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Full Idea
Under strong Kleene tables, a disjunction will be true if one of the disjuncts is true, regardless of whether or not the other disjunct has a truth-value; under the weak table it is required that the other disjunct also have a value. So for other cases.
Clarification
'Kleene' is (oddly) pronounced 'Claynee'
Gist of Idea
Strong Kleene disjunction just needs one true disjunct; Weak needs the other to have some value
Source
Kit Fine (Some Puzzles of Ground [2010], n7)
Book Ref
-: 'Notre Dame Journal of Formal Logic' [-], p.116
A Reaction
[see also p.111 of Fine's article] The Kleene tables seem to be the established form of modern three-valued logic, with the third value being indeterminate.
8942 | Lukasiewicz's L3 logic has three truth-values, T, F and I (for 'indeterminate') [Lukasiewicz, by Fisher] |
14263 | Strong Kleene disjunction just needs one true disjunct; Weak needs the other to have some value [Fine,K] |
21602 | Many-valued logics don't solve vagueness; its presence at the meta-level is ignored [Williamson] |
18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
8943 | Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher] |
16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |