The value of the four values

Artificial Intelligence

Volumn 102, Issue 1, 1998, Pages 97-141

  Arieli, Ofer ^a   Avron, Arnon ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Bilattices; Multiple valued systems; Paraconsistency; Preferential logics; Reasoning

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTERS; MATHEMATICAL TECHNIQUES; THEOREM PROVING;

FORMAL LOGIC;

EID: 0032093523     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0004-3702(98)00032-0     Document Type: Article

References (46)

1. A.R. Anderson, N.D. Belnap, Entailment, Vol. 1, Princeton University Press, Princeton, NJ, 1975.
2. O. Arieli, A. Avron, Logical bilattices and inconsistent data, in: Proceedings 9th IEEE Annual Symposium on Logic in Computer Science, IEEE Press, 1994, pp. 468-476.
3. O. Arieli, A. Avron, Reasoning with logical bilattices, J. Logic, Language and Information 5 (1) (1996) 25-63.
4. O. Arieli, A. Avron, Bilattices and paraconsistency, in: Proceedings First World Congress on Paraconsistency. 1997.
5. O. Arieli, A. Avron, A model-theoretic approach to recover consistent data from inconsistent knowledge-bases, J. Automat, Reasoning, to appear.
6. A. Avron, Natural 3-valued logics: characterization and proof theory, J. Symbolic Logic 56 (1) (1991) 276-294.
7. A. Avron, The structure of interlaced bilattices. J. Math. Structures in Computer Science 6 (1996) 287-299.
8. N.D. Belnap, A useful four-valued logic, in: G. Epstein, J.M. Dunn (Eds)., Modern Uses of Multiple-Valued Logic, Reidel Publishing Company, Boston, 1977, pp. 7-73.
9. N.D. Belnap, How computer should think, in: G, Ryle (Ed.), Contemporary Aspects of Philosophy, Oriel Press, 1977, pp. 30-56.
10. N.C.A. da Costa, On the theory of inconsistent formal systems, Notre Dame J. Formal Logic 15 (1974) 497-510.
11. C.V. Damasio, L.M. Pereira, A model theory for paraconsistent logic programming, in: Proceedings 7th Portuguese Conference on Artificial Intelligence, Lecture Notes in AI, Vol. 990, Springer, Berlin, 1995. pp. 409-418.
12. M. Davis, Note on the mathematics of nonmonotonic reasoning. Artificial Intelligence 13 (1980) 73-80.
13. I.L.M. D'Ottaviano, The completeness and compactness of a three-valued first-order logic, Revista Colombiana de Matematicas XIX (1-2) (1985) 31-42.
14. J.M. Dunn, Relevant logic and entailment, in: D. Gabbay, F. Guenthner (Eds.), Handbook of Philosophical Logic III, 1986.
15. R.L. Epstein, The Semantic Foundation of Logic. Vol. I: Propositional Logics, Kluwer Academic Publishers, Dordrecht, Netherlands, 1990.
16. M. Fitting, Negation as refutation, in: Proceedings 4th Annual Symposium on Logic in Computer Science, IEEE Press, 1989, pp. 63-70.
17. M. Fitting, Bilattices in logic programming, in: G. Epstein (Ed.), 20th International Symposium on Multiple-Valued Logic, IEEE Press, 1990, pp. 238-246.
18. M. Fitting, Kleene's logic, generalized, J. Logic Comput. 1 (1990) 797-810.
19. M. Fitting, Bilattices and the semantics of logic programming, J. Logic Programming 11 (2) (1991) 91-116.
20. M. Fitting, The family of stable models, J. Logic Programming 17 (1993) 197-225.
21. M. Fitting, Kleene's three-valued logics and their children, Fundamenta Informaticae 20 (1994) 113-131.
22. J. M. Font, M. Moussavi, Note on a six-valued extension of three-valued logic, J. Appl. Non-Classical Logic 3 (2) (1993) 173-187.
