Partiality and its Dual

Studia Logica

Volumn 66, Issue 1, 2000, Pages 5-40

  Michael Dunn, J ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Consequence; Constructible falsity; Four valued; Intuitionistic logic; Paraconsistent; Partial; Relevance logic; Three valued

Indexed keywords

EID: 0008003063     PISSN: 00393215     EISSN: 15728730     Source Type: Journal    
DOI: 10.1023/a:1026740726955     Document Type: Article

References (74)

1. ALMUKDAD, A., and D. NELSON (1984), 'Constructible falsity and inexact predicates', The Journal of Symbolic Logic 49, 231-233.
2. ANDERSON, A.R., and N.D. BELNAP, et al (1975), Entailment: The Logic of Relevance and Necessity, vol. 1, Princeton (Princeton University Press).
3. ANDERSON, A. R., N. D. BELNAP, and J. M. DUNN, et al (1992), Entailment: The Logic of Relevance and Necessity, vol. 2, Princeton (Princeton University Press).
4. AsENJO, F., (1966), 'A calculus of antinomies', Noire Dame Journal of Formal Logic VII, 103-105.
5. BELNAP, N. D., (1970), 'Restricted quantification and conditional assertion', Nous 4, 1-12. Fuller version in H. Leblanc (ed.), Truth, Syntax and Modality, Amsterdam, NorthHolland Publishing Company, p. 48-75, 1973.
6. BELNAP, N.D., (1975), 'A useful four-valued logic', abstract in Proceedings of the 1975 International Symposium on Multiple-Valued Logic, Indiana University, Bloomington.
7. BELNAP, N.D., (1977a), 'A useful four-valued logic', in Modern Uses of Multiple-Valued Logic, J. M. Dunn and G. Epstein (eds.), Dordrecht, D. Reidel Publishing Co.
8. BELNAP, N.D., (1977b), 'How a computer should think', in Contemporary Aspects of Philosophy, G. Ryle (ed.), Stocksfield, Oriel Press Ltd, p. 30-55.
9. BLAMEY, S., (1986), 'Partial logics', in Handbook of Philosophical Logic vol. Ill, Alternatives to Classical Logic, D. Gabbay and F. Guenthner (eds.), Dordrecht, D. Reidel Publishing Company), p. 1-70.
10. DUNN, J. M., (1966), The Algebra of Intensional Logics, Doctoral Dissertation, University of Pittsburgh, Ann Arbor (University Microfilms). Some portions relevant to this paper are reprinted in Anderson, Belnap, et al. (1975) as §8 and §28.2.
11. DUNN, J. M., (1967), 'The effective equivalence of certain propositions about De Morgan lattices', The Journal of Symbolic Logic 32, 433-434.
12. DUNN, J. M., (1969), 'Natural language versus formal language', unpublished manuscript. Presented at the joint APA-ASL symposium, New York, Dec. 27.
13. DUNN, J. M., (1971), 'An intuitive semantics for first degree relevant implications' (abstract), The Journal of Symbolic Logic 36, 362-363.
14. DUNN, J. M., (1976a), 'Intuitive semantics for first-degree entailments and coupled trees', Philosophical Studies 29, 149-168.
15. DUNN, J. M., (1976b), 'A Kripke-style semantics for R-mingle using a binary accessibility relation', Studia Logica 35, 163-172.
16. DUNN, J. M., (1979), 'A theorem in 3-valued model theory with connections to number theory, type theory, and relevant logic', Studia Logica 38, 149-169.
17. DUNN, J. M., (1986), 'Relevance logic and entailment', in Handbook of Philosophical Logic vol. Ill, Alternatives to Classical Logic, D. Gabbay and F. Guenthner (eds.), Dordrecht, D. Reidel Publishing Company.
18. DUNN, J. M., (1993), 'Perp and star: Two treatments of negation', in Philosophical Perspectives 7: Language and Logic, J. Tomberlin (ed.), p. 331-357.
19. DUNN, J. M., (1997), 'A comparative study of various model-theoretic treatments of negation: A history of formal negation', D. Gabbay and H. Wansing (eds.), Dordrecht, Kluwer Academic Publishing.
20. DUNN, J. M., and N. D. BELNAP (1968), 'Homomorphisms of intensionally complemented distributive lattices', Mathematische Annalen 176, 28-38.
