The Nature of Information: A Relevant Approach Edwin Mares

Introduction
In (Mar09), I advocate replacing the notion of a truth condition in the
semantics for relevant logic with the notion of an information condition.
In the present paper, I explore the notion of information that underlies
this reading of the semantics and explain my motivations for using it.
In (Mar09) I use an objective notion of information. In this paper
I give a more detailed characterization of the notion of objective in-
formation and outline how it …ts with the semantics for relevant logic.
The notion of objective information is of information that is available
in an environment, as opposed to information that is available in one’s
mind or in a database. The key notion here is that of availability in an
environment, and I try in this paper to make that notion rather precise.
As we shall see, I am very liberal in my understanding of availability,
and this liberality is important to the relationship between information
in the present sense and logic.
The notion of information itself, although interesting, is only a means
to an end for me. I want it to be a central feature of a semantics for a
logical system. So, after my general remarks on the nature of availabil-
ity, I outline how the notion of objective information is incorporated
into the interpretation of the semantics for relevant logic. But before I
do this, I present a natural deduction formulation of relevant logic. This
natural deduction formulation itself not only provides a target system
for the semantics to characterize, but also helps with the interpretation
of the semantics itself. The natural deduction system helps to explain
what sort of information can be used to support inferences and how it
can be used in this way.