Formal analysis of Peterson's rules for checking validity of syllogisms with intermediate quantifiers
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA2302GXS" target="_blank" >RIV/61988987:17610/22:A2302GXS - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0888613X22001141" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0888613X22001141</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ijar.2022.08.002" target="_blank" >10.1016/j.ijar.2022.08.002</a>
Alternative languages
Result language
angličtina
Original language name
Formal analysis of Peterson's rules for checking validity of syllogisms with intermediate quantifiers
Original language description
In this paper, we follow up on previous publications in which we studied generalized Peterson's syllogisms with intermediate quantifiers. We present results of two kinds. First we show that on semantic level all the valid syllogisms follow from two inequalities and one equality. Furthermore, we focus on six rules suggested by Peterson in his book using which he was able to verify validity of all syllogisms. The problem is that the rules are formulated in free natural language and so, they do not provide formal means using which it would be possible to explain why the rules do their job. Therefore, we suggested formal reformulation of them and showed that all the valid syllogisms with intermediate quantifiers indeed satisfy Peterson's rules.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Approximate Reasoning
ISSN
0888-613X
e-ISSN
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Volume of the periodical
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Issue of the periodical within the volume
150
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
16
Pages from-to
122-138
UT code for WoS article
000863227500007
EID of the result in the Scopus database
2-s2.0-85136565604