Copyright © 1998 Published by Elsevier Science B.V.
Probabilistic semantics for Delgrande's conditional logic and a counterexample to his default logic
Received 3 June 1997;
Abstract
This paper establishes two results. First, that a corrected version of the propositional part of Delgrande's conditional logic corresponds to Adams' extended probability logic and has both an infinitesimal and a noninfinitesimal probability semantics. Second, that there is a defect in Delgrande's default logic: it may produce inconsistent extensions.
Author Keywords: Conditional logic; Probabilistic semantics; Default logic
References
[1]. E.W. Adams, The Logic of Conditionals. , Reidel, Dordrecht (1975).
[2]. E.W. Adams, A note on comparing probabilistic and modal logics of conditionals. Theoria 43 (1977), pp. 186–194.
[3]. E.W. Adams, On the logic of high probability. J. Philosophical Logic 15 (1986), pp. 255–279. View Record in Scopus | Cited By in Scopus (11)
[4]. D. Bamber, Probabilistic entailment of conditionals by conditionals. IEEE Trans. Systems Man. Cybernet. 24 (1994), pp. 1714–1723. View Record in Scopus | Cited By in Scopus (5)
[5]. S. Benferhat, D. Dubois and H. Prade, Possibilistic and Standard probabilistic semantics of conditional knowledge. In: Proceedings National Conference on Artificial Intelligence (AAAI-97) (1997).
[6]. C. Boutilier, Revision sequences and nested conditionals. In: Proceedings International Joint Conference on Artificial Intelligence (IJCAI-93) (1993), pp. 519–525.
[7]. G. Brewka, Nonmonotonic Reasoning. The Logic of Commonsense. , Cambridge University Press (1991).
[8]. J.P. Delgrande, A first-order conditional logic for prototypical properties. Artificial Intelligence 33 (1987), pp. 105–130. Abstract |
PDF (1207 K)
| View Record in Scopus | Cited By in Scopus (18)
[9]. J.P. Delgrande, An approach to default reasoning based on a first-order conditional logic: revised report. Artificial Intelligence 36 (1988), pp. 63–90. Abstract |
PDF (1332 K)
| View Record in Scopus | Cited By in Scopus (22)
[10]. A.M. Frisch and P. Haddawy, Anytime deduction for probabilistic logic. Artificial Intelligence 69 (1994), pp. 93–122. Abstract |
PDF (1758 K)
| View Record in Scopus | Cited By in Scopus (38)
[11]. P. Gärdenfors and D. Makinson, Nonmonotonic inference based on expectations. Artificial Intelligence 65 (1994), pp. 197–245. Abstract |
PDF (2850 K)
| View Record in Scopus | Cited By in Scopus (62)
[12]. M. Goldszmidt and J. Pearl, Qualitative probabilities for default reasoning, belief revision and causal modeling. Artificial Intelligence 84 (1996), pp. 57–112. Article |
PDF (4044 K)
| View Record in Scopus | Cited By in Scopus (40)
[13]. G.E. Hughes and M.J. Cresswell, A Companion to Modal Logic. , Methuen, London and New York (1984).
[14]. S. Kraus, D. Lehmann and M. Magidor, Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44 (1990), pp. 167–207. Abstract |
PDF (2136 K)
| View Record in Scopus | Cited By in Scopus (256)
[15]. D. Lehmann and M. Magidor, What does a conditional knowledge base entail?. Artificial Intelligence 55 (1992), pp. 1–60. Abstract |
PDF (3350 K)
| View Record in Scopus | Cited By in Scopus (126)
[16]. W. Nejdl, The P-systems: a systematic classification of logics of nonmonotonicity—extended report. In: Technical Report, Technical University of Vienna (1992).
[17]. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. , Morgan Kaufmann, San Mateo, CA (1988).
[18]. G. Schurz, Probabilistic default logic based on irrelevance and relevance assumptions. In: Qualitative and Quantitative Practical ReasoningD. Gabbay et al.Lecture Notes in Artificial Intelligence Vol. 1244, Springer, Berlin (1997), pp. 536–553.






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