Up: A LOGICAL AI APPROACH
Here are some features of our formalizations.
- We offer no definition of context. There are mathematical
context structures of different properties, some of which are
useful. Asking what a context is is like asking what a group
element is. See section 4 for more on this.
- Sentences about propositions and contexts are built up from a
formula ist(c,p) which is to be understood as asserting that the
proposition p is true in the context c. When we
have entered the context c, we can write
Once a program has inferred a sentence q from p, it can
leave the context c and have ist(c,q). This generalizes
- Reasoning and communicating in context permits taking only
limited phenomena into account. Treating contexts as objects
permits stating the limitations explicitly within the formalism.
- Statements about contexts are themselves in contexts.
- There is no universal context. This is a fact of epistemology
(both of the physical world and the mathematical world). It is
always possible to generalize the concepts one has used up to the
present. Attempts at ultimate definitions always fail--and usually
in uninteresting ways. Humans and machines must start at middle
levels of the conceptual world and both specialize and
- We can deal with this phenomenon in our formalism by
ensuring that it is always possible to transcend the
outermost context used so far. Thus a robot designed in this way is
not stuck with the concepts it has been given.
- Because of the possibility of transcendence, the use of contexts
as objects is not just a matter of efficiency. Any given set of
sentences including contexts can always be flattened (at the
cost of lengthening) to eliminate explicit contexts. However, the
resulting flat theory can no longer be transcended within the
formalism, because it is not an object that can be referred to as a
- There is often a theory associated with a context--the set of
sentences true in the context. However, two contexts with the same
theory need not be the same, because they may have different
relations with other contexts. Not all useful contexts will be
closed under logical inference.
- We advocate using propositions as discussed in
[McC79] for the objects true in contexts rather than logical
or natural language sentences. This has the advantage that the set
of propositions true in a context may be finite when the set of
sentences that can express these propositions will be infinite.
However, our present applications of context would work equally well
if sentences were used. Buvac and Mason
[BBM95] treat ist(c,p) as a modal logic
formula in a propositional theory.
- Besides the truth of propositions in contexts, we consider the
value value(c,exp) of a term exp representing an
individual concept in a context c as discussed in
[McC79]. This presents problems beyond those presented by
propositions, because in general the space of values of individual
concepts will depend on some outer context.
Up: A LOGICAL AI APPROACH
Wed Feb 28 22:47:51 PST 1996