Computer Science Software Engineering Theory of Computation Data Structures, Cryptology and Information Theory Artificial Intelligence (incl. Robotics) Information Systems Applications (incl.Internet)
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Computer Science Applications Software Hardware and Architecture

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