Graded tableaux for Rational Pavelka Logic

✍ Scribed by Luigi Di Lascio; Antonio Gisolfi

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 134 KB
• Volume: 20
• Category: Article
• ISSN: 0884-8173
• DOI: 10.1002/int.20117

✦ Synopsis

In this article, a sound and complete tableau system for Rational Pavelka Logic ~RPL! is introduced. Extended formulas are used as the counterpart of the graded formulas. In this calculus, if we want to show that the graded formula ~x, r! is tableau provable ~in the finite fuzzy theory F, respectively!, we develop a tableau for the extended formula @r, x# ~for the set of extended formulas $@r, x# , @x 1 , a 1 # , . . . , @x n , a n # %, respectively!. If this tableau closes we claim that ~x, r! is tableau provable ~in the fuzzy theory F, respectively!. We claim also that x is valid at the degree equal to the l.u.b. that allows the closure of the tableaux. Our tableaux are a first step toward efficient procedures of automated deduction in narrow fuzzy logic with truth constants.