The value of the four values

Preferences in artificial intelligence

“…The common idea behind these approaches is that the negative information (reasons, values) is not just the complement of the positive one, but needs to be considered explicitly and formalised appropriately. In formal logic this idea has been further developing multi-valued logics and more precisely four-valued logics (see in [17], [18], [32], [100], [109], [106], [121], [155], [248], [253]). In the case of preference modelling, the use of such logics was first suggested in [252] and [82].…”

An Anytime Algorithm for Computing Inconsistency Measurement

“…Compared to two truth values used by classical semantics, the set of truth values for four-valued semantics [13,14] contains four elements: true, false, unknown and both, written by t, f, N, B, respectively. The truth value B stands for contradictory information, hence four-valued logic leads itself to dealing with inconsistencies.…”

Four-Valued Extension of Rough Sets

“…In contrast to the internal implication ⊃ proposed in [2], our implication does not satisfy the Modus Ponens, if we assume that {t, i} is the set of designated values. For instance, i → f = i.…”

“…Moreover, we have then that i → u should also be defined as i. Other implication connectives have been proposed by other authors (see, e.g., [2]). Let us make a brief comparison.…”

“…when we only consider the logical values t and f. It also extends the implication of the Kleene three-valued logic [5,16] in the sense that when we restrict truth values to {t, f, u} (or {t, f, i}), we obtain Kleene's implication. On the other hand, our implication differs from the material implication → proposed in [2], on the following two cases: u → i = t while u → i = i and i → u = t while i → u = i. The material implication → can be defined by means of negation and disjunction.…”