23. M. Freund, D. Lehmann, P. Morris. Rationality, transitivity and contraposition, Artificial Intelligence 52 (1991) 191-203.
24. D.M. Gabbay, Theoretical foundation for nonmonotonic reasoning in expert systems, in: K.P. Apt (Ed.), Proceedings NATO Advanced Study Inst. on Logic and Models of Concurent Systems, Springer, Berlin, 1985, pp. 439-457.
25. M. Gelfond, V. Lifschitz, The stable model semantics for logic programming, in: R.A. Kowalski, K.A. Bowen (Eds.), Proceedings 5th Logic Programming Symposium, MIT Press, Cambridge, MA, 1988, pp. 1070-1080.
26. M.L. Ginsberg, Multi-valued logics, in: M.L. Ginsberg (Ed.), Readings in Nonmonotonic Reasoning, Morgan Kaufmann, Los Altos, CA, 1987, pp. 251-258.
27. M.L. Ginsberg, Multivalued logics: a uniform approach to reasoning in AI, Computer Intelligence 4 (1988) 256-316.
28. M. Kifer, E.L. Lozinskii. A logic for reasoning with inconsistency, J. Automat. Reasoning 9 (2) (1992) 179-215.
29. S. Kraus, D. Lehmann, M. Magidor, Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence 44 (1-2) (1990) 167-207.
30. D. Lehmann, Plausibility logic, in: Proceedings 5th Conference of Computer Science Logic, Springer, Berlin, 1992, pp. 227-241.
31. D. Lehmann, M. Magidor, What does a conditional knowledge base entail?, Artificial Intelligence 55 (1992) 1-60.
32. V. Lifschitz, Benchmark problems for formal nonmonotonic reasoning, in: Proceedings 2nd International Workshop on Nonmonotonic Reasoning, Springer, Berlin, 1988, pp. 202-219.
33. D. Makinson, General theory of cumulative inference, nonmonotonic reasoning, M. Reinfrank (Ed.), Lecture Notes in AI, Vol. 346, Springer, Berlin, 1989, pp. 1-18.
34. D. Makinson, General patterns in nonmonotonic reasoning, in: D. Gabbay, C. Hogger, J. Robinson (Eds.), Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 3, Oxford Science Publishers, 1994, pp. 35-110.
35. J.M. McCarthy, Circumscription - a form of nonmonotonic reasoning, Artificial Intelligence 13 (1980) 27-39.
36. F.J. Pelletier, Seventy-five problems for testing automatic theorem provers, J. Automat. Reasoning 2 (1986) 191-216.
37. G. Priest, Reasoning about truth, Artificial Intelligence 39 (1989) 231-244.
38. G. Priest, Minimally Inconsistent LP, Studia Logica 50 (1991) 321-331.
39. L.I. Rozoner, On interpretation of inconsistent theories. Information Sciences 47 (1989) 243-266.
40. K. Schlechta, Nonmonotonic logics - basic concepts, results, and techniques, in: Lecture Notes in AI, Vol. 1187, Springer, Berlin, 1997.
41. A. Schoter, Evidential bilattice logic and lexical inferences, J. Logic, Language and Information 5 (1) (1996) 65-105.
42. Y. Shoham, A semantical approach to nonmonotonic logics, in: M.L. Ginsberg (Ed.), Readings in Nonmonotonic Reasoning, Morgan Kaufmann, Los Altos, CA, 1987, pp. 227-249.
43. Y. Shoham, Reasoning about Change: Time and Causation from the Standpoint of Artificial Intelligence, MIT Press, Cambridge, MA, 1988.
44. V.S. Subrahmanian, Mechanical proof procedures for many valued lattice-based logic programming, J. Nonclassical Logic 7 (1990) 7-41.
45. V.S. Subrahmanian, Paraconsistent disjunctive deductive databases, in: Proceedings 20th International Symposium on Multiple Logic, IEEE Press, 1990, pp. 339-345.
46. G. Wagner, Disjunctive, deductive and active knowledge bases, Technical Report 22/94 (ver 1.0), Freien Universität Berlin, 1994.