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Normal Modal Preferential Consequence [chapter]

Katarina Britz, Thomas Meyer, Ivan Varzinczak
2012 Lecture Notes in Computer Science  
In recent work we provided the semantic foundation for extending defeasible consequence relations to modal logics and description logics.  ...  One of the most successful approaches to the formalization of commonsense reasoning is the work by Lehmann and colleagues, known as the KLM approach, in which defeasible consequence relations with a preferential  ...  Any opinion, findings and conclusions or recommendations expressed in this material are those of the author(s) and therefore the NRF do not accept any liability in regard thereto.  ... 
doi:10.1007/978-3-642-35101-3_43 fatcat:gzjwcuhxmze67oqvpuhncvwdku

On Rational Entailment for Propositional Typicality Logic [article]

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2018 arXiv   pre-print
for KLM-style conditionals, and constructed using different notions of minimality.  ...  The semantics of PTL is in terms of ranked models as studied in the well-known KLM approach to preferential reasoning and therefore KLM-style rational consequence relations can be embedded in PTL.  ...  Similarly to KLM in the propositional case, we would ideally like the defeasible conditional induced by Cn ?  ... 
arXiv:1809.10946v1 fatcat:ie4gy5swkfg7jarmrwcc2l67oi

On rational entailment for propositional typicality logic

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2019 Artificial Intelligence  
for KLM-style conditionals, and constructed using different notions of minimality. * This technical report presents an extended and elaborated version of a paper presented at  ...  The semantics of PTL is in terms of ranked models as studied in the well-known KLM approach to preferential reasoning and therefore KLM-style rational consequence relations can be embedded in PTL.  ...  modal logics of defeasibility [7, 9, 11, 13] .  ... 
doi:10.1016/j.artint.2019.103178 fatcat:6wtakpxhyza2bomgyllnpqxoka

Theoretical Foundations of Defeasible Description Logics [article]

Katarina Britz, Giovanni Casini, Thomas Meyer, Kody Moodley, Uli Sattler, Ivan Varzinczak
2019 arXiv   pre-print
In particular, we consider a natural and intuitive semantics for defeasible subsumption, and investigate KLM-style syntactic properties for both preferential and rational subsumption.  ...  We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional case.  ...  Defeasible subsumption relations and their KLM-style properties In a sense, class subsumption (alias concept inclusion) of the form C ⊑ D is the main notion in DL ontologies.  ... 
arXiv:1904.07559v1 fatcat:icpvjvw6izctjd7uhirgyifxji

A reconstruction of the multipreference closure [article]

Laura Giordano, Valentina Gliozzi
2020 arXiv   pre-print
Several solutions have been proposed to face this problem and the lexicographic closure is the most notable one.  ...  The paper describes a preferential approach for dealing with exceptions in KLM preferential logics, based on the rational closure.  ...  We will come back on this point with some examples in Sections 3 and 4.  ... 
arXiv:1905.03855v2 fatcat:pcyihz765jebrdlit2b5a2lyxq

A Propositional Typicality Logic for Extending Rational Consequence

Richard Booth, Thomas Meyer, Ivan Varzinczak
2012 Proceedings of the 13th European Conference on Logics in Artificial Intelligence   unpublished
The semantics is in terms of ranked models as studied in KLM-style preferential reasoning. This allows us to show that KLM-style rational consequence relations can be embedded in our logic.  ...  Building on the existing link between propositional rational consequence and belief revision, we show that the same correspondence holds in the case of rational consequence and belief revision defined  ...  Acknowledgements The authors are grateful to the anonymous referees for their constructive and useful remarks on an earlier version of this text.  ... 
fatcat:fo5tdiyxknhl5kptlk4hi5ahqq

Modeling belief in dynamic systems, part I: Foundations

Nir Friedman, Joseph Y. Halpern
1997 Artificial Intelligence  
We claim that a better understanding of belief change can be gained from examining appropriate semanfic models. In this paper we propose a general framework in which to model belief change.  ...  This notion can be captured by using prior plausibilities, an analogue to prior probabilities, which can be updated by "conditioning".  ...  Vardi for comments on previous versions of this paper and useful discussions relating to this work.  ... 
doi:10.1016/s0004-3702(97)00040-4 fatcat:zpjibkssizac5egi4o2qurjile

What Does Entailment for PTL Mean?

