zbMATH — the first resource for mathematics

The Liar paradox and fuzzy logic. (English) Zbl 0945.03031
Summary: Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate \(\text{Tr}(x)\) saying “\(x\) is true” and satisfying the “dequotation schema” \(\varphi\equiv \text{Tr}(\overline\varphi)\) for all sentences \(\varphi\)? This problem is investigated in the frame of Łukasiewicz infinitely valued logic.

03B50 Many-valued logic
03F30 First-order arithmetic and fragments
03B52 Fuzzy logic; logic of vagueness
Full Text: DOI
[1] SOFSEM’95: Theory and practice of infor-matics (Milovy, Czech Republic, 1995) 1012 pp 31–
[2] The philosophical computer (1998)
[3] Mehrwertige Logik (1988)
[4] Mathematische Annalen 71 pp 97– (1910)
[5] Liar’s paradox and truth-qualification principle (1979)
[6] DOI: 10.1023/A:1004948116720 · Zbl 0869.03015
[7] Sitzngsberichte Berliner Mathematische Gesellschaft 58 pp 41– (1957)
[8] Die Nichtaxiomatisierbarkeit des unendlichwertigen PrÄdikatenkalkÜls von Łukasiewicz 27 pp 159– (1962)
[9] Metamathematics of first-order arithmetic pp 460– (1993)
[10] On the definition of an infinitely-valued predicate calculus 25 pp 212– (1960) · Zbl 0105.00501
[11] Metamathematics of fuzzy logic (1998) · Zbl 0937.03030
[12] Fixed point theorems (1974)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.