http://oldmfl.ricerca.di.unimi.it/api.php?action=feedcontributions&user=Sdzhjun&feedformat=atomMathfuzzlog - User contributions [en]2020-05-29T04:25:29ZUser contributionsMediaWiki 1.27.1http://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Guojun_Wang&diff=1517Category:Publications by Guojun Wang2008-04-29T14:04:25Z<p>Sdzhjun: </p>
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<div>Publications by [[Guojun Wang]].<br />
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[[Category:Publication by author|Wang, Guojun]]</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Guojun_Wang&diff=1516Category:Publications by Guojun Wang2008-04-29T14:03:25Z<p>Sdzhjun: </p>
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<div>{{Paper|<br />
author=Guojun Wang|<br />
title=The R0-type fuzzy logic metric space and an algorithm for solving fuzzy modus ponens<br />
|<br />
journal=Computers & Mathematics with Applications<br />
|<br />
volume=55|<br />
number=9|<br />
pages=1974-1987|<br />
year=2008}}</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Guojun_Wang&diff=1515Category:Publications by Guojun Wang2008-04-29T14:01:07Z<p>Sdzhjun: </p>
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<div>Publications by [[Guojun Wang]].<br />
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Articles in category "Publications by Guojun Wang"<br />
<br />
{{Paper|<br />
author=Guojun Wang|<br />
title=The R0-type fuzzy logic metric space and an algorithm for solving fuzzy modus ponens<br />
|<br />
journal=Computers & Mathematics with Applications<br />
|<br />
volume=55|<br />
number=9|<br />
pages=1974-1987|<br />
year=2008}}</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Guojun_Wang&diff=1514Category:Publications by Guojun Wang2008-04-29T14:00:33Z<p>Sdzhjun: </p>
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<div>Publications by [[Guojun Wang]].<br />
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Articles in category "Publications by Guojun Wang"</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Guojun_Wang&diff=1513Category:Publications by Guojun Wang2008-04-29T13:57:23Z<p>Sdzhjun: </p>
<hr />
<div>Publications by [[Guojun Wang]].<br />
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[[Category:Publication by author|Wang, Guojun]]</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Guojun_Wang&diff=1512Category:Publications by Guojun Wang2008-04-29T13:56:31Z<p>Sdzhjun: Removing all content from page</p>
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<div></div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Guojun_Wang&diff=1511Guojun Wang2008-04-29T13:55:15Z<p>Sdzhjun: </p>
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<div>{{Researcher<br />
|name=Guojun<br />
|surname=Wang<br />
|birth=<br />
|advisor=<br />
|page=<br />
|affiliation=Shaanxi Normal University, Xi'an Jiaotong University<br />
}}</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Guojun_Wang&diff=1510Category:Publications by Guojun Wang2008-04-29T13:52:24Z<p>Sdzhjun: </p>
<hr />
<div>Publications by [[Guojun Wang]].<br />
<br />
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[[Category:Publication by author|Wang, Guojun]]</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Guojun_Wang&diff=1509Category:Publications by Guojun Wang2008-04-29T13:51:46Z<p>Sdzhjun: </p>
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<div>Publications by [[Guojun Wang]].<br />
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[[Category:Publication by author|Wang, Guojun]]<br />
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<br />
{{Paper|<br />
author=Guojun Wang|<br />
title=The R0-type fuzzy logic metric space and an algorithm for solving fuzzy modus ponens<br />
|<br />
journal=Computers & Mathematics with Applications<br />
|<br />
volume=55|<br />
number=9|<br />
pages=1974-1987|<br />
year=2008}}</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=User_talk:Sdzhjun&diff=1508User talk:Sdzhjun2008-04-28T14:19:02Z<p>Sdzhjun: </p>
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<div>'''Welcome to ''Mathfuzzlog''!''' We hope you will contribute much and well. <br />
You'll probably want to read the [[Help:Contents|help pages]]. Again, welcome and have fun! [[User:Cnoguera|cnoguera]] 22:26, 1 January 2008 (CET)<br />
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== First contributions ==<br />
<br />