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
unpublished
We take as a starting point the notion of Rational Closure defined for KLM-style conditionals.  ...  We show that the additional ex-pressivity of PTL results in different versions of Rational Closure for PTL-versions that are equivalent with respect to the conditional language originally proposed by KLM  ...  Varzinczak 2011; Giordano et al. 2013 ) and logics of defeasible modalities .  ... 
fatcat:26nytjdcofcvxmxy2pn6cjhzp4

Modeling Belief in Dynamic Systems, Part I: Foundations [article]

Nir Friedman, Joseph Y. Halpern
2003 arXiv   pre-print
This notion can be captured by using prior plausibilities, an analogue to prior probabilities, which can be updated by "conditioning".  ...  We claim that a better understanding of belief change can be gained from examining appropriate semantic models. In this paper we propose a general framework in which to model belief change.  ...  Vardi for comments on previous versions of this paper and useful discussions relating to this work.  ... 
arXiv:cs/0307070v1 fatcat:kmd4w5epnrduramzp6q4vmr7aa

New foundations for epistemic change*

Anthony S. Gillies
2004 Synthese  
An adequate notion of belief change has to respect the distinction between modal and non-modal formulas: the kinematics of learning that it normally is sunny in Tucson are very different from the kinematics  ...  nonmonotonic consequence relations which meet certain KLM properties (Kraus et al. 1990 ) and so on.  ... 
doi:10.1023/b:synt.0000012202.66263.b2 fatcat:r56lnbkn7zccxid72e6rllazoq

Boolean algebras of conditionals, probability and logic

Tommaso Flaminio, Lluis Godo, Hykel Hosni
2020 Artificial Intelligence  
By doing so we distinguish the properties of conditional events which depend on probability and those which are intrinsic to the logico-algebraic structure of conditionals.  ...  A logical valuation (or simply a valuation) of L is a map from v : V → {0, 1}, which uniquely extends to a function, that we denote by the same symbol v, from L to {0, 1} in accordance with the usual Boolean  ...  Acknowledgements The authors are thankful to the anonymous reviewers for their helpful remarks and suggestions.  ... 
doi:10.1016/j.artint.2020.103347 fatcat:zly7mg5skzervbua55imr4ffqa

Boolean algebras of conditionals, probability and logic [article]

Tommaso Flaminio, Lluis Godo, Hykel Hosni
2020 arXiv   pre-print
By doing so we distinguish the properties of conditional events which depend on probability and those which are intrinsic to the logico-algebraic structure of conditionals.  ...  In particular we introduce a construction which defines a (finite) Boolean algebra of conditionals from any (finite) Boolean algebra of events.  ...  Acknowledgments The authors are thankful to the anonymous reviewers for their helpful remarks and suggestions.  ... 
arXiv:2006.04673v1 fatcat:fhifv4zsezegngnhzyfepseizi

Reasoning in Non-probabilistic Uncertainty: Logic Programming and Neural-Symbolic Computing as Examples

Tarek R. Besold, Artur d'Avila Garcez, Keith Stenning, Leendert van der Torre, Michiel van Lambalgen
2017 Minds and Machines  
This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty (and even more, that there are kinds of uncertainty which are for principled reasons not  ...  addressable with probabilistic means); and to provide evidence that logic-based methods can well support reasoning with uncertainty.  ...  , Laura Martignon, Alan Perotti, and Alexandra Varga.  ... 
doi:10.1007/s11023-017-9428-3 fatcat:unbwsv3civd45hivgh5xpuzlzu

Reasoning in Non-Probabilistic Uncertainty: Logic Programming and Neural-Symbolic Computing as Examples [article]

Tarek R. Besold, Artur d'Avila Garcez, Keith Stenning, Leendert van der Torre, Michiel van Lambalgen
2017 arXiv   pre-print
This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty (and even more, that there are kinds of uncertainty which are for principled reasons not  ...  addressable with probabilistic means); and to provide evidence that logic-based methods can well support reasoning with uncertainty.  ...  , Laura Martignon, Alan Perotti, and Alexandra Varga.  ... 
arXiv:1701.05226v2 fatcat:eg67ppsao5cmvnxv5s5vquchma

Preferential description logics: reasoning in the presence of inconsistencies

Graham Deane, Krysia Broda, Alessandra Russo, Engineering And Physical Sciences Research Council
2016
A p-ALC knowledge base is comprised of defeasible and non-defeasible axioms.  ...  The defeasible ABox and TBox are labelled with weights that reflect a relative measure of confidence in each axiom and provide a mechanism to "arbitrate" between inconsistencies.  ...  Theorem 5.24 (Correspondence back).  ... 
doi:10.25560/40430 fatcat:e75lckhh7jfcddk7vejwl5uleu
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