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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Gödel Logics – A Survey
verfasst von : Norbert Preining
Erschienen in: Logic for Programming, Artificial Intelligence, and Reasoning
Verlag: Springer Berlin Heidelberg
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The logics we present in this tutorial, Gödel logics, can be characterized in a rough-and-ready way as follows: The language is standard, defined at different levels: propositional, quantified-propositional, first-order. The logics are many-valued, and the sets of truth values considered are (closed) subsets of [0, 1] which contain both 0 and 1. 1 is the ‘designated value,’ i.e., a formula is valid if it receives the value 1 in every interpretation. The truth functions of conjunction and disjunction are minimum and maximum, respectively, and in the first-order case quantifiers are defined by infimum and supremum over subsets of the set of truth values.