Details

Autor(en) / Beteiligte

• Turunen, Esko

Titel

An algebraic study of Peterson’s Intermediate Syllogisms

Ist Teil von

• Soft computing (Berlin, Germany), 2014-12, Vol.18 (12), p.2431-2444

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2014

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Peterson’s Intermediate Syllogisms, generalizing Aristotelian syllogisms by intermediate quantifiers ‘Many’, ‘Most’ and ‘Almost all’, are studied. It is demonstrated that, by associating certain values V, W and U on standard Łukasiewicz MV-algebra with the first and second premise and the conclusion, respectively, the validity of a corresponding intermediate syllogism is determined by a simple MV-algebra (in-)equation. Possible conservative extensions of Peterson’s system are discussed. Finally it is shown that Peterson’s bivalued intermediate syllogisms can be viewed as fuzzy theories in Pavelka’s fuzzy propositional logic, i.e. a fuzzy version of Peterson’s Intermediate Syllogisms is introduced.