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A preferential model semantics for default logic [chapter]

Frans Voorbraak
1991 Lecture Notes in Computer Science  
In this paper a preferential model semantics for default logic is given, by defining a preference relation on partial models called hypervaluations.  ...  default logic and circumscription.  ...  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

Preference-Based Semantics for Nonmonotonic Logics

Frans Voorbraak
1993 International Joint Conference on Artificial Intelligence  
A variant is proposed of the preference-based se mantics for nonmonotonic logics that was origi nally considered by Shoham [1987; 1988].  ...  Further, the view is defended that the rationality of cumulative monotonicity does not imply thai nonmonotonic logics have to be cumulative, but only that a rational agent should not believe a set of default  ...  Conclusion Default logic can be given a preferential semantics, provided Shoham's original requirement that the semantics has to be based on a strict partial order on the set of standard models is dropped  ... 
dblp:conf/ijcai/Voorbraak93 fatcat:6wxmoqtxq5cvnksafeajbzb3ca

A Cumulative-Model Semantics for Dynamic Preferences on Assumptions

Ulrich Junker
1997 International Joint Conference on Artificial Intelligence  
We elaborate a preferential semantics based on Lehmann's cumulative models, as well as a corresponding constructive characterization, which specifies how to correctly treat dynamic preferences in the default  ...  for defining preferred models.  ...  Acknowledgements I would like to thank Gerd Brewka, Markus Junker, and the anonymous reviewers for helpful comments that improved the quality of this paper.  ... 
dblp:conf/ijcai/Junker97 fatcat:4hlo73hmafeutef4wqwa6u2uoq

Two Paradigms of Nonmonotonic Reasoning

Alexander Bochman
2006 International Symposium on Artificial Intelligence and Mathematics  
We provide a conceptual description of the field of nonmonotonic reasoning as comprising two essentially different theories, preferential and explanatory nonmonotonic reasoning.  ...  The relationship between the two constitutes the main theoretical problem of nonmonotonic reasoning, and its solution should hopefully provide an impetus for the future development of the field.  ...  This naturally creates a preferential setting, in which the normality of models is measured by the set of defaults they support (see below).  ... 
dblp:conf/isaim/Bochman06 fatcat:lyrvt6ppj5gozo7oon2djy7z5q

Strengthening the Rational Closure for Description Logics: An Overview

Laura Giordano, Valentina Gliozzi
2019 Italian Conference on Computational Logic  
The paper describes a preferential approach for dealing with exceptions in Description Logics, based on the rational closure.  ...  The semantics of ALC with typicality is defined in terms of preferential models, extending to ALC the preferential semantics by Kraus, Lehmann and Magidor in [44, 45] : ordinary models of ALC are equipped  ...  A semantic characterization of the MP-closure for the description logic ALC was developed in [29] using bi-preferential (BP) interpretations, preferential interpretations developed along the lines of  ... 
dblp:conf/cilc/0001G19 fatcat:oqam5jspxbhqbmazx7wsn6wlsm

Inaccessible Worlds and Irrelevance: Preliminary Report

Craig Boutilier
1991 International Joint Conference on Artificial Intelligence  
Recently, the relationship between several forms of default reasoning based on conditional defaults has been investigated, In particular, the systems based on e-semantics, preferential models t and (fragments  ...  These systems form a plausible core for default inference, but are too weak in general, failing to deal adequately with irrelevance.  ...  Acknowledgements Thanks to Ray Reiter, Hector Levesque and especially Moises Goldszmidt for helpful discussion and criticism.  ... 
dblp:conf/ijcai/Boutilier91 fatcat:ewbbd5bojncjtldvwp3rud7bju

A Framework for a Modular Multi-Concept Lexicographic Closure Semantics (an abridged report)

Laura Giordano, Daniele Theseider Dupré
2021 Italian Conference on Computational Logic  
We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality.  ...  The preferential semantics of the knowledge base can then be defined as a combination of the preferences of the single modules.  ...  In the following we will assume that the knowledge base T ∪ D, A is consistent in the logic ALC + T, that is, it has a preferential model.  ... 
dblp:conf/cilc/0001D21 fatcat:a4gdmd6cy5hhlhmiycrdl3ynx4