21. FAGIN, R., and J.Y. HALPERN (1985), 'Belief, awareness and limited reasoning: Preliminary report', in Proceedings of the Ninth International Joint Conference on Artificial Intelligence, Los Altos, Morgan Kaufmann, p. 491-501.
22. FAGIN, R., and J.Y. HALPERN (1987), 'Belief, awareness and limited reasoning', Artificial Intelligence 34, 39-76.
23. FAGIN, R., J.Y. HALPERN, Y. MOSES, M.Y. VARDI (1995), Reasoning about Knowledge, Cambridge, U.S.A, The MIT Press.
24. FINE, K., (1974), 'Models for entailment', Journal of Philosophical Logic 3, 347-372.
25. FITTING, M., (1988), 'Logic programming on a topological bilattice', Fundamenta Informatica 11, 209-218.
26. FITTING, M., (1989), 'Bilattices and the theory of truth', Journal of Philosophical Logic 18, 225-256.
27. GlNSBERG, M. L., (1987), 'Multi-valued logics', Technical Report, The Logic Group Knowledge Systems Laboratory, Department of Computer Science, Stanford University.
28. GlRARD, J.-Y., (1987), 'Linear logic', Theoretical Computer Science 50, 1-102.
29. GRZEGORCZYK, A., (1964), 'A philosophically plausible formal interpretation of intuitionistic logic', Indagiones Mathematicae 26, 596-601.
30. GuREVICH, Y., (1977), 'Intuitionistic logic with strong negation', Studia Logica 36, 49-59.
31. HAZEN, A., (199+), 'Subminimal negation', unpublished ms.
32. HORN, L., (1989), A natural history of negation, Chicago, University of Chicago Press.
33. JASPARS, J., (1994), Calculi for Constructive Communication, Ph.D. Dissertation, University of Tilburg.
34. KALMAN, J. A., (1958), 'Lattices with involution', Transactions of the American Mathematical Society 87, 485-491.
35. KLEENE, S.C., (1952), Introduction to Metamathematics, New York, D. Van Nostrand Company.
36. KRIPKE, S., (1965), 'Semantic analysis of intuitionistic logic I', in Formal Systems and Recursive Functions, J. Crossley and M. Dummett (eds.), Amsterdam, North-Holland Publishing Company, p. 92-129.
37. KRIPKE, S., (1975), 'Outline of a theory of truth', The Journal of Philosophy 72, 690-716.
38. von KUTSCHERA, F., (1969), 'Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalküle', Archiv für Mathematische Logik und Grundlagenforschung 12, 104-118.
39. LEVESQUE, H. J., (1984), 'A logic of implicit and explicit belief, in Proceedings of the National Conference on Artificial Intelligence, Los Altos, Morgan Kaufman, p. 198-202.
40. MARKOV, A.A., (1950), 'Konstruktivnaja logika', Uspéhi Matematiĉéskih Nauk, 5, no. 3, 187-188.
41. MARTIN, R. L., P.W. WOODRUFF (1975), 'On representing 'true-in-L' in L', Philosophia 5, 213-217.
42. MEYER, R. K., (1971), 'Entailment', The Journal of Philosophy 68, 808-818.
43. MEYER, R. K., (1973), 'Intuitionism, entailment, negation', in Truth, Syntax, and Modality, H. Leblanc (éd.), Amsterdam, North-Holland Publishing Co., p. 168-198.
44. MEYER, R. K., (1979), 'A Boolean-valued semantics for R', Research Paper No. 4, Australian National University, Logic Group, Research School of Social Sciences, Canberra.
45. MEYER, R. K., S. GIAMBRONE, and R. BRADY (1984), 'Where gamma fails', Studia Logica 247-256.
46. NELSON, D., (1949), 'Constructible falsity', The Journal of Symbolic Logic 14, 16-26.
47. NELSON, D., (1959), 'Negation and separation of concepts in constructive systems', in Constructivity in Mathematics, A. Heyting (ed.), Amsterdam, North-Holland Publishing Company, p. 208-225.
48. PEARCE, D., (1991), 'n Reasons for Choosing N\ Technical Report 14/91, Gruppe für Logik, Wissenstheorie und Information, Freie Universität Berlin.
