Set Theory and Logic


General Logic-Systems that Determine Significant Collections of Consequence Operators

Authors: Robert A. Herrmann

Relative to universal logic, it is demonstrated how useful it is to utilize general logic-systems to investigate finite consequences operators (operations). Among many other examples relative to the lattice of finite consequence operators, a general characterization for the lattice-theoretic supremum for a nonempty collection of finite consequence operators is given. Further, it is shown that for any denumerable language there is a rather simple collection of finite consequence operators and for a propositional language, three simple modifications to the finitary rule of inference that demonstrate that the lattice of finite consequence operators is not meet-complete.

Comments: 19 Pages.

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Submission history

[v1] 2013-09-04 07:32:54
[v2] 2015-01-05 06:23:27
[v3] 2015-11-30 06:58:58

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