General Logic-Systems that Determine Significant Collections of Consequence Operators

Details General Logic-Systems that Determine Significant Collections of Consequence Operators General Logic-Systems that Determine Significant Collections of Consequence Operators

2006-03-24

arxiv.org/abs/math/0603573v8

Mathematics

General Mathematics

Plain Tex, 23 pages. In this version, corrections and improvements are made in the examples in section 4, which is also greatl

Scientific paper

In this paper, general logic-systems and a necessary and sufficient algorithm are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a deduction is restricted, then such deduction does not yield a consequence operator. (2) In general, for any non-organized infinite language L, there is a special class of finite consequence operators that is not meet-complete. (3) For classical deduction, three different examples of modified propositional deduction yield collections of finite consequence operators that are not meet-complete. Other general logic-system examples are given. In a final section, the notion of potentially finite is investigated.

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