next up previous
Next: Conclusion Up: Formalizing Context (Expanded Notes) Previous: Mental States as Outer



1. Guha has put contexts into Cyc, largely in the form of microtheories. The tex2html_wrap_inline3980 example is a microtheory. See [29] for some of the details.

2. We have mentioned various ways of getting new contexts from old ones: by specializing the time or place, by specializing the situation, by making abbreviations, by specializing the subject matter (e.g. to U.S. legal history), by making assumptions and by specializing to the context of a conversation. These are all specializations of one kind or another. Getting a new context by transcending an old context, e.g. by dropping the assumption of a gravitational field, gives rise to a whole new class of ways of getting new contexts.

These are too many ways of getting new contexts to be treated separately.

3. We have used natural language examples in this article, although natural language is not our main concern. Nevertheless, we hope that formalizing context in the ways we propose may be useful in studying the semantics of natural language. Natural language exhibits the striking phenomenon that context may vary on a very small scale; several contexts may occur in a single sentence.

Consider the context of an operation in which the surgeon says, ``Scalpel''. In context, this may be equivalent to the sentence, ``Please give me the number 3 scalpel''.

4. tex2html_wrap_inline3755 can be considered a modal operator dependent on c applied to p. In this sense much of our analysis amounts to reasoning in a certain systems of modal logic or temporal logic; see [16, 22, 8].

In the propositional case, given a context language containing a set of contexts C, we can define a modal language containing modalities tex2html_wrap_inline4793 , one for each context from C. By replacing each occurrence of tex2html_wrap_inline4797 with tex2html_wrap_inline4799 , we can define a bijective translation function which to each formula of the propositional context logic assigns a well-formed modal formula. Based on this translation, [12] shows a reduction of the propositional logic of context to a propositional multi-modal logic. Similar results are obtained using proof theoretic tools in [26].

However, these results do not carry over to the quantificational case. The quantificational logic of context, for example, enables us to state that the formula tex2html_wrap_inline4514 is true in contexts which satisfy some property p(x) as follows: tex2html_wrap_inline4805 This formula has no obvious translation into standard multi-modal logic, and the meaning of such formulas which quantify over modalities is beyond the analysis commonly done in quantificational modal logic. See [9] for details.  

5. Proof theoretic approach to context has been emphasized by Richard W. Weyhrauch and Fausto Giunchiglia and his group. See [60, 61, 25, 26, 17].

6. It would be useful to have a formal theory of the natural phenomenon of context, human life, as distinct from inventing a form of context useful for AI systems using logic for representation. This is likely to be an approximate theory in the sense described in [37]. That is, the term ``context'' will appear in useful axioms and other sentences but will not have a definition involving ``if and only if''. [30] outlines one such taxonomy of contexts.

7. Useful nonmonotonic rules for lifting will surely be more complex than the examples given. See [20] for context limited consistency check.    

8. Theories along the lines of [6] are in many ways similar to formal theories of context; [59] gives one comparison. [44, 2] represent context using the tools of situation theory.

9. [23] proposes fibred semantics as a way of ``weaving of logics''. For a comparison of this approach to the formal theories of context, see [24].  

next up previous
Next: Conclusion Up: Formalizing Context (Expanded Notes) Previous: Mental States as Outer

Sasa Buvac
Sun Jul 12 14:45:30 PDT 1998