2006/03/24 by Robert A. Herrmann, Herrmann, Robert A.
Computer Science · Engineering · Mathematics · #03B22 #03B65 #Algebra over a field #Arithmetic #Axiom #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #Computer science #Control and Stability of Dynamical Systems #Countable set #Description logic #Discrete mathematics #FOS: Mathematics #Finitary #Finite set #General Mathematics (math.GM) #Infimum and supremum #Intermediate logic #Logic (math.LO) #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematics #Operator (biology) #Physics and Engineering Research Articles #Programming language #Pure mathematics #Simple (philosophy) #Theoretical computer science #math.GM #math.LO #msc:03B22 #msc:03B65
paper · pdf · doi:10.48550/arxiv.math/0603573
Plain Tex, 15 pages. In this version, the material in section 6 is removed since for the C-set theory employed the set X used in Theorem 6.2 (i) apparently cannot be shown to exist
openalex publication_date 2006/03/24 · arxiv created 2014/12/28 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.