Dear Hongjun, I salute your first contributions to our web site. It is great to receive feedback from the members of the group and collaborate to build together a useful site. As you will see, I have modified some of your new entries to keep the general structure we are using in the site. So, let me thank you for your input and encourage you to keep on editing. Cheers, --[[User:Cnoguera|cnoguera]] 15:24, 27 April 2008 (CEST)<br />
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Hi again! You will see I have created the entries for your advisor and your research center. Maybe you could complete them by providing some more information. It would be also interesting if you could add some of the most relevant publications of [[Guojun Wang]] (those under the scope of our group as described in [[Mathematical Fuzzy Logic]]). Cheers, --[[User:Cnoguera|cnoguera]] 10:51, 28 April 2008 (CEST)<br />
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Dear Cnoguera, Thanks very much for your editing. I am pleased to talk and make friends with you here. I hope further exchanges of new ideas and information on logic. I will add relevant publications of my advisor as soon as possible. Bestwishes, [[Hongjun Zhou]] 22:18, Beijing time, 28 April 2008 (Xi'an)</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Hongjun_Zhou&diff=1485Hongjun Zhou2008-04-28T01:11:09Z<p>Sdzhjun: </p>
<hr />
<div>{{Researcher<br />
|name=Hongjun<br />
|surname=Zhou<br />
|birth= 12 March 1980<br />
|photo=<br />
|advisor=Guojun Wang<br />
|advisor2=<br />
|page=<br />
|affiliation=Shaanxi Normal University}}<br />
<br />
<br />
[[Category:Members|Zhou, Hongjun]]</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Hongjun_Zhou&diff=1484Hongjun Zhou2008-04-28T01:09:15Z<p>Sdzhjun: </p>
<hr />
<div>{{Researcher<br />
|name=Hongjun<br />
|surname=Zhou<br />
|birth= 12 March 1980<br />
|photo=<br />
|advisor=Guojun Wang<br />
|advisor2=<br />
|page=<br />
|affiliation= Institute of Mathematics, Shaanxi Normal University, Xi'an China<br />
}}<br />
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[[Category:Members|Zhou, Hongjun]]</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Generalized_consistency_degrees_of_theories_w.r.t._formulas_in_several_standard_complete_logic_systems&diff=1483Generalized consistency degrees of theories w.r.t. formulas in several standard complete logic systems2008-04-28T00:56:29Z<p>Sdzhjun: /* Abstract */</p>
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<div>{{Paper|<br />
author=Hongjun Zhou|<br />
title=Generalized consistency degrees of theories w.r.t. formulas in several standard complete logic systems|<br />
journal=Fuzzy Sets and Systems|<br />
volume=157|<br />
number=15|<br />
pages=2058-2073|<br />
year=2006}}<br />
<br />
<br />
== Abstract ==<br />
The present paper carries out a deep analysis on the inconsistency of theories by means of deduction theorems, completeness theorems and satisfiability degrees of formulas, and introduces the concept of the degree of entailment of a contradiction from a theory in classical two-valued logic system, Łukasiewicz fuzzy logic system, Gödel fuzzy logic system, product fuzzy logic system and the R0-fuzzy logic system. It is proved that in classical two-valued logic system, Łukasiewicz fuzzy logic system and the R0-fuzzy logic system, respectively, the concept of consistency degrees of theories defined by the divergence degrees of theories in [X.N. Zhou, G.J. Wang, Consistency degrees of theories in some systems of propositional fuzzy logic, Fuzzy Sets and Systems 152 (2005) 321–331; H.J. Zhou, G.J.Wang, A new theory index based on deduction theorems in several logic systems, Fuzzy Sets and Systems 157(2006) 427–443] is reasonable and can accurately measure the consistency degrees of theories. The concept of the degree of entailment of a contradiction from a theory is generalized by replacing the contradiction with a general formula and then the generalized consistency degrees of theories w.r.t. general formulas in the above-mentioned logic systems is established.</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Characterizations_of_maximal_consistent_theories_in_the_formal_deductive_system_(NM-logic)_and_Cantor_space&diff=1482Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space2008-04-28T00:52:08Z<p>Sdzhjun: </p>
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<div>{{Paper|<br />
author=Hongjun Zhou|<br />
title=Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space|<br />
journal=Fuzzy Sets and Systems|<br />
volume=158|<br />
number=|<br />
pages=2591-2604|<br />
year=2007}}<br />
== Abstract ==<br />
