An algebraic study of Peterson%26apos;s Intermediate Syllogisms

作者：Turunen Esko^*

来源：Soft Computing, 2014, 18(12): 2431-2444.

DOI：10.1007/s00500-013-1216-2

• Aristotelian syllogism
• Intermediate syllogism
• Fuzzy logic
• MV-algebra

Peterson%26apos;s Intermediate Syllogisms, generalizing Aristotelian syllogisms by intermediate quantifiers %26apos;Many%26apos;, %26apos;Most%26apos; and %26apos;Almost all%26apos;, are studied. It is demonstrated that, by associating certain values V, W and U on standard Lukasiewicz 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%26apos;s system are discussed. Finally it is shown that Peterson%26apos;s bivalued intermediate syllogisms can be viewed as fuzzy theories in Pavelka%26apos;s fuzzy propositional logic, i.e. a fuzzy version of Peterson%26apos;s Intermediate Syllogisms is introduced.

• 出版日期2014-12