Many-valued logic vs. many-valued semantics
By Jaroslav Peregrin
Hence the task of the logician, viewed from this perspective, is the delimitation of the range of acceptable truth-valuations of the sentences of the given language – taking note of all the "lawful" features of the separation of true sentences from false ones. Let us call this the separation problem.
Consider the language of classical propositional calculus (and consequently the part of natural language which it purports to regiment). Here the ensuing "laws of truth" are quite transparent:(i) ¬A is true iff A is not true
(ii) A^B is true iff A is true and B is true
(iii) A∨B is true iff A is true or B is true
(iv) A→B is true iff A is not true or B is true
Every truth-valuation which fulfills these constraints is acceptable and every acceptable truth-valuation does fulfill them. But the situation is, as is well known, not so simple once we abandon the calm waters of the classical propositional calculus.
Posted by Tony Marmo at 00:01 BST