Abstract
A Gentzen calculus has the ‘display property’ if every antecedent [consequent] constituent can be displayed as the antecedent [consequent] standing alone. It is explained why this property is interesting. The ‘display problem’ is the problem of designing a calculus with the display property. A perspective is suggested from which the solution of Wansing [19] can easily be seen to be incomparable with that of [4]. The perspective suggests some other solutions, which are briefly surveyed. Additional questions are raised.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Allwein, C. Hartonas. Duality for bounded lattices. Unpublished manuscript, Indiana University Logic Group Preprint Series, 1993.
A. R. Anderson, N. D. Belnap. Entailment: the logic of relevance and necessity. Vol. I, Princeton University Press, Princeton, 1975.
A. R. Anderson, N. D. Belnap, J. M. Dunn. Entailment: the logic of relevance and necessity. Vol. II, Princeton University Press, Princeton, 1992.
N. Belnap. Display logic. Journal of Philosophical Logic,11 375–417, 1982. Republished with minor changes as §62 of [3].
N. Belnap. Linear logic displayed. Notre Dame Journal of Formal Logic, 31, 14–25, 1990.
H. B. Curry. A theory of formal deducibility. Notre Dame mathematical lectures, vol. no. 6, Notre Dame University Press, Notre Dame, 1950.
J. M. Dunn. Gaggle theory: an abstraction of Galois connections and residuation with applications to negation and various logical operations. In: J. van Eijck (ed.), Logics in Al: Proceedings European Workshop JELJA 1990, pp. 31–51, Lecture Notes in Computer Sci. 478, Springer-Verlag, Berlin, 1990.
J. M. Dunn. Partial-gaggles applied to sub-structural logics. In: P. Schroeder-Heister, K. Dosen (eds.), Substructural logics, pp. 63–108, Oxford University Press, Oxford, 1993.
J. M. Dunn. A representation of relation algebras using Routley-Meyer frames. Unpublished manuscript, Indiana University Logic Group Preprint Series, 1993.
J. M. Dunn. Perp and Star: two treatments of negation. In: J. Tomberlin (ed.), Philosophical Perspectives, vol. 7, Language and Logic, pp. 331–157, 1993.
by M. E. Szabo in: The Collected Papers of Gerhard Gentzen, M. E. Szabo (ed.), pp. 69–131, North-Holland, Amsterdam, 1969.
R. Goré. Displayed intuitionistic modal logics. Technical report in preparation, Australian National University, April, 1994.
R. Goré. Displaying sub-intuitionistic logics. Technical report in preparation, Australian National University, April 1994b.
R. Goré. Intuitionistic logic redisplayed. Technical report, TR-ARP-1–1995, Australian National University, January 1995.
C. Hartonas. Lattices with operators: a unified semantics for substructural logics. Unpublished manuscript, Indiana University Logic Group Preprint Series, 1993.
C. Hartonas, J. M. Dunn. Duality theorems for partial orders, semilattices, and Galois connections and lattices. Unpublished manuscript, Indiana University Logic Group Preprint Series, 1993.
M. Kracht. Power and weakness of the modal display calculus. Technical report, Free University of Berlin, Mathematics Institute II, August, 1993.
R. K. Meyer. A general Gentzen system for implicational calculi. Relevance Logic Newsletter, 1, 198–201, 1976.
H. Wansing. Sequent calculi for normal modal propositional logics. Technical report, n. LP-92–12, University of Amsterdam, 1992, Journal of Logic and Computation, 4, 124–142, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Belnap, N. (1996). The Display Problem. In: Wansing, H. (eds) Proof Theory of Modal Logic. Applied Logic Series, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2798-3_6
Download citation
DOI: https://doi.org/10.1007/978-94-017-2798-3_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4720-5
Online ISBN: 978-94-017-2798-3
eBook Packages: Springer Book Archive