Default logic generalized and simplified

We study a generalization of default logic obtained by extending its logical, monotonic basis to disjunctive (multiple-conclusion) rules. Special attention will be paid to the representation opportunities created by such rules, in particular to the use of default justifications in the heads of the rules. On the other hand, it will be shown that even the generalized default logic can be simplified to a formal system that involves only monotonic inference rules and unconditional (‘supernormal’) default assumptions.

[1]  Alexander Bochman On the Relation Between Default and Modal Consequence Relations , 1994, KR.

[2]  Fangzhen Lin,et al.  Embracing Causality in Specifying the Indirect Effects of Actions , 1995, IJCAI.

[3]  Hudson Turner,et al.  Causal Theories of Action and Change , 1997, AAAI/IAAI.

[4]  Dov M. Gabbay,et al.  Investigations in modal and tense logics with applications to problems in philosophy and linguistics , 1976 .

[5]  Fangzhen Lin,et al.  Argument Systems: A Uniform Basis for Nonmonotonic Reasoning , 1989, KR.

[6]  Michael Gelfond,et al.  Classical negation in logic programs and disjunctive databases , 1991, New Generation Computing.

[7]  Fangzhen Lin,et al.  A Logic of Knowledge and Justified Assumptions , 1992, Artif. Intell..

[8]  Ryszard Wójcicki,et al.  Theory of Logical Calculi , 1988 .

[9]  Victor W. Marek,et al.  Modal nonmonotonic logics: ranges, characterization, computation , 1991, JACM.

[10]  Alexander Bochman,et al.  A causal approach to nonmonotonic reasoning , 2004, Artif. Intell..

[11]  Vladimir Lifschitz,et al.  Extended Logic Programs as Autoepistemic Theories , 1993, LPNMR.

[12]  Chiaki Sakama,et al.  Negation as Failure in the Head , 1998, J. Log. Program..

[13]  David Poole,et al.  A Logical Framework for Default Reasoning , 1988, Artif. Intell..

[14]  A.R.C.S. A. H. Loveless What is an abstract ? , 1990 .

[15]  Vladimir Lifschitz,et al.  Answer Sets in General Nonmonotonic Reasoning (Preliminary Report) , 1992, KR.

[16]  Alexander Bochman,et al.  Explanatory Nonmonotonic Reasoning , 2005, Advances in Logic.

[17]  Hudson Turner,et al.  On Relating Causal Theories to Other Formalisms , 1997 .

[18]  D. Gabbay Semantical investigations in Heyting's intuitionistic logic , 1981 .

[19]  David Pearce,et al.  Strongly equivalent logic programs , 2001, ACM Trans. Comput. Log..

[20]  D. Scott Completeness and axiomatizability in many-valued logic , 1974 .

[21]  Vladimir Lifschitz Minimal Belief and Negation as Failure , 1994, Artif. Intell..

[22]  Alexander Bochman,et al.  Biconsequence Relations: A Four-Valued Formalism of Reasoning with Inconsistency and Incompleteness , 1998, Notre Dame J. Formal Log..

[23]  D. J. Shoesmith,et al.  Multiple-Conclusion Logic , 1978 .

[24]  Victor W. Marek,et al.  Nonmonotonic logic - context-dependent reasoning , 1997, Artificial intelligence.

[25]  G. Gentzen Untersuchungen über das logische Schließen. I , 1935 .

[26]  Alexander Bochman On Bimodal Nonmonotonic Logics and Their Unimodal and Nonmodal Equivalents , 1995, IJCAI.

[27]  G. A. Miller,et al.  MATHEMATISCHE ZEITSCHRIFT. , 1920, Science.

[28]  Tomi Janhunen On the Effect of Default Negation on the Expressiveness of Disjunctive Rules , 2001, LPNMR.

[29]  Victor W. Marek,et al.  Relating Autoepistemic and Default Logics , 1989, KR.

[30]  Hudson Turner,et al.  A Logic of Universal Causation , 1999, Artif. Intell..

[31]  Victor W. Marek,et al.  A theory of nonmonotonic rule systems I , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[32]  M. Gelfond,et al.  Disjunctive Defaults , 1991 .

[33]  Drew McDermott,et al.  Nonmonotonic Logic II: Nonmonotonic Modal Theories , 1982, JACM.

[34]  Drew McDermott,et al.  Non-Monotonic Logic I , 1987, Artif. Intell..

[35]  Tomi Janhunen,et al.  On the intertranslatability of non‐monotonic logics , 1999, Annals of Mathematics and Artificial Intelligence.

[36]  Phan Minh Dung,et al.  An Abstract, Argumentation-Theoretic Approach to Default Reasoning , 1997, Artif. Intell..

[37]  J. Horty Nonmonotonic Logic , 2001 .

[38]  K. Segerberg Classical propositional operators , 1982 .

[39]  Alexander Bochman,et al.  A Logical Theory of Nonmonotonic Inference and Belief Change , 2001, Artificial Intelligence.

[40]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[41]  V. Wiktor Marek,et al.  Nonmonotonic Logic , 1993, Artificial Intelligence.

[42]  Robert C. Moore Semantical Considerations on Nonmonotonic Logic , 1985, IJCAI.