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	A note on Trillas' CHC models
	Qiu, Daowen
	2010-05-06 ; 2010-05-06
关键词	orthocomplemented lattices orthomodular lattices residuated lattices conjectures consequences quantum logic CONJECTURES LATTICES LOGIC CONSEQUENCES HYPOTHESES Computer Science, Artificial Intelligence
中文摘要	Trillas et al. [E. Trillas, S. Cubillo, E. Castiheira, On conjectures in orthocomplemented lattices, Artificial Intelligence 117 (2000) 255-275] recently proposed a mathematical model for conjectures, hypotheses and consequences (abbr. CHCs), and with this model we can execute certain mathematical reasoning and reformulate some important theorems in classical logic. We demonstrate that the orthomodular condition is not necessary for holding Watanabe's structure theorem of hypotheses, and indeed, in some orthocomplemented but not orthomodular lattices, this theorem is still valid. We use the CHC operators to describe the theorem of deduction, the theorem of contradiction and the Lindenbaum theorem of classical logic, and clarify their existence in the CHC models; a number of examples is presented. And we re-define the CHC operators in residuated lattices, and particularly reveal the essential differences between the CHC operators in orthocomplemented lattices and residuated lattices. (c) 2006 Elsevier B.V. All rights reserved.
语种	英语 ; 英语
出版者	ELSEVIER SCIENCE BV ; AMSTERDAM ; PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/10106]
专题	清华大学
推荐引用方式 GB/T 7714	Qiu, Daowen. A note on Trillas' CHC models[J],2010, 2010.
APA	Qiu, Daowen.(2010).A note on Trillas' CHC models..
MLA	Qiu, Daowen."A note on Trillas' CHC models".(2010).

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