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NDL maintains a global set of formulas called
the assumption base. We can think of the elements of the
assumption base as our premises--formulas that we regard as true.
Initially the system starts with the empty assumption base.
Every time an assertion is made or a theorem is proved,
the corresponding formula is inserted into the assumption base.
We will use the letter
to designate a typical assumption base.
In what follows we describe the assumption-base semantics of each possible
type of NDL proof.
A key idea behind NDL is that the meaning of a proof is a function
over assumption bases. Put more plainly, the meaning of a proof
depends on what assumption base we evaluate that proof in.
This is similar to how the meaning of an imperative program
is formally captured. We say that the meaning of x := y + 3;
is a function over stores. That is, the result we get by
executing this instruction depends on (or ``is relative to'')
a given store.
Note: the assumption base can be inspected at any point by selecting
Options and then View assumption base from the top menu bar.
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2004-08-06