(Enter summary)
Abstract: this paper. Here,
drawing on all the research mentioned above for inspiration, we present a coherent
unified theory of nonmonotonic formal systems.
At the level of abstraction we achieve, we are finally able to see that nonmonotone
systems pervade ordinary mathematical practice. There is no sign of any realization
of the existence of such mathematical examples in the previous nonmonotonic logic
literature. Perhaps these connections can only be seen by having a common abstract
notion. What this... (Update)
Context of citations to this paper: More
...the first model theoretic semantics to Reiter s logic. This was a system based on sets of first order models. Marek, Nerode, and Remmel [8], gave a semantics for nonmonotonic rule systems. They translated Reiter s default rules into finitary formulas of a certain special...
...treatments which handle only Herbrand domains. Many of these languages can be used to express the recursive nonmonotonic rule systems of [17] in a finite way. After some preliminary definitions in the following section, we discuss in section 3 two important topics in reasoning...
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8: A Logic for Default Reasoning (context) - Reiter - 1980
7: The Stable Model Semantics for Logic Programming
- Gelfond - 1988
6: Foundations of Logic Programming (context) - Lloyd - 1987
BibTeX entry: (Update)
W. Marek, A. Nerode, and J. Remmel. A theory of nonmonotonic rule systems. In Proceedings of 5th IEEE Symposium on Logic in Computer Science, pages 79--94, 1990. http://citeseer.ist.psu.edu/marek90theory.html More
@inproceedings{ marek90theory,
author = "V. Wiktor Marek and Anil Nerode and Jeffrey B. Remmel",
title = "A Theory of Nonmonotonic Rule Systems",
booktitle = "Logic in Computer Science",
pages = "79-94",
year = "1990",
url = "citeseer.ist.psu.edu/marek90theory.html" }
Citations (may not include all citations):
850
A Logic for Default Reasoning (context) - Reiter - 1980
451
Circumscription --- a form of nonmonotonic reasoning (context) - McCarthy - 1980
435
Towards a theory of declarative knowledge (context) - Apt, Blair et al. - 1987
334
A Truth Maintenance System (context) - Doyle - 1979
311
Semantical Considerations on Non-Monotonic Logic (context) - Moore - 1985
304
A framework for representing knowledge (context) - Minsky - 1975
275
The Science of Programming (context) - Gries - 1981
264
Knowledge and Common Knowledge in a Distributed Environment
- Halpern, Moses - 1984
229
Theory of Recursive Functions and Effective Computability Mc.. (context) - Rogers - 1967
146
Introduction to Logic Programming (context) - Apt - 1988
132
An Assumption-based TMS (context) - de Kleer - 1986
108
A decomposition theorem for partially ordered sets (context) - Dilworth - 1950
94
the Relation between Default and Autoepistemic Logic (context) - Konolige - 1988
47
Relating Autoepistemic and Default Logics (context) - Marek, Truszczy'nski - 1989
44
Stable Semantics for Logic Programs (context) - Gelfond, Lifschitz - 1988
27
Journal of London Mathematical Society (context) - On, subsets - 1935
18
Transversal Theory (context) - Mirsky - 1971
7
Recursive Boolean Algebras (context) - Remmel - 1989
5
Effective Content of Field Theory (context) - Metakides, Nerode - 1977
5
the Relation between Truth Maintenance and Non-Monotonic Log.. (context) - Reinfrank, Dressler - 1989
4
Inheritance Reasoning in Autoepistemic Logic (context) - Gelfond, Przymusi'nska - 1989
4
Bulletin of American Mathematical Society (context) - Hall, of - 1948
3
Cornell University Press (context) - Knowledge - 1962
2
the Relationship between Circumscription and Autoepistemic L.. (context) - Gelfond, Przymusi'nska - 1986
2
Monotone Logic Programming (context) - Blair, Brown et al. - 1989
2
Logic Programming with Classical Negation (context) - Gelfond, Lifschitz - 1989
1
Complexity-theoretic Algebra III: Bases of Vector Spaces (context) - Nerode, Remmel - 1990
1
Applications of Pure Recursion Theory to Recursive Analysis (context) - Huang, Nerode - 1985
1
default logic semantics (context) - Bidoit, Froidevaux et al. - 1988
1
Metamathematics Oxford (context) - Tarski, Semantics - 1956
1
Decision procedure for default logic Mathematical Sciences I.. (context) - Marek, Nerode - 1990
1
Complexity-theoretic Algebra I: Vector Spaces over Finite Fi.. (context) - Nerode, Remmel - 1987
1
Stable models for logic programs and default logic (context) - Marek, Truszczy'nski - 1989
1
Complexity-theoretic Algebra II: Boolean Algebras (context) - Nerode, Remmel - 1989
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