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Nonmonotonic inference operations

MICHAEL FREUND, DANIEL LEHMANN
1993 Logic Journal of the IGPL  
These operations describe the nonmonotonic logics both humans and machines seem to be using when infering defeasible information from incomplete knowledge.  ...  This study of in nitary inference operations is inspired by the results of 11] on nitary nonmonotonic operations, but this paper is self-contained. 1. is asymmetric i 8s; t 2 U such that s t, we have t  ...  Conclusions and Further Work We have presented a number of families of nonmonotonic inference operations.  ... 
doi:10.1093/jigpal/1.1.23 fatcat:5fqmsuxcorahress7mj5b7hup4

Nonmonotonic inference operations [article]

Michael Freund, Daniel Lehmann
2002 arXiv   pre-print
This study of infinitary inference operations is inspired by the results of Kraus, Lehmann and Magidor on finitary nonmonotonic operations, but this paper is self-contained.  ...  These operations describe the nonmonotonic logics both humans and machines seem to be using when infering defeasible information from incomplete knowledge.  ...  Conclusions and Further Work We have presented a number of families of nonmonotonic inference operations.  ... 
arXiv:cs/0202031v1 fatcat:div4ti5ueza5pcwf5ltz2pgdmm

Deductive Nonmonotonic Inference Operations: Antitonic Representations

YURI KALUZHNY, DANIEL LEHMANN
1995 Journal of Logic and Computation  
We provide a characterization of those nonmonotonic inference operations C for which C(X) may be described as the set of all logical consequences of X together with some set of additional assumptions S  ...  Our results provide a satisfactory notion of pseudo-compactness, generalizing to deductive nonmonotonic operations the notion of compactness for monotonic operations.  ...  operation has a unique compact monotonic extension, but compact extensions of nonmonotonic operations are not unique.  ... 
doi:10.1093/logcom/5.1.111 fatcat:bvi5gmuj7fhebe5rtt3qgrq6dy

Deductive Nonmonotonic Inference Operations: Antitonic Representations [article]

Yuri Kaluzhny, Daniel Lehmann
2002 arXiv   pre-print
We provide a characterization of those nonmonotonic inference operations C for which C(X) may be described as the set of all logical consequences of X together with some set of additional assumptions S  ...  Our results provide a satisfactory notion of pseudo-compactness, generalizing to deductive nonmonotonic operations the notion of compactness for monotonic operations.  ...  operation has a unique compact monotonic extension, but compact extensions of nonmonotonic operations are not unique.  ... 
arXiv:cs/0203003v1 fatcat:lwp3bjkmsncqjhctn3ch5ulitu

Book Reviews: David Makinson, "Bridges from Classical to Nonmonotonic Logic", King's College Publications, London, 2005

Tomasz Jarmużek
2007 Logic and Logical Philosophy  
One of the chapter is completely devoted to connections between nonmonotonic and probabilistic inferences 2 .  ...  In the last chapter we can read about relations that connect nonmonotonic inferences with other kinds of logic.  ... 
doi:10.12775/llp.2007.007 fatcat:c3t7mjdazvbnxhbehg5rxsjz2q

Logical problems with nonmonotonicity

Piotr Łukowski
2014 Logic and Logical Philosophy  
inference.  ...  I analyzed the problem from two points of view: (1) non-formal examples for nonmonotonicity and (2) formal constructions of nonmonotonic operations/relations.  ...  Operations/relations given by the first or the third formal construction seem to be nonmonotonic, but they are not  the definiens of the definition of nonmonotonic inference is not satisfied.  ... 
doi:10.12775/llp.2014.004 fatcat:jgt7aikfdfgw3bawesyrlc46me

Ordering-based representations of rational inference [chapter]

Konstantinos Georgatos
1996 Lecture Notes in Computer Science  
Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base.  ...  The finitary fragment of this class of consequence operators has been employed by recent default logic formalisms based on maxiconsistency.  ...  This should hardly be surprising, as ranked consequence operators play the role of axiomatizing a nonmonotonic "theory", that is, a rational inference.  ... 
doi:10.1007/3-540-61630-6_12 fatcat:2abmeqsjbrdztmnzu7w4y2tgu4