A maximal consistent theory is a maximal theory with respect to its consistency. The present paper is divided into two parts. The first one is devoted to characterize the maximality of a consistent theory in the formal deductive system L* (which is a logic system equivalent to the nilpotent minimum logic). It is proved that each maximal consistent theory in this logic must be the deductive closure of a collection of simple compound formulas. Hence, it follows that there is a one-to-one correspondence between the set of all maximal consistent theories and the set of evaluations e assigning to each propositional variable p its truth degree e(p) ∈ {0, 1<br />
2 , 1}. The Satisfiability Theorem and Compactness Theorem of L* are obtained. The second part is to investigate the topological structure of the set of all maximal consistent theories over L*, and the results show that this topological space is a Cantor space</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Characterizations_of_maximal_consistent_theories_in_the_formal_deductive_system_(NM-logic)_and_Cantor_space&diff=1481Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space2008-04-28T00:48:41Z<p>Sdzhjun: </p>
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<div>{{Paper|<br />
author=Hongjun Zhou, Guojun Wang|<br />
title=Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space|<br />
journal=Fuzzy Sets and Systems|<br />
volume=158|<br />
number=|<br />
pages=2591-2604|<br />
year=2007}}<br />
<br />
== Abstract ==<br />
A maximal consistent theory is a maximal theory with respect to its consistency. The present paper is divided into two parts. The first one is devoted to characterize the maximality of a consistent theory in the formal deductive system L* (which is a logic system equivalent to the nilpotent minimum logic). It is proved that each maximal consistent theory in this logic must be the deductive closure of a collection of simple compound formulas. Hence, it follows that there is a one-to-one correspondence between the set of all maximal consistent theories and the set of evaluations e assigning to each propositional variable p its truth degree e(p) ∈ {0, 1<br />
2 , 1}. The Satisfiability Theorem and Compactness Theorem of L* are obtained. The second part is to investigate the topological structure of the set of all maximal consistent theories over L*, and the results show that this topological space is a Cantor space</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Characterizations_of_maximal_consistent_theories_in_the_formal_deductive_system_(NM-logic)_and_Cantor_space&diff=1480Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space2008-04-28T00:47:52Z<p>Sdzhjun: </p>
<hr />
<div>{{Paper|<br />
author=Hongjun Zhou, Guojun Wang|<br />
title=Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space|<br />
journal=Fuzzy Sets and Systems|<br />
volume=158|<br />
number=|<br />
pages=2591-2604|<br />
year=2007}}<br />
<br />
<br />
== Abstract ==<br />
A maximal consistent theory is a maximal theory with respect to its consistency. The present paper is divided into two parts. The first one is devoted to characterize the maximality of a consistent theory in the formal deductive system L* (which is a logic system equivalent to the nilpotent minimum logic). It is proved that each maximal consistent theory in this logic must be the deductive closure of a collection of simple compound formulas. Hence, it follows that there is a one-to-one correspondence between the set of all maximal consistent theories and the set of evaluations e assigning to each propositional variable p its truth degree e(p) ∈ {0, 1<br />
2 , 1}. The Satisfiability Theorem and Compactness Theorem of L* are obtained. The second part is to investigate the topological structure of the set of all maximal consistent theories over L*, and the results show that this topological space is a Cantor space</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Characterizations_of_maximal_consistent_theories_in_the_formal_deductive_system_(NM-logic)_and_Cantor_space&diff=1479Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space2008-04-28T00:47:22Z<p>Sdzhjun: </p>
<hr />
<div>{{Paper|<br />
author=Hongjun Zhou|Guojun Wang|<br />
title=Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space|<br />
journal=Fuzzy Sets and Systems|<br />
volume=158|<br />
number=|<br />
pages=2591-2604|<br />
year=2007}}<br />
<br />
<br />
== Abstract ==<br />
