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In the medium of these unassuming examples, we begin to see the activities of logical inference and methodical inquiry as ''information clarifying operations'' (ICO's).

In the medium of these unassuming examples, we begin to see the activities of logical inference and methodical inquiry as ''information clarifying operations''.

First, we drew a distinction between information maintaining and information reducing processes and we noted the related distinction between equational and implicational inferences.  I will use the acronyms EROI and IROI, respectively, for the equational and implicational analogues of the various rules of inference.

First, we drew a distinction between information preserving and information reducing processes and we noted the related distinction between equational and implicational inferences.  I will use the acronyms EROI and IROI, respectively, for the equational and implicational analogues of the various rules of inference.

For example, we considered the brands of ''information fusion'' that are involved in a couple of standard rules of inference, taken in both their equational and their illative variants.

For example, we considered the brands of ''information fusion'' that are involved in a couple of standard rules of inference, taken in both their equational and their illative variants.

In particular, let us assume that we begin from a state of uncertainty about the universe of discourse ''X'' = '''B'''³ that is standardly represented by a uniform distribution ''u'' : ''X'' → '''B''' such that ''u''(''x'') = 1 for all ''x'' in ''X'', in short, by the constant proposition 1 : ''X'' → '''B'''.  This amounts to the ''maximum entropy sign state'' (MESS).  As a measure of uncertainty, let us use either the multiplicative measure given by the cardinality of ''X'', commonly notated as |''X''|, or else the additive measure given by log |X|.  In this frame we have |''X''| = 8 and log |''X''| = 3, to wit, 3 bits of doubt.

In particular, let us assume that we begin from a state of uncertainty about the universe of discourse <math>X = \mathbb{B}^3</math> that is standardly represented by a uniform distribution <math>u : X \to \mathbb{B}</math> such that <math>u(x) = 1\!</math> for all <math>x\!</math> in <math>X,\!</math> in short, by the constant proposition <math>1 : X \to \mathbb{B}.</math> This amounts to the ''maximum entropy sign state'' (MESS).  As a measure of uncertainty, let us use either the multiplicative measure given by the cardinality of <math>X,\!</math> commonly notated as <math>|X|,\!</math> or else the additive measure given by <math>\log_2 |X|.\!</math> In this frame we have <math>|X| = 8\!</math> and <math>\log_2 |X| = 3,\!</math> to wit, 3 bits of doubt.

Let us now consider the various rules of inference for transitivity in the light of their performance as information-developing actions.

Let us now consider the various rules of inference for transitivity in the light of their performance as information-developing actions.