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A KLM Perspective on Defeasible Reasoning for Description Logics [chapter]

Katarina Britz, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2019 Lecture Notes in Computer Science  
In this paper we present an approach to defeasible reasoning for the description logic ALC.  ...  In addition to showing that the semantics is appropriate, these results pave the way for more eective decision procedures for defeasible reasoning in description logics.  ...  semantics for description logics.  ... 
doi:10.1007/978-3-030-22102-7_7 fatcat:jqmd6rc2pbbk5lz2guo2lugete

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  ...  This work was partially funded by Project number 247601, Net2: Network for Enabling Networked Knowledge, from the FP7-PEOPLE-2009-IRSES call.  ... 
doi:10.1007/978-3-642-35101-3_43 fatcat:gzjwcuhxmze67oqvpuhncvwdku

Defeasible reasoning in Description Logics: an overview on DL^N [article]

Piero A. Bonatti, Iliana M. Petrova, Luigi Sauro
2020 arXiv   pre-print
DL^N is a recent approach that extends description logics with defeasible reasoning capabilities.  ...  We also compare DL^N with some alternative nonmonotonic semantics, enlightening the relationships between the KLM postulates and DL^N.  ...  In fact, the underlying descriptions logics (DLs), which are based on the monotonic semantics of FOL, do not allow to express and reason on defeasible knowledge and exceptions.  ... 
arXiv:2009.04978v2 fatcat:ppf7mbzloba6xlnnf4k6dh6bmy

Algorithmic definitions for KLM-style defeasible disjunctive Datalog

Matthew Morris, Tala Ross, Thomas Meyer
2020 South African Computer Journal  
The KLM approach to defeasible reasoning is an axiomatic approach based on the concept of plausible inference.  ...  We present a systematic approach for extending the KLM properties and a well-known form of defeasible entailment: Rational Closure.  ...  INTRODUCTION The KLM approach, proposed by Kraus et al. (1990) , is a well-known framework for defeasible reasoning.  ... 
doi:10.18489/sacj.v32i2.846 fatcat:s5unmlbyjzeanizj6wmqcwfheq

Defeasible Modalities [article]

Katarina Britz, Ivan Varzinczak
2013 arXiv   pre-print
The resulting family of modal logics allow for the elegant expression of defeasible modalities.  ...  Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the associated normality (or abnormality) of its constituents.  ...  This work was partially funded by Project # 247601, Net2: Network for Enabling Networked Knowledge, from the FP7-PEOPLE-2009-IRSES call.  ... 
arXiv:1310.6409v1 fatcat:xxbgo543njdftmyyy2322ga7pq

On rational entailment for propositional typicality logic

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2019 Artificial Intelligence  
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional  ...  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.  ...  Propositional Typicality Logic PTL [1] is a logical formalism explicitly allowing for the representation of and reasoning about a notion of typicality.  ... 
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
We extend description logics (DLs) with non-monotonic reasoning features.  ...  In particular, we consider a natural and intuitive semantics for defeasible subsumption, and investigate KLM-style syntactic properties for both preferential and rational subsumption.  ...  Relevant closure: A new form of defeasible reasoning for description logics. In Logics in Artificial Intelligence, pages 92-106. Springer, 2014.  ... 
arXiv:1904.07559v1 fatcat:icpvjvw6izctjd7uhirgyifxji

On Rational Entailment for Propositional Typicality Logic [article]

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2018 arXiv   pre-print
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional  ...  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.  ...  Semantically, they do so by placing an (absolute) ordering on objects in first-order domains in order to define versions of defeasible subsumption relations in the description logic ALC.  ... 
arXiv:1809.10946v1 fatcat:ie4gy5swkfg7jarmrwcc2l67oi

From Common Sense Reasoning to Neural Network Models through Multiple Preferences: an overview [article]

