Fluted logic is the restriction of pure predicate logic to formulas in which variables play no essential role. Although fluted logic is significantly weaker than pure predicate logic, it is of interest because it seems closely to parallel natural logic, the logic that is conducted in natural language. It has been known since 1969 that if conjunction in fluted formulas is restricted to subformulas of equal arity, satisfiability is decidable. However, the decidability of sublogics lying between this restricted (homogeneous) fluted logic and full predicate logic remained unknown. In 1994 it was shown that the satisfiability of fluted formulas without restriction is decidable, thus reducing the unknown region significantly. This paper further reduces the unknown region. It shows that fluted logic with the logical identity is decidable. Since the reflection functor can be defined in fluted logic with identity, it follows that fluted logic with the reflection functor also lies within the region of decidability. Relevance to natural logic is increased since the identity permits definition of singular predicates, which can represent anaphoric pronouns.
Notre Dame J. Formal Logic
37(1):
84-104
(Winter 1996).
DOI: 10.1305/ndjfl/1040067318
Andrews, P. B., An Introduction to Mathematical Logic and Type Theory, Academic Press, Orlando, 1986. Zbl 0617.03001 MR 88g:03001 0617.03001 Andrews, P. B., An Introduction to Mathematical Logic and Type Theory, Academic Press, Orlando, 1986. Zbl 0617.03001 MR 88g:03001 0617.03001
Enderton, H. B., A Mathematical Introduction to Logic, Academic Press, New York, 1972. Zbl 0298.02002 MR 49:2239 0298.02002 Enderton, H. B., A Mathematical Introduction to Logic, Academic Press, New York, 1972. Zbl 0298.02002 MR 49:2239 0298.02002
Hintikka, J., “Surface information and depth information,” pp. 263–297 in Information and Inference, edited by J. Hintikka and P. Suppes, Reidel, Dordrecht, 1970. Zbl 0265.02005 MR 43:4625 Hintikka, J., “Surface information and depth information,” pp. 263–297 in Information and Inference, edited by J. Hintikka and P. Suppes, Reidel, Dordrecht, 1970. Zbl 0265.02005 MR 43:4625
Hintikka, J., Logic, Language-Games and Information, Clarendon Press, Oxford, 1973. Zbl 0253.02005 MR 54:4911 0253.02005 Hintikka, J., Logic, Language-Games and Information, Clarendon Press, Oxford, 1973. Zbl 0253.02005 MR 54:4911 0253.02005
Noah, A., “Predicate-functors and the limits of decidability in logic,” Notre Dame Journal of Formal Logic, vol. 21 (1980), pp. 701–707. Zbl 0416.03014 MR 82b:03042 0416.03014 10.1305/ndjfl/1093883255 euclid.ndjfl/1093883255 Noah, A., “Predicate-functors and the limits of decidability in logic,” Notre Dame Journal of Formal Logic, vol. 21 (1980), pp. 701–707. Zbl 0416.03014 MR 82b:03042 0416.03014 10.1305/ndjfl/1093883255 euclid.ndjfl/1093883255
Purdy, W. C., “A variable-free logic for anaphora,” pp. 41–70 in Patrick Suppes: Scientific Philosopher, edited by P. Humphreys, vol. 3, Kluwer Academic Publishers, Dordrecht, 1994. MR 96e:03036 Purdy, W. C., “A variable-free logic for anaphora,” pp. 41–70 in Patrick Suppes: Scientific Philosopher, edited by P. Humphreys, vol. 3, Kluwer Academic Publishers, Dordrecht, 1994. MR 96e:03036
