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Non-Archimedean Valued Sequent Logic
Timisoara, Romania September 26-September 29
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/SYNASC.2006.57Eighth International Symposium on Sym ...
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Andrew Schumann, "Non-Archimedean Valued Sequent Logic," Symbolic and Numeric Algorithms for Scientific Computing, International Symposium on, pp. 89-92, Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'06), 2006.
 
 
BibTex
x
 
@article{ 10.1109/SYNASC.2006.57,
author = {Andrew Schumann},
title = {Non-Archimedean Valued Sequent Logic},
journal ={Symbolic and Numeric Algorithms for Scientific Computing, International Symposium on},
volume = {0},
year = {2006},
isbn = {0-7695-2740-X},
pages = {89-92},
doi = {http://doi.ieeecomputersociety.org/10.1109/SYNASC.2006.57},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
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TY - CONF
JO - Symbolic and Numeric Algorithms for Scientific Computing, International Symposium on
TI - Non-Archimedean Valued Sequent Logic
SN - 0-7695-2740-X
SP89
EP92
A1 - Andrew Schumann,
PY - 2006
KW - null
VL - 0
JA - Symbolic and Numeric Algorithms for Scientific Computing, International Symposium on
ER -
 
Andrew Schumann, Belarusian State University, Belarus
In this paper I propose non-Archimedean multiple-validity and construct the logical language with the related semantics. Further I build non-Archimedean valued sequent logic. Notice that non-Archimedean valued logical system is considered for the first time.

The Polish logician Jan Lukasiewicz began to create systems of many-valued logic, using a third value "possible" to deal with Aristotle?s paradox of the sea battle. Now many-valued logic has applications in diverse fields. In the earlier years of development of multiple-validity idea, the most promising field of its application is artificial intelligence. This application concerns vague notions and commonsense reasoning, e.g. in expert systems. In this context fuzzy logic is also interesting, because multiple-validity is modeled in artificial intelligence via fuzzy sets and fuzzy logic.

There exist various many-valued logical systems. However non-Archimedean valued logic isn?t yet constructed. The idea of non-Archimedean multiple-validity is that (1) the set of truth values is uncountable infinite and (2) this set isn?t well-ordered. This idea can have a lot of applications in probabilistic reasoning (see [4, 1]).

Citation:
Andrew Schumann, "Non-Archimedean Valued Sequent Logic," synasc, pp.89-92, Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'06), 2006
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