Details

Autor(en) / Beteiligte

• Murinová, Petra
• Novák, Vilém
• González-Hidalgo, Manuel
• Massanet, Sebastia
• Ruiz-Aguilera, Daniel
• Montes, Susana

Titel

Verifying Validity of Selected Forms of Syllogisms with Intermediate Quantifiers Using Peterson’s Rules

Ist Teil von

• Fuzzy Logic and Technology, and Aggregation Operators, p.357-368

Ort / Verlag

Cham: Springer Nature Switzerland

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The most reliable method for how the validity of a logical syllogism can be verified is to formalize it and show that there is either a formal proof or it is true in any model. A specific method for proving validity is to use special rules that have been used by logicians. However, we cannot be sure that they indeed verify the validity of syllogisms. The goal of this paper is to show that the rules indeed work. In his book [15], Peterson studied syllogisms with intermediate quantifiers and suggested extension of the rules also to them. In this paper, we formalize them and prove that a logical syllogism of Figure I with intermediate quantifiers is valid iff it satisfies four extended Peterson’s rules.