A maximal consistent theory is a maximal theory with respect to its consistency. The present paper is divided into two parts. The first one is devoted to characterize the maximality of a consistent theory in the formal deductive system L* (which is a logic system equivalent to the nilpotent minimum logic). It is proved that each maximal consistent theory in this logic must be the deductive closure of a collection of simple compound formulas. Hence, it follows that there is a one-to-one correspondence between the set of all maximal consistent theories and the set of evaluations e assigning to each propositional variable p its truth degree e(p) ∈ {0, 1<br />
2 , 1}. The Satisfiability Theorem and Compactness Theorem of L* are obtained. The second part is to investigate the topological structure of the set of all maximal consistent theories over L*, and the results show that this topological space is a Cantor space</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Characterizations_of_maximal_consistent_theories_in_the_formal_deductive_system_(NM-logic)_and_Cantor_space&diff=1478Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space2008-04-28T00:45:54Z<p>Sdzhjun: /* Abstract */</p>
<hr />
<div>{{Paper|<br />
author=Hongjun Zhou|<br />
title=Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space|<br />
journal=Fuzzy Sets and Systems|<br />
volume=158|<br />
number=|<br />
pages=2591-2604|<br />
year=2007}}<br />
<br />
<br />
== Abstract ==<br />
A maximal consistent theory is a maximal theory with respect to its consistency. The present paper is divided into two parts. The first one is devoted to characterize the maximality of a consistent theory in the formal deductive system L* (which is a logic system equivalent to the nilpotent minimum logic). It is proved that each maximal consistent theory in this logic must be the deductive closure of a collection of simple compound formulas. Hence, it follows that there is a one-to-one correspondence between the set of all maximal consistent theories and the set of evaluations e assigning to each propositional variable p its truth degree e(p) ∈ {0, 1<br />
2 , 1}. The Satisfiability Theorem and Compactness Theorem of L* are obtained. The second part is to investigate the topological structure of the set of all maximal consistent theories over L*, and the results show that this topological space is a Cantor space</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Characterizations_of_maximal_consistent_theories_in_the_formal_deductive_system_(NM-logic)_and_Cantor_space&diff=1477Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space2008-04-28T00:45:26Z<p>Sdzhjun: /* Abstract */</p>
<hr />
<div>{{Paper|<br />
author=Hongjun Zhou|<br />
title=Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space|<br />
journal=Fuzzy Sets and Systems|<br />
volume=158|<br />
number=|<br />
pages=2591-2604|<br />
year=2007}}<br />
<br />
<br />
== Abstract ==<br />
A maximal consistent theory is a maximal theory with respect to its consistency. The present paper is divided into two parts. The first one is devoted to characterize the maximality of a consistent theory in the formal deductive system L* (which is a logic system equivalent to the nilpotent minimum logic). It is proved that each maximal consistent theory in this logic must be the deductive closure of a collection of simple compound formulas. Hence, it follows that there is a one-to-one correspondence between the set of all maximal consistent theories and the set of evaluations e assigning to each propositional variable p its truth degree e(p) ∈ {0, 1<br />
2 , 1}. The Satisfiability Theorem and Compactness Theorem ofL∗ are obtained. The second part is to investigate the topological structure of the set of all maximal consistent theories over L*, and the results show that this topological space is a Cantor space</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=A_new_theory_consistency_index_based_on_deduction_theorems_in_several_logic_systems&diff=1476A new theory consistency index based on deduction theorems in several logic systems2008-04-28T00:43:17Z<p>Sdzhjun: /* Abstract */</p>
<hr />
<div>{{Paper|<br />
author=Hongjun Zhou|<br />
title=A new theory consistency index based on deduction theorems in several logic systems|<br />
journal=Fuzzy Sets and Systems|<br />
volume=157|<br />
number=3|<br />
pages=427-443|<br />
year=2006}}<br />
<br />
<br />
== Abstract ==<br />