Laura Giordano, Valentina Gliozzi, Daniele Theseider Dupré
2021 arXiv   pre-print
We propose a concept-wise multipreference semantics, recently introduced for defeasible description logics to take into account preferences with respect to different concepts, as a tool for providing a  ...  In this paper we discuss the relationships between conditional and preferential logics and neural network models, based on a multi-preferential semantics.  ...  That a conditional logic, belonging to a family of logics which are normally used for hypothetical and counterfactual reasoning, for common sense reasoning, and for reasoning with exceptions, can be used  ... 
arXiv:2107.04870v1 fatcat:qxz55dvfibaabffni7pwawdm3q

Situated Conditional Reasoning [article]

Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2021 arXiv   pre-print
We then propose an intuitive semantics for these conditionals, and present a representation result which shows that our semantic construction corresponds exactly to the description in terms of postulates  ...  In this paper we make the case for a form of conditional that is situation-based.  ...  KLM-style rational defeasible consequence A defeasible consequence relation |∼ is a binary relation on L.  ... 
arXiv:2109.01552v1 fatcat:pfj7chc4nnef7bxmfaztrndgma

Defaults and Infinitesimals: Defeasible Inference by Nonarchimedean Entropy-Maximization [article]

Emil Weydert
2013 arXiv   pre-print
We develop a new semantics for defeasible inference based on extended probability measures allowed to take infinitesimal values, on the interpretation of defaults as generalized conditional probability  ...  constraints and on a preferred-model implementation of entropy maximization.  ...  ACKNOWLEDGEMENTS Thanks to the anonymous referees, who have helped to make this paper a less obscure one.  ... 
arXiv:1302.4988v1 fatcat:q55wyeuvcberde6hkrp6zelqey

Rational Defeasible Belief Change

Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2020 Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning  
We present a formal framework for modelling belief change within a nonmonotonic reasoning system.  ...  We characterise a family of operators for iterated revision, followed by an analogous characterisation of operators for iterated contraction.  ...  KLM-style defeasible reasoning can therefore be viewed as an extension of propositional logic.  ... 
doi:10.24963/kr.2020/22 dblp:conf/kr/CasiniMV20 fatcat:gj7sruxl7jbvrm2pwftpeaww4u

Credulous Nonmonotonic Inference [chapter]

Alexander Bochman
2001 A Logical Theory of Nonmonotonic Inference and Belief Change  
We present a formal characterization and semantic representation for a number of credulous inference relations based on the notion of a,n epistemic state.  ...  X-logics. [Siegel and Forget, 1996 ] suggested a new description of nonmonotonic inference relations that they called X~logics.  ...  Introduction The approach to nonmonotonic and commonsense reasoning based on describing associated inference relations forms one of the most influential and effective tools in studying such a reasoning  ... 
doi:10.1007/978-3-662-04560-2_9 fatcat:xvtqirszijh7zfu2w65g22jpvu

PTL: A Propositional Typicality Logic [chapter]

Richard Booth, Thomas Meyer, Ivan Varzinczak
2012 Lecture Notes in Computer Science  
We introduce Propositional Typicality Logic (PTL), a logic for reasoning about typicality.  ...  The semantics is in terms of ranked models as studied in KLM-style preferential reasoning. This allows us to show that rational consequence relations can be embedded in our logic.  ...  Entailment for PTL In this section we focus on what is perhaps the central question concerning PTL from the perspective of knowledge representation and reasoning: What does it mean for a PTL formula to  ... 
doi:10.1007/978-3-642-33353-8_9 fatcat:mwucomtwcfe3vcp7nwaqa34bui

Towards Defeasible Mappings for Tractable Description Logics [chapter]

Kunal Sengupta, Pascal Hitzler
2015 Lecture Notes in Computer Science  
We provide the formal semantics for the defeasible mappings and show that reasoning under such a setting is decidable even when the defeasible axioms apply to unknowns.  ...  Furthermore, we show that this semantics actually is strongly related to the idea of answer sets for logic programs.  ...  The authors also thank an anonymous reviewer of a previous version of this paper for detecting a flaw in our initial semantics, which has now been removed.  ... 
doi:10.1007/978-3-319-25007-6_14 fatcat:j6rmhqfifbbgbio46ld4vpyvja
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