Predicate logics on display

Studia Logica

Volumn 62, Issue 1, 1999, Pages 49-75

  Wansing, Heinrich ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Display logic; Modal logic; Predicate logic; Quantifiers

Indexed keywords

EID: 52549119114     PISSN: 00393215     EISSN: 15728730     Source Type: Journal    
DOI: 10.1023/A:1005125717300     Document Type: Article

References (40)

1. ALECHINA, N., and M. VAN LAMBALGEN, Generalized Quantification as Sub structural Logic, Technical Report, ILLC, University of Amsterdam, 1995.
2. ANDRÉKA, H., J. VAN BENTHEM and I. NÉMETI, 'Back and forth between modal logic and classical logic', Journal of the Interest Group in Pure and Applied Logic 3, 685-720, 1995.
3. BELNAP, N., 'Display Logic', Journal of Philosophical Logic 11, 375-417, 1982.
4. BELNAP, N., 'Linear Logic Displayed' Notre Dame Journal of Formal Logic 31, 14-25, 1990.
5. BELNAP, N., 'The Display problem', in H. Wansing (ed.), Proof Theory of Modal Logic, 79-93, Dordrecht, Kluwer Academic Publishers, 1996.
6. VAN BENTHEM, J., Modal Foundations of Predicate Logic, Center for the Study of Language and Information, Report No. CSLI-94-191, Stanford University, 1994.
7. VAN BENTHEM, J., Exploring Logical Dynamics, CSLI Publications, Stanford, 1996.
8. DUNN, J. M., 'Gaggle theory: an abstraction of Galois connections and residuation with applications to negation and various logical operations', in J. van Eijk (ed.), Logics in AI, Proceedings European Workshop JELIA 1990, Lecture Notes in Computer Science 478, 31-51, Berlin, Springer-Verlag, 1990.
9. ENDERTON, H., A Mathematical Introduction to Logic, Academic Press, New York, Reidel, Dordrecht, 1972.
10. FITTING, M., 'Basic modal logic', in: D. M. Gabbay et al. (eds.), Handbook of Logic in Artificial Intelligence and Logic Programming. Vol. 1, Logical Foundations, Oxford UP, Oxford, 365-448, 1993.
11. GABBAY D., 'A general theory of structured consequence relations', in K. Došen and P. Schroeder-Heister (eds.), Substructural Logics, 109-151, Oxford, Clarendon Press, 1994.
12. GOLDBLATT, R., Topoi. The Categorical Analysis of Logic, Amsterdam, North-Holland, 1979.
13. GORÉ, R., 'Intuitionistic logic redisplayed' (manuscript), Department of Computer Science, University of Manchester, 1994.
14. GORÉ, R., A Uniform Display System for Intuitionistic and Dual Intuitionistic Logic, Technical Report TR-SRS-2-95, Australian National University, 1995.
15. GORE, R., 'On the completeness of classical modal display lolgic', in H. Wansing (ed.), Proof Theory of Modal Logic, 137-140, Dordrecht, Kluwer Academic Publishers, 1996.
16. GORE, R., Cut-free Dispaly Calculi for Relation Algebras, Technical Report TRARP-19-95, Australian National University, Canberra, 1995.
17. GRISHIN, V.N., 'A nonstandard logic and its application to set theory' (in Russian), in: Studies in Formalized Languages and Nonclassical Logics (in Russian), Moscow, Nauka, 135-171, 1974.
18. HUGHES, G. E., and M. J. CRESSWELL, An Introduction to Modal Logic, Methuen, London, 1968.
19. KRACHT, M., 'Power and weakness of the modal display calculus', in H. Wansing (ed.), Proof Theory of Modal Logic, 95-122, Dordrecht, Kluwer Academic Publishers, 1996.
20. KUHN, S., 'Quantifiers as modal operators', Studia Logica 39, 145-158, 1980.
21. VAN LAMBALGEN, M., 'Natural deduction for generalized quantifiers', in J. van der Does and J. van Eijck (eds.), Generalized Quantifier Theory and Applications, 143-154, Dutch Network for Language, Logic and Information, Amsterdam, 1991,
22. MARX, M., and Y. VENEMA, A Modal Logic of Relations, Technical Report IR-396, Vrije Universiteit Amsterdam, 1995 (to appear in: Studia Logica).
23. MEYER-VIOL, W., Instantial Logic, PhD thesis, University of Amsterdam, Institute of Logic, Language and Computationj, 1995.
24. MONTAGUE, R., 'Logical necessity, physical necessity, ethics and quantifiers', Inquiry 4, 259-269, 1960.
25. NÉMETI, I., 'Algebraizations of quantifier logics: an introductory overview', Studia Logica 50, 485-570, 1991.
26. RESTALL, G, Displaying and Deciding Substructural Logics 1: Logics with Contraposition, Technical Report TR-ARP-11-94, Australian National University, Canberra, 1994 (to appear in: Journal of Philosophical Logic).
27. RESTALL, G., 'Display logic and gaggle theory', Reports on Mathematical Logic 29, 133-146, 1995 (published 1996).
28. ROORDA, D., 'Dyadic modalities and Lambek calculus', in: M. de Rijke (ed.), Diamonds and Defaults, 215-253, Dordrecht, Kluwer Academic Publishers, 1993.
29. DE RIJKE, M., Extending Modal Logic, PhD thesis, University of Amsterdam, Institute of Logic, Language and Computationj, 1993.
30. RYAN, M., P.-Y. SCHOBBENS and O. RODRIGUES, 'Counterfactuals and updates as inverse modalities', in: Y. Shoam (ed.), TARK '96. Proceedings Theoretical Aspects of Rationality and Knowldege, 163-173. San Francisco. Morgan Kaufmann, 1996.
31. VENEMA, Y., Many-Dimensional Modal Logic, PhD thesis, University of Amsterdam, Math. Institutue, 1991.
32. VENEMA, Y., 'Cylindric modal logic', Journal of Symbolic Logic 60, 591-623, 1995.
33. VENEMA, Y., 'A modal logic of quantification and substitution', in L. Czirmaz, D. Gabbay and M. de Rijke (eds.), Logic Colloquium '92, 293-309, CSLI Publications, 1995.
34. WANG, H., A Survey of Mathematical Logic, Peking, Science Press, 1962.
35. WANSING, H., 'Sequent calculi for normal modal propositional logics', Journal of Logic and Computation 4, 125-142, 1994.
36. WANSING, H., 'A proof-theoretic proof of functional completeness for many modal and tense logics', in H. Wansing (ed.), Proof Theory of Modal Logic, 123-136, Dordrecht, Kluwer Academic Publishers, 1996.
37. t' Bulletin of the Section of Logic 25, 1996. 60-62.
38. WANSING, H., 'Strong cut-elimination in Display Logic', Reports on Mathematical Logic 29, 117-131, 1995 (published 1996).
39. WANSING, H., 'A full-circle theorem for simple tense logic', in M. de Rijke (ed.), Advances in Intensional Logic, Kluwer Academic Publishers, Dordrecht, 171-190, 1997.
40. WANSING, H., 'Displaying as temporalizing. Sequent systems for subintuitionistic logics', in S. Akama (ed.), Logic, Language and Computation, Kluwer Academic Publishers, Dordrecht, 159-178, 1997.