Formal analysis of Peterson's rules for checking validity of syllogisms with intermediate quantifiers

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Formal analysis of Peterson's rules for checking validity of syllogisms with intermediate quantifiers

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Formal analysis of Peterson's rules for checking validity of syllogisms with intermediate quantifiers

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centrum pro výzkum a vývoj metod umělé intelligence v automobilovém průmyslu regionu</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Approximate Reasoning

ISSN

0888-613X

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

150

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

122-138

Kód UT WoS článku

000863227500007

EID výsledku v databázi Scopus

2-s2.0-85136565604