Semantical considerations on nonmonotonic logic

Robert C. Moore
1985 Artificial Intelligence  
Commonsense reasoning is "nonmonotonic" in  ...  and Doyle provide for nonmonotonic logic, all the nonmonotonic inferences are valid.  ...  The problem with attempting to follow this pattern with nonmonotonic inference rules Is that we cannot reliably draw nonmonotonic Inferences at any particular stage, since something inferred at a later  ... 
doi:10.1016/0004-3702(85)90042-6 fatcat:ja5havlclrhn3azysylysdrz7i

Nonmonotonic Logics and Their Algebraic Foundations [chapter]

Mirosław Truszczyński
2006 Lecture Notes in Computer Science  
We briefly discuss motivations that led to the emergence of nonmonotonic logics and introduce two major nonmonotonic formalisms, default and autoepistemic logics.  ...  We conclude with comments on other major research directions in nonmonotonic logics.  ...  with such formulas supporting nonmonotonic inferences.  ... 
doi:10.1007/11874683_4 fatcat:u7klqrtejfe43c67l2vm2ga5x4

A Causal Theory of Abduction

A. Bochman
2007 Journal of Logic and Computation  
The paper provides a uniform representation of abductive reasoning in the logical framework of causal inference relations.  ...  Exact theories are precisely fixed points of the production operator C. Since the latter operator is monotonic and continuous, exact theories (and hence the nonmonotonic semantics) always exist.  ...  A causal nonmonotonic semantics of a production inference relation or a causal theory is the set of all its exact worlds.  ... 
doi:10.1093/logcom/exm045 fatcat:4ow5dp6kazb2pnlnxufemelr3q

A causal approach to nonmonotonic reasoning

Alexander Bochman
2004 Artificial Intelligence  
The results of the study suggest production and causal inference as general nonmonotonic formalisms providing an alternative representation for a significant part of nonmonotonic reasoning.  ...  These inference relations will be assigned, however, both standard semantics (giving interpretation to their rules), and natural nonmonotonic semantics based on the principle of explanation closure.  ...  Exact theories are precisely fixed points of the production operator C. Since the latter operator is monotonic and continuous, exact theories (and hence the nonmonotonic semantics) always exist.  ... 
doi:10.1016/j.artint.2004.07.002 fatcat:f7yp7jaly5bcrlwggu3nex7gj4

A non-monotonic ATMS based on annotated logic programs with strong negation [chapter]

Kazumi Nakamatsu, Atsuyuki Suzuki
1998 Lecture Notes in Computer Science  
Dressler's ATMS includes two meta-rules of inference, the Consistent Belief Rule and the Nogood Inference Rule, and an axiom, the Negation Axiom.  ...  We also show that these inference rules and the axiom can be reduced into the ALPSN stable model computing.  ...  An operator R E;J maps a set S of nodes to a set of nodes in the following way : (S)=fw j S`wg is a consequence operator.  ... 
doi:10.1007/bfb0055021 fatcat:47ogdeu23jg5zczcja4hebkf7e

Semantics-based Nonmonotonic Inference

Heinrich Wansing
1995 Notre Dame Journal of Formal Logic  
In this paper we discuss Gabbay's idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner's suggestion of replacing the intuitionistic  ...  Moreover, in N a more general notion of consistency can be defined and nonmonotonic deduction can thus be based on a logical system satisfying the Deduction Theorem.  ...  In order to avoid fixed-point definitions of nonmonotonic inference, in [5] Gabbay suggested basing nonmonotonic deduction on semantic consequence in a logical system extended by a consistency operator  ... 
doi:10.1305/ndjfl/1040308828 dblp:journals/ndjfl/Wansing95 fatcat:vui7sw2gh5g2vb33a3apq7vryq

Entrenchment Relations: A Uniform Approach to Nonmonotonicity [article]

Konstantinos Georgatos
2000 arXiv   pre-print
We show that Gabbay's nonmonotonic consequence relations can be reduced to a new family of relations, called entrenchment relations.  ...  Entrenchment relations provide a direct generalization of epistemic entrenchment and expectation ordering introduced by Gardenfors and Makinson for the study of belief revision and expectation inference  ...  Finally, ranked operators ( [Geo95] ), as well as, the AGM belief revision operator belong to the class of rational inference relations.  ... 
arXiv:cs/0007040v1 fatcat:h5hw72npzbchhbjjevvvyfh3vy

Page 3223 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
68T Artificial intelligence 98e:68241 focus attention on inference operations that are supraclassical in the sense of extending classical consequence.  ...  Summary: “The study of abstract properties of nonmonotonic inference has thrown up a number of general conditions on infer- ence relations that are often thought to be desirable, and sometimes even essential  ... 
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