A co-inductive language and truth degrees

Authors:
Shunsuke Yatabe
Affiliations:
Collaborate Research Team for Verification, National Institute of Advanced Industrial Science and Technology, Japan
Venue:
MOL'11 Proceedings of the 12th biennial conference on The mathematics of language
Year:
2011

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Abstract

We investigate what happens if PAŁTr2, a co-inductive language, formalizes itself. We analyze the truth concept in fuzzy logics by formalizing truth degree theory in the framework of truth theories in fuzzy logics. Hájek-Paris-Shepherdson's paradox [HPS00] involves that so called truth degrees do not represent the degrees of truthhood (defined by the truth predicate) correctly in Łukasiewicz infinite-valued predicate logic ∀Ł, therefore truth degree theory fails there.