Abstract
We introduce a subclass of Kripke's fixed points in which falsehood is the preferred truth value. In all of these the truthteller evaluates to false, while the liar evaluates to undefined (or overdefined). The mathematical structure of this family of fixed points is investigated and is shown to have many nice features. It is noted that a similar class of fixed points, preferring truth, can also be studied. The notion of intrinsic is shown to relativize to these two subclasses. The mathematical ideas presented here originated in investigations of so-called stable models in the semantics of logic programming.
REFERENCES
Belnap, N. D., Jr.: A useful four-valued logic, In: J. M. Dunn and G. Epstein (eds.), Modern Uses of Multiple-Valued Logic, D. Reidel, 1977.
Dunn, J. M.: Intuitive semantics for first-degree entailments and coupled trees, Philosophical Studies 29(1976), 149–168.
Fine, K.: The justification of negation as failure, In: J. E. Fenstad, I. T. Frolov and R. Hilpinen (eds.), Logic, Methodology and Philosophy of Science VIII, North-Holland, Amsterdam, 1989, 263–301.
Fitting, M. C.: A Kripke/Kleene semantics for logic programs, Journal of Logic Programming 2(1985), 295–312.
Fitting, M. C.: Notes on the mathematical aspects of Kripke's theory of truth, Notre Dame Journal of Formal Logic 27(1986), 75–88.
Fitting, M. C.: Bilattices and the theory of truth, Journal of Philosophical Logic 18(1989), 225–256.
Fitting, M. C.: Kleene's logic, generalized, Journal of Logic and Computation 1(1992), 797–810.
Fitting, M. C.: The family of stable models, Journal of Logic Programming 17(1993), 197–225.
Gelfond, M. and Lifschitz, V.: The stable model semantics for logic programming, In: R. Kowalski and K. Bowen (eds.), Proc. of the Fifth Logic Programming Symposium, MIT Press, Cambridge, MA, 1988, 1070–1080.
Ginsberg, M. L.: Multivalued logics: a uniform approach to reasoning in artificial intelligence, Computational Intelligence 4(1988), 265–316.
Gupta, A. K.: Truth and paradox, Journal of Philosophical Logic 11(1982), 1–60.
Herzberger, H. G.: Naive semantics and the liar paradox, Journal of Philosophy 79(1982), 479–497.
Kripke, S.: Outline of a theory of truth, The Journal of Philosophy 72(1975), 690–716, Reprinted in: New Essays on Truth and the Liar Paradox, R. L. Martin (ed.), Oxford 1983.
Manna, Z. and Shamir, A.: The optimal approach to recursive programs, Comm. ACM 20(1977), 824–831.
Martin, R. L. and Woodruff, P. W.: On representing “true-in-l” in l, Philosophia 5(1975), 217–221, Reprinted in: Recent Essays on Truth and the Liar Paradox, R. L. Martin (ed.), Oxford, 1984.
Tarski, A.: A lattice-theoretical theorem and its applications, Pacific Journal of Mathematics 5(1955), 285–309.
Visser, A.: Four valued semantics and the liar, Journal of Philosophical Logic 13(1984), 181–212.
Woodruff, P. W.: Paradox, truth and logic, part I, Journal of Philosophical Logic 13(1984), 213–232.
Yablo, S.: Truth and reflection, Journal of Philosophical Logic 14(1985), 297–349.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fitting, M. A Theory of Truth that Prefers Falsehood. Journal of Philosophical Logic 26, 477–500 (1997). https://doi.org/10.1023/A:1004217812355
Issue Date:
DOI: https://doi.org/10.1023/A:1004217812355