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Nonmonotonic reasoning, preferential models and cumulative logics

Sarit Kraus, Daniel Lehmann, Menachem Magidor
1990 Artificial Intelligence  
The preferential models proposed here are a much stronger tool than Adams' probabilistic semantics. The basic language used in this paper is that of propositional logic.  ...  W e study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the eld of nonmonotonic reasoning by reference to positive properties.  ...  Acknowledgments Discussions with and remarks from David Makinson, Johan van Benthem, David Israel, Benjamin Grosof and an anonymous referee helped us put this work in perspective and improve its presentation  ... 
doi:10.1016/0004-3702(90)90101-5 fatcat:sygj72isgbdjlmsmaz2ynsmacu

Nonmonotonic Reasoning, Preferential Models and Cumulative Logics [article]

Sarit Kraus, Daniel Lehmann, Menachem Magidor
2002 arXiv   pre-print
The "preferential" models proposed here are a much stronger tool than Adams' probabilistic semantics. The basic language used in this paper is that of propositional logic.  ...  We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties.  ...  Monotonic and and cumulative monotonic reasoning are too powerful, i.e. simple cumulative and simple preferential models are too restrictive to represent the wealth of nonmonotonic inference procedures  ... 
arXiv:cs/0202021v1 fatcat:rnf6yj3dobcebaata3vdb6p5ei

General patterns for nonmonotonic reasoning: from basic entailments to plausible relations

O Arieli
2000 Logic Journal of the IGPL  
In addition, we present a general method for constructing plausible nonmonotonic relations. This method is based on a multiple-valued semantics, and on Shoham's idea of preferential models. 1 L.  ...  These generalizations allow the use of monotonic nonclassical logics as the underlying logic upon which nonmonotonic reasoning may be based.  ...  Acknowledgment This research was supported by The Israel Science Foundation founded by The Israel Academy of Sciences and Humanities.  ... 
doi:10.1093/jigpal/8.2.119 fatcat:rx6sovbmbngjbg4mktqux53uvi

Page 3888 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
This model of quality-based uncertain reasoning is entirely embedded in a terminological logic framework.”  ...  Considering uncertain reasoning as a preferential choice problem between alternative hypotheses, the model we provide assigns quality labeis to single evidences for or against a hypothesis, combines the  ... 

Nonmonotonic inconsistency

Charles B. Cross
2003 Artificial Intelligence  
After considering and dismissing two possible analyses relating nonmonotonic consequence and a nonmonotonic counterpart of logical inconsistency, this paper offers a set of postulates for nonmonotonic  ...  And, like logical consequence, logical inconsistency is monotonic.  ...  10 Classical preferential entailment is always supraclassical (see [6, p. 88]) since in a classical preferential model, if p ∈ Cn(X) and state m preferentially satisfies X, then m satisfies X and so  ... 
doi:10.1016/s0004-3702(03)00074-2 fatcat:5wzp2lmfkjazhll2as5sw3spk4

Second International Workshop on Nonmonotonic Reasoning (Report)

Michael Reinfrank
1989 The AI Magazine  
During the workshop, many links Semantical Theories The preferential models approach to the semantics of nonmonotonic reasoning seems to have become the predominant one, and some extensions to it have  ...  These areas included nonmonotonic logic, truth maintenance, logic programming, and philosophy.  ...  nonmonotonic reasoning.  ... 
doi:10.1609/aimag.v10i1.733 dblp:journals/aim/Reinfrank89 fatcat:l66ygywy7zhi5mjoa7ui7jzoau

Stereotypical Reasoning: Logical Properties [article]

Daniel Lehmann
2002 arXiv   pre-print
It is one of the most basic forms of nonmonotonic reasoning. A formal model for stereotypical reasoning is proposed and the logical properties of this form of reasoning are studied.  ...  Stereotypical reasoning is shown to be cumulative under weak assumptions.  ...  Reasoning".  ... 
arXiv:cs/0203004v1 fatcat:2z25ohs5onddfhwoqhrqh2sda4

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  ...  Shoham's preferential models.  ... 
arXiv:cs/0007040v1 fatcat:h5hw72npzbchhbjjevvvyfh3vy

A preferential model semantics for default logic [chapter]

Frans Voorbraak
1991 Lecture Notes in Computer Science  
of nonmonotonic reasoning.  ...  In this paper a preferential model semantics for default logic is given, by defining a preference relation on partial models called hypervaluations.  ...  Acknowledgments I would like to thank Albert Visser for commenting on preliminary versions of this paper and the members of the (Dutch) National Working Group on Non-Monotonc Reasoning for enduring a presentation  ... 
doi:10.1007/3-540-54659-6_113 fatcat:pz3j3prkifcyzdgkkxr2uuk7je

Page 2386 of Mathematical Reviews Vol. , Issue 92e [page]

1992 Mathematical Reviews  
(IL-HEBR-C); Magidor, Menachem (IL-HEBR) Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44 (1990), no. 1-2, 167-207.  ...  in the nonmonotonic reasoning procedure known as circumscription.  ... 

Ordering-based representations of rational inference [chapter]

Konstantinos Georgatos
1996 Lecture Notes in Computer Science  
However, there has been no simple characterization of these relations, other than its original representation by preferential models.  ...  The finitary fragment of this class of consequence operators has been employed by recent default logic formalisms based on maxiconsistency.  ...  Acknowledgements: I would like to thank Gianni Amati and R. Ramanujam for their helpful comments on a preliminary version of this paper.  ... 
doi:10.1007/3-540-61630-6_12 fatcat:2abmeqsjbrdztmnzu7w4y2tgu4

Finite Algebras and AI: From Matrix Semantics to Stochastic Local Search [chapter]

Zbigniew Stachniak
2004 Lecture Notes in Computer Science  
Beyond Monotonicity: Preferential Matrices The notion of cumulativity arose as a result of the search for desired and natural formal properties of nonmonotonic inference systems.  ...  A similar approach of admitting only some interpretations to model non-structural nonmonotonic inference systems has been also developed for preferential model semantics (cf. [7] ).  ... 
doi:10.1007/978-3-540-30210-0_2 fatcat:vzlccfeqijg3tfh3v73lelk7du

Page 4913 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
and cumulative inference operations.  ...  .; Mantha, Surya; Wakayama, Toshiro Preference logics: towards a unified approach to nonmonotonicity in deductive reasoning. (English summary) Artificial intelligence and mathematics, III. Ann. Math.  ... 

Page 6170 of Mathematical Reviews Vol. , Issue 91K [page]

1991 Mathematical Reviews  
Schulz, Preferential cumulative reasoning and nonmonotonic semantic nets (pp. 223-240); David Pearce and Wolfgang Rautenberg, Propositional logic based on the dynamics of disbelief (pp. 243-258); André  ...  . 23-37); Fangqing Dong and Hiroshi Nakagawa, Se- mantics of nonmonotonic reasoning based on perfect model (pp. 38-53); Yihua Shi and Setsuo Arikawa, Time-bounded reason- ing in first order knowledge base  ... 

Page 448 of Mathematical Reviews Vol. , Issue 92a [page]

1992 Mathematical Reviews  
—a three-valued cumulative nonmonotonic formalism.  ...  The semantics is based on the notion of preferential entailment, where a set of sentences T preferentially entails a sentence a if and only if a preferred set of the models of I are models of a.  ... 
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