Based on deduction theorems, completeness theorems and by means of the theory of truth degrees of formulas and the concept of divergence degrees of theories, the present paper proposes another new index reflecting the extent to which a general theory is consistent in five different logic systems, i.e., classical (two-valued) logic system C2, Łukasiewicz fuzzy logic system Łuk, Gödel fuzzy logic system Göd, product fuzzy logic system � and the R0-fuzzy logic system L*. The concepts of normal consistency and almost inconsistency of theories in the above-mentioned<br />
logic systems are introduced, and sufficient and necessary conditions for theories being normal consistent or almost<br />
inconsistent are given. Finally, comparison with the existing concept of consistency degrees of theories is analyzed.</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Characterizations_of_maximal_consistent_theories_in_the_formal_deductive_system_(NM-logic)_and_Cantor_space&diff=1457Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space2008-04-27T08:12:05Z<p>Sdzhjun: New page: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V05-4NS2GBB-3&_user=1489432&_coverDate=12%2F01%2F2007&_alid=730578653&_rdoc=2&_fmt=high&_orig=search&_cdi=5637&_sort=d&_docanchor...</p>
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<div>http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V05-4NS2GBB-3&_user=1489432&_coverDate=12%2F01%2F2007&_alid=730578653&_rdoc=2&_fmt=high&_orig=search&_cdi=5637&_sort=d&_docanchor=&view=c&_ct=3&_acct=C000053063&_version=1&_urlVersion=0&_userid=1489432&md5=ba57b4f98112752ec1f401682d965649</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Hongjun_Zhou&diff=1456Category:Publications by Hongjun Zhou2008-04-27T01:29:24Z<p>Sdzhjun: </p>
<hr />
<div>Publications by [[Hongjun Zhou]].<br />
<br />
[[Category:Publication by author|Zhou, Hongjun]]<br />
<br />
1. [[Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic)]] to appear in Fuzzy Sets and Systems.<br />
<br />
2. [[Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space]], Fuzzy Sets and Systems 158 (2007) 2591-2604.<br />
<br />
3. [[Generalized consistency degrees of theories w.r.t. formulas in several standard complete logic systems]], Fuzzy Sets and Systems, 157(15) (2006) 2058-2073.<br />
<br />
4. [[A new theory consistency index based on deduction theorems in several logic systems]], Fuzzy Sets and Systems, Volume 157, Issue 3, 1 February 2006, Pages 427-443<br />
<br />
<br />
5. [[ Consistency degrees of theories and methods of graded reasoning in n-valued R0-logic (NM-logic)]], International Journal of Approximate Reasoning, Volume 43, Issue 2, October 2006, Pages 117-132.</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Hongjun_Zhou&diff=1455Category:Publications by Hongjun Zhou2008-04-27T01:28:09Z<p>Sdzhjun: </p>
<hr />
<div>Publications by [[Hongjun Zhou]].<br />
<br />
[[Category:Publication by author|Zhou, Hongjun]]<br />
<br />
1. [[Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic)]] to appear in Fuzzy Sets and Systems.<br />
<br />
2. [Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space], Fuzzy Sets and Systems 158 (2007) 2591-2604.<br />
<br />
3. [[Generalized consistency degrees of theories w.r.t. formulas in several standard complete logic systems]], Fuzzy Sets and Systems, 157(15) (2006) 2058-2073.<br />
<br />
4. [[A new theory consistency index based on deduction theorems in several logic systems]], Fuzzy Sets and Systems, Volume 157, Issue 3, 1 February 2006, Pages 427-443<br />
<br />
<br />
5. [[ Consistency degrees of theories and methods of graded reasoning in n-valued R0-logic (NM-logic)]], International Journal of Approximate Reasoning, Volume 43, Issue 2, October 2006, Pages 117-132.</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Help:Contents&diff=1454Help:Contents2008-04-27T01:16:38Z<p>Sdzhjun: Removing all content from page</p>
<hr />
<div></div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Category:Publications_by_Hongjun_Zhou&diff=1453Category:Publications by Hongjun Zhou2008-04-27T01:15:49Z<p>Sdzhjun: </p>
<hr />
<div>Publications by [[Hongjun Zhou]].<br />
<br />
[[Category:Publication by author|Zhou, Hongjun]]<br />
<br />
1. [[Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic)]] to appear in Fuzzy Sets and Systems.<br />
<br />
2. [[Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space]], Fuzzy Sets and Systems 158 (2007) 2591-2604.<br />
<br />
3. [[Generalized consistency degrees of theories w.r.t. formulas in several standard complete logic systems]], Fuzzy Sets and Systems, 157(15) (2006) 2058-2073.<br />
<br />
4. [[A new theory consistency index based on deduction theorems in several logic systems]], Fuzzy Sets and Systems, Volume 157, Issue 3, 1 February 2006, Pages 427-443<br />