A framework for a modular multi-concept lexicographic closure semantics [article]

Laura Giordano, Daniele Theseider Dupré
2020 arXiv   pre-print
We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality.  ...  The preferential semantics of the knowledge base can then be defined as a combination of the preferences of the single modules.  ...  Acknowledgement: We thank the anonymous referees for their helpful comments and suggestions. This research is partially supported by INDAM-GNCS Project 2019.  ... 
arXiv:2009.00964v2 fatcat:zlhzj3epynavpear2yghztr7ne

Preferential Semantics for Plausible Subsumption in Possibility Theory

Guilin Qi, Zhizheng Zhang
2013 Minds and Machines  
In this paper, we propose several preferential semantics for plausible subsumption to deal with exceptions in description logic-based knowledge bases.  ...  Finally, we show that our semantics for plausible subsumption can be reduced to standard semantics of an expressive description logic.  ...  The authors would like to thanks anonymous reviewers for their insightful comments, which are helpful to improve the quality of this paper.  ... 
doi:10.1007/s11023-012-9300-4 fatcat:ghvnkbcn7bcfxngjpt4rpovnsm

Possibilistic Logic, Preferential Models, Non-monotonicity and Related Issues

Didier Dubois, Henri Prade
1991 International Joint Conference on Artificial Intelligence  
We obtain the possibilistic counterpart of Adams' e-semantics of conditional probabilities which is the basis of the probabilistic model of non-monotonic logic proposed by Geffner and Pearl.  ...  Starting from a fuzzy set of preferential interpretations of a propositional theory, we prove that the notion of preferential entailment is closely related to a previously introduced notion of conditional  ...  Acknowledgements : The authors are grateful to a referee for pointing out the problem of preferential entailment from inconsistent premises, and for various other remarks that significantly improved the  ... 
dblp:conf/ijcai/DuboisP91 fatcat:fcu7srqa6zfqhbex7le7366p6e

Page 2748 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
In this paper we discuss default logic at both the proof-theoretic and semantics levels and show that default logic provides a clear and formal framework for understanding the logical nature of commonsense  ...  Behind the application of the preferential structures for deontic and non-monotonic logics lies the idea that the “importance” of the models can be reinterpreted in terms of those logics, namely, as “morally  ... 

A reconstruction of the multipreference closure [article]

Laura Giordano, Valentina Gliozzi
2020 arXiv   pre-print
The paper describes a preferential approach for dealing with exceptions in KLM preferential logics, based on the rational closure.  ...  , and determines a preferential consequence relation rather than a rational consequence relation.  ...  ] with multiple typicality operators, a logic which exploits a different minimal model semantics w.r.t. rational closure semantics.  ... 
arXiv:1905.03855v2 fatcat:pcyihz765jebrdlit2b5a2lyxq

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

1992 Mathematical Reviews  
The logic has an intu- itive model-theoretic semantics without any appeal to the use of a fixpoint semantics for the default operator.  ...  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.  ... 

Reasoning about Typicality and Probabilities in Preferential Description Logics [article]

Laura Giordano, Valentina Gliozzi, Antonio Lieto, Nicola Olivetti, Gian Luca Pozzato
2020 arXiv   pre-print
This extension is based on a minimal model semantics corresponding to a notion of rational closure, built upon preferential models.  ...  We also present two extensions of the preferential semantics: on the one hand, we consider probabilistic extensions, based on a distributed semantics that is suitable for tackling the problem of commonsense  ...  It turns out that the minimal model semantics of the logic ALC + T R corresponds to a natural extension of the notion of rational closure, defined in [13] for propositional logic, to Description Logics  ... 
arXiv:2004.09507v2 fatcat:a6lvdkq27rgpbkp3pkfot6dvvm

Page 7534 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
Summary: “It is well known that preferential inference relations can be semantically represented through a smooth order defined on the set of states of a preferential model, but it is also possible to  ...  Logic Comput. 8 (1998), no. 2, 169-187. Summary: “We analyse the semantical definition of extensions for open default theories.  ... 
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