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Embedding Logics into Product Logic (1998)

Baaz, Matthias ; Hájek, Petr ; Švejda, David ; [et al.]

Springer

Studia logica 61 (1998), S. 35-47

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ISSN: 1572-8730

Keywords: fuzzy logic ; Łukasiewicz logic ; Gödel logic ; product logic ; computational complexity ; arithmetical hierarchy

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Philosophy

Notes: Abstract We construct a faithful interpretation of Łukasiewicz's logic in product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable. We prove a completeness theorem for product logic extended by a unary connective δ of Baaz [1]. We show that Gödel's logic is a sublogic of this extended product logic. We also prove NP-completeness of the set of propositional formulas satisfiable in product logic (resp. in Gödel's logic).

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1005026229560

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