General Logic-Systems and Finite Consequence Operators |
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Authors: | Robert A Herrmann |
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Institution: | (1) Institute for Mathematics and Philosophy, 44890 Rivermont Terr # 100, USA-20147 Ashburn, VA, United States of America |
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Abstract: | In this paper, the significance of using general logic-systems and finite consequence operators defined on non-organized languages
is discussed. Results are established that show how properties of finite consequence operators are independent from language
organization and that, in some cases, they depend only upon one simple language characteristic. For example, it is shown that
there are infinitely many finite consequence operators defined on any non-organized infinite language L that cannot be generated from any finite logic-system. On the other hand, it is shown that for any nonempty language L, a set map
is a finite consequence operator if and only if it is defined by a general logic-system. Simple logic-system examples that
determine specific consequence operator properties are given.
Mathematics Subject Classification (2000): Primary 03B22, Secondary 03B65 |
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Keywords: | Logic-system rules of inference consequence operator |
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