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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • Volume of the periodical

  • 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