Arina Britz

2020

Britz, K. ., Casini, G. ., Meyer, T. ., Moodley, K. ., Sattler, U. ., & Varzinczak, I. . (2020). Principles of KLM-style Defeasible Description Logics. Transactions on Computational Logic, 22 (1). http://doi.org/10.1145/3420258

Abstract BibTex Entry BibTeX Download PDF

3420258.pdf

The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. 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. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC.

@article{433,
  author = {Katarina Britz and Giovanni Casini and Tommie Meyer and Kody Moodley and Uli Sattler and Ivan Varzinczak},
  title = {Principles of KLM-style Defeasible Description Logics},
  abstract = {The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. 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. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic
constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC.},
  year = {2020},
  journal = {Transactions on Computational Logic},
  volume = {22 (1)},
  pages = {1-46},
  publisher = {ACM},
  url = {https://dl-acm-org.ezproxy.uct.ac.za/doi/abs/10.1145/3420258},
  doi = {10.1145/3420258},
}

2019

Britz, K. ., & Varzinczak, I. . (2019). Preferential tableaux for contextual defeasible ALC. In 28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX). Springer LNAI no. 11714. Retrieved from https://www.springer.com/gp/book/9783030290252

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Tableaux-dALC.pdf

In recent work, we addressed an important limitation in previous ex- tensions of description logics to represent defeasible knowledge, namely the re- striction in the semantics of defeasible concept inclusion to a