49. PEARCE, D., (1993), 'Answer sets and constructive logic II: Extended logic programs and related non-monotonic formalisms', in Logic Programming and Non-monotonic Reasoning, L. Pereira and A. Nerode (eds.), Cambridge, MA, MIT Press.
50. PEARCE, D., and G. WAGNER (1990), 'Logic programming with strong negation', in Proceedings of the Workshop on Extensions of Logic Programming, Logic Notes in AI, 475, P. Schroeder-Heister (ed.), Berlin, Springer-Verlag.
51. PRIEST, G., (1977), 'The logic of paradox' (abstract), Relevance Logic Newsletter 2, 105. Reprinted in the Bulletin of the Section of Logic 6 (1977), 140-141.
52. PRIEST, G., (1979), 'The logic of paradox', Journal of Philosophical Logic 9, 415-435.
53. PRIEST, G., (1987), In Contradiction, The Hague, Martinus Nijhoff.
54. RAJU, P. T., (1954), 'The principle of four-cornered negation in Indian philosophy', Review of Metaphysics 7, 694-713.
55. RASIOWA, H., (1974), An Algebraic Approach to Non-classical Logics, Amsterdam, NorthHolland Publishing Company.
56. ROUTLEY, R., and R. K. MEYER (1972-73), 'The semantics of entailment I', in Truth, Syntax and Modality, H. Leblanc (ed.), Amsterdam, North-Holland Publishing Company, 1973, p. 199-243. 'The semantics of entailment II-IIP, Journal of Philosophical Logic 1 (1972), 53-73, 192-208.
57. ROUTLEY, R., and R. K. MEYER (1976), 'Dialectical logic, classical logic, and the consistency of the world', Studies in Soviet Thought 16, 1-25.
58. ROUTLEY, R., and R. V. ROUTLEY (1972), 'Semantics of first-degree entailment', Nous, 335-359.
59. SCOTT, D., (1973), 'Models of various type-free calculi', in Logic, Methodology and Philosophy of Science IV, P. Suppes et al (eds.), Amsterdam, North-Holland Publishing Co., p. 157-187.
60. SHRAMKO, Y., (1999), Intuitionismus und Relevanz, Berlin, Logos-Verlag.
61. SHRAMKO, Y., (2000), 'American plan for intuitionistic logic 1: An intuitive background', LOG 1C A Yearbook '99, Academy of Sciences of the Czech Republic.
62. SLANEY, J., (1989), 'The implications of paraconsistency', Technical Report TR-ARP3/89, Automated Reasoning Project, Australian national University, Canberra.
63. SLANEY, J., T. SURENDONK, and R. GIRLE (1989), 'Time, truth, and logic', Technical Report TR-ARP-11/89, Automated Reasoning Project, Australian national University, Canberra.
64. STRAWSON, P.P., (1952), Introduction to Logical Theory, London, Methuen and Co. Ltd.
65. THUSSE, E., (1992), Partial Logic and Knowledge Representation, Delft, Holland, Eburon Publishers.
66. THOMASON, R. H., (1969), 'A semantical study of constructive falsity', Zeitschrift für mathematische Logik und Grundlagen der Mathematik 15, 247-257.
67. URQUHART, A., (1986), 'Many-valued logic', in Handbook of Philosophical Logic vol. III, Alternatives to Classical Logic, D. Gabbay and F. Guenthner (eds.), Dordrecht, D. Reidel Publishing Company, p. 71-116.
68. VlSSER, A., (1984), 'Four valued semantics and the liar', Journal of Philosophical Logic 13, 181-212.
69. WAGNER, G., (1991), 'Logic programming with strong negation and inexact predicates', Journal of Logic and Computation 1, 835-859.
70. WAGNER, G., (1994), Vivid Logic: Know ledge-Based Reasoning with Two kinds of Negation, Lecture Notes in AI, 764, Berlin, Springer-Verlag.
71. WANSING, H., (1993), The Logic of Information Structures, Lectures Notes in AI, 681, Berlin, Springer-Verlag.
72. WANSING, H., (1995a), 'Semantics-based nonmonotonic inference', Noire Dame Journal of Formal Logic 36, 44-54.
73. WANSING, H., (1995b), 'Tarskian structured consequence relations and functional completeness', Mathematical Logic Quarterly 41, 73-92.
74. WOODRUFF, P. W., (1984), 'Paradox, truth and logic, part I: Paradox and truth', Journal of Philosophical Logic 13, 213-232.