Abstract
We study the Knights and Knaves problem, and find that for a proper treatment via theorem-proving, an interaction with natural language processing research is helpful. In particular, we discuss Ohlbach's claim that first-order logic is not well suited to handling this problem. Then we provide an interpretation of the problem using indexicals, axiomatize it, and prove the desired result. We conclude by suggesting a broader context for dealing with ‘self-utterances’ in automatic theorem-proving.
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References
Allen, J., ‘Toward a general theory of action and time’, Artificial Intelligence, 23, 123–154 (1984).
Allen, J. and Perrault, R., ‘Analyzing intentions in utterances’, Artificial Intelligence, 15, 143–178 (1980).
Barwise, J. and Perry, J., Situations and Attitudes, MIT Press, Cambridge, Massachusetts (1983).
Harper, M. and Charniak, E., ‘Time and tense in English’, Proceedings of the 24th Annual Meeting of the Association for Computational Linguistics, Columbia University, New York, 3–9 (1986).
Ohlbach, H. J., ‘Predicate logic hacker tricks’, J. of Automated Reasoning 1, 435–440 (1984).
Perlis, D., ‘Languages with self-reference I’, Artificial Intelligence 25, 301–322 (1985).
Smith, B., ‘Varieties of self-reference’, in J. Halpern (ed.), Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning About Knowledge, Morgan Kaufmann, Los Altos, California (1986).
Smullyan, R., What is the Name of this Book?, Prentice-Hall, Englewood Cliffs, New Jersey (1978).
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Miller, M., Perlis, D. Proving self-utterances. J Autom Reasoning 3, 329–338 (1987). https://doi.org/10.1007/BF00243796
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DOI: https://doi.org/10.1007/BF00243796