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Language Non-monotonicity

All the non-monotonic formalisms to date have worked within a fixed language. The result of non-monotonic reasoning gave a theory, that was perhaps different from the logical closure of the information given, but was expressed in the same language. A novelty we propose to examine is that often we change the language we use to represent the world, because of new information we are given.

Thus, not only is our reasoning non-monotonic, but our language may change, in non-trivial ways, as the result of additional information. In the previous example, our language changed, as our states went from three-tuples to four-tuples.

If we wish to map theories in one language into theories in a possibly different language, then we need a way of referring to languages and theories as objects. Most usually theories are used as the representation of the information about a particular subject. In contrast, we intend to consider representing information about theories. That is, we intend to reason about theories, not in them.

We propose that first order theories, which we call contexts, be represented as objects. This follows the suggestions of McCarthy [McC87a]. McCarthy [McC93] stresses one particular way of relating contexts--by writing sentences that state if one sentence is true in one context, than another sentence is true in a second context. These are called lifting axioms. We also consider structural relations between contexts.

Eyal Amir
Sat Mar 15 22:18:39 PST 1997