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Semantic Foundation for Preferential Description Logics [chapter]

Katarina Britz, Thomas Meyer, Ivan Varzinczak
2011 Lecture Notes in Computer Science  
We present representation results for the description logic ALC for both preferential and rational consequence relations.  ...  Nevertheless, there is at present no generally accepted semantics, with corresponding syntactic characterization, for preferential consequence in description logics.  ...  Acknowledgments This work was partially funded by Project number 247601, Net2: Network for Enabling Networked Knowledge, from the FP7-PEOPLE-2009-IRSES call.  ... 
doi:10.1007/978-3-642-25832-9_50 fatcat:yqsn7tbff5aizh7zedinz5jlvu

Preferential Reasoning for Modal Logics

Katarina Britz, Thomas Meyer, Ivan Varzinczak
2011 Electronical Notes in Theoretical Computer Science  
We argue that our semantics constitutes the foundation on which to explore preferential reasoning in modal logics in general.  ...  Nevertheless, there is at present no generally accepted semantics, with corresponding syntactic characterization, for preferential consequence in modal logics.  ...  In what follows we present the semantic foundation of preferential reasoning for modal and multi-modal logics.  ... 
doi:10.1016/j.entcs.2011.10.006 fatcat:4bhmdz76ufa7rh7dho3zlpm3uq

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.  ...  In particular, we show that the additional constraints we impose on the preferential semantics ensure that the rule of necessitation holds for the corresponding consequence relations, as one would expect  ...  Acknowledgements This work is based upon research supported by the National Research Foundation.  ... 
doi:10.1007/978-3-642-35101-3_43 fatcat:gzjwcuhxmze67oqvpuhncvwdku

Page 3630 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
The paper is devoted to the description of sequent calculi allowing the comparison of sentences in Post logics.  ...  (c) As a direct application of the above, we show that Poole’s (syntax-based) system of default reasoning and Shoham’s preferential semantic for non-monotonic reasoning are also expressively equivalent  ... 

Page 501 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
In this paper a general mathematical foundation for the qualitative and numerical theory of evidence is developed.  ...  objects, a purely qualita- tive counterpart to conditional probabilities, offer a very simple semantics, based on a 3-valued calculus, for the preferential en- tailment, while in the purely ordinal setting  ... 

Page 6410 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
We give a description in terms of rela- tional Kripke semantics for intermediate logics having the finite model property and preserving admissible rules for H.  ...  (RS-TVER; Tver’) Concurrency problem for Horn fragment of Girard’s linear logic. (English summary) Logical foundations of computer science (St. Petersburg, 1994), 18-22, Lecture Notes in Comput.  ... 

A conditional, a fuzzy and a probabilistic interpretation of self-organising maps [article]

Laura Giordano, Valentina Gliozzi, Daniele Theseider Dupré
2021 arXiv   pre-print
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological  ...  on a concept-wise multipreference semantics, which takes into account preferences with respect to different concepts and has been recently proposed for ranked and for weighted defeasible description logics  ...  Acknowledgement: We thank the anonymous referees for their helpful comments and suggestions that helped to improve the paper. This research has been partially supported by INDAM-GNCS Project 2020.  ... 
arXiv:2103.06854v2 fatcat:df5kf433xbbajbc7n7ndrerj6m

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

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.  ...  Introduction Description logics (DLs) [1] are central to many modern AI and database applications since they provide the logical foundation of formal ontologies.  ... 
arXiv:1904.07559v1 fatcat:icpvjvw6izctjd7uhirgyifxji

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.  ...  [(d, e) ∈ R I → e ∈ C I ]} Preliminaries Description logics are a family of formal languages representing the logical foundations of the W3C Ontology Web Language (OWL2).  ... 
arXiv:2009.04978v2 fatcat:ppf7mbzloba6xlnnf4k6dh6bmy

Discourse Preferences in Dynamic Logic [article]

Jan Jaspars
1997 arXiv   pre-print
In order to enrich dynamic semantic theories with a 'pragmatic' capacity, we combine dynamic and nonmonotonic (preferential) logics in a modal logic setting.  ...  We will show how this setting can be used for a dynamic logical analysis of preferential resolutions of ambiguous pronouns in discourse.  ...  For instance, natural language semantics has recently developed a relatively simple dynamic model-theoretic understanding of the interplay between indefinite descriptions and anaphoric bindings.  ... 
arXiv:cmp-lg/9707004v1 fatcat:wwdgmrzpr5a3dgxhg25y7eswle

On a plausible concept-wise multipreference semantics and its relations with self-organising maps [article]

Laura Giordano, Valentina Gliozzi, Daniele Theseider Dupré
2020 arXiv   pre-print
Inthispaperwedescribeaconcept-wisemulti-preferencesemantics for description logic which has its root in the preferential approach for modeling defeasible reasoning in knowledge representation.  ...  We motivate the plausibility of the concept-wise multi-preference semantics by developing a logical semantics of self-organising maps, which have been proposed as possible candidates to explain the psychological  ...  logical semantics for the SOM which is well-defined, as M som is a preferential consequence relation, and therefore satisfies all KLM properties of a preferential consequence relations.  ... 
arXiv:2008.13278v1 fatcat:ppvnpbtmjfa7rp3d6z4y7sjpvy

On the KLM properties of a fuzzy DL with Typicality [article]

Laura Giordano
2021 arXiv   pre-print
First, a monotonic extension of a fuzzy ALC with typicality is considered (called ALC^FT) and a reformulation the KLM properties of a preferential consequence relation for this logic is devised.  ...  The extension of fuzzy logic with a typicality operator was proposed in recent work to define a fuzzy multipreference semantics for Multilayer Perceptrons, by regarding the deep neural network as a conditional  ...  The description logic ALC and fuzzy ALC In this section we recall the syntax and semantics of the description logic ALC [1] and of its fuzzy extension [41] .  ... 
arXiv:2106.00390v2 fatcat:yn3hdr4zl5hk5p2dqo57oqbhla

Defeasible Modalities [article]

Katarina Britz, Ivan Varzinczak
2013 arXiv   pre-print
We also propose a tableau calculus which is sound and complete with respect to our preferential semantics.  ...  The resulting family of modal logics allow for the elegant expression of defeasible modalities.  ...  Acknowledgments The authors are grateful to the anonymous referees for their constructive and useful remarks. This work is based upon research supported by the National Research Foundation (NRF).  ... 
arXiv:1310.6409v1 fatcat:xxbgo543njdftmyyy2322ga7pq

Page 790 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
Section 2 presents preferential de- fault logic, the “logic of disputation” used in the paper. Section 3 presents a version of the situation calculus for capturing argu- ments.  ...  (181-202); Sten Lindstrém, An exposition and development of Kanger’s early semantics for modal logic (203 233); Quentin Smith, A more comprehensive history of the new theory of reference (235-283).  ... 
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