<br />
<br />
5. [[ Consistency degrees of theories and methods of graded reasoning in n-valued R0-logic (NM-logic)]], International Journal of Approximate Reasoning, Volume 43, Issue 2, October 2006, Pages 117-132.</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Three_and_two-valued_%C5%81ukasiewicz_theories_in_the_formal_deductive_system_L*_(NM-logic)&diff=1452Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic)2008-04-27T01:06:26Z<p>Sdzhjun: ABSTRACT</p>
<hr />
<div>'''Abstract''' In order to offer a logic foundation for fuzzy reasoning and to reduce the gap between fuzzy reasoning and artificial intelligence, a new formal deductive system L* was introduced in 1996. It was proved that the prominent nilpotent minimum logic is a logic system equivalent to L*. As is well known, in classical propositional logic, there is a one-to-one correspondence between deductively closed theories and topologically closed subsets of the Stone space of all maximally consistent theories. Recently, by means of the strong completeness of L*, we obtained the structural and topological characterizations of maximally consistent theories in this logic. It was proved that the set of all maximally consistent theories over L* with an induced topology is a Cantor space. In order to establish a similar connection between theories over L* and closed subsets of this topological space to the classical case, we introduce in this paper the notion of threevalued Lukasiewicz theory and the notion of two-valued Lukasiewicz (Boolean) theory. We prove that there is also a one-to-one correspondence between deductively closed three-valued Lukasiewicz theories and closed subsets of the space, and Boolean theories correspond to the closed subsets of the subspace of all maximally consistent Boolean theories. Lastly, we give an alternative proof for the structural characterization of the maximality of consistent theories over L* by induction on the complexity of formulas, which is independent of the strong completeness of L* and also<br />
independent of the perfectness of the standard R0-algebra.</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Help:Contents&diff=1451Help:Contents2008-04-27T01:02:10Z<p>Sdzhjun: Publications by Hongjun Zhou</p>
<hr />
<div><br />
1. [[Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic)]] to appear in Fuzzy Sets and Systems.<br />
<br />
2. [[Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space]], Fuzzy Sets and Systems 158 (2007) 2591-2604.<br />
<br />
3. [[Generalized consistency degrees of theories w.r.t. formulas in several standard complete logic systems]], Fuzzy Sets and Systems, 157(15) (2006) 2058-2073.<br />
<br />
4. [[A new theory consistency index based on deduction theorems in several logic systems]], Fuzzy Sets and Systems, Volume 157, Issue 3, 1 February 2006, Pages 427-443<br />
<br />
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5. [[ Consistency degrees of theories and methods of graded reasoning in n-valued R0-logic (NM-logic)]], International Journal of Approximate Reasoning, Volume 43, Issue 2, October 2006, Pages 117-132.</div>Sdzhjunhttp://oldmfl.ricerca.di.unimi.it/index.php?title=Help:Contents&diff=1450Help:Contents2008-04-27T01:01:36Z<p>Sdzhjun: New page: Publications: 1. Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic) to appear in Fuzzy Sets and Systems. 2. [[Characterizations of maximal consist...</p>
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<div>Publications:<br />
1. [[Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic)]] to appear in Fuzzy Sets and Systems.<br />
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2. [[Characterizations of maximal consistent theories in the formal deductive system (NM-logic) and Cantor space]], Fuzzy Sets and Systems 158 (2007) 2591-2604.<br />
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3. [[Generalized consistency degrees of theories w.r.t. formulas in several standard complete logic systems]], Fuzzy Sets and Systems, 157(15) (2006) 2058-2073.<br />
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4. [[A new theory consistency index based on deduction theorems in several logic systems]], Fuzzy Sets and Systems, Volume 157, Issue 3, 1 February 2006, Pages 427-443<br />
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5. [[ Consistency degrees of theories and methods of graded reasoning in n-valued R0-logic (NM-logic)]], International Journal of Approximate Reasoning, Volume 43, Issue 2, October 2006, Pages 117-132.</div>Sdzhjun