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On the logic of incomplete answers

Published online by Cambridge University Press:  12 March 2014

M. J. Cresswell
M. J. Cresswell*
Affiliation:
Victoria University of Wellington, Wellington, New Zealand
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Extract

I have argued in [1] that a concept bearing some resemblance to ‘p is the answer to d’ (p a proposition and d a question) can be defined wherever d has the form,

‘For which a's is it the case that A (a)?’ (Qa)A(a)

where a is a variable and A a wff containing a. To say that p is the true and complete answer to (Qa)A(a) is expressed as saying that p is logically equivalent to the true conjunction of A(a) or ~A(a) for each a. It is defined as;

Such a concept of answer is like Belnap's [2] direct true answer to a complete list question, or like Harrah's use [3] (p. 43) of the notion of a state description. The main difference between my approach and that of Belnap and Harrah is that while they are concerned to develop a formal metalanguage for discussion of questions and answers I am concerned to express, as far as possible in existing systems, certain interrogative statements; in particular statements of the form ‘— is the (an) answer to —’.

While the account in [1] does give a formal analysis of one ‘answer’ concept there are respects in which it is inadequate.

1. Since it uses entailment (or strict implication) to define the relation between p the answer and d the question we can shew that if p is the answer to d and q is logically equivalent to p then q is the answer to d.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 30 , Issue 1 , March 1965 , pp. 65 - 68
Copyright
Copyright © Association for Symbolic Logic 1965

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References

REFERENCES

[1]Cresswell, M. J., The Logic of Interrogatives, Proceedings of the 1963 Logic Colloquium: Formal Systems and Recursive Functions, North Holland (forthcoming).Google Scholar
[2]Belnap, Nuel D. Jr., An Analysis of Questions: Preliminary Report, System Development Corporation (1963).Google Scholar
[3]Harrah, David, Communication: A Logical Model, M.I.T. Press (1963).Google Scholar
[4]Prior, A. N., Time and Modality, Oxford (1963).Google Scholar
[5]Tarski, A., Logic, Semantics and Metamathematics, Oxford (1956).Google Scholar
[6]Whitehead, A. N. and Russell, B. A. W., Principia Mathematica, Cambridge (1910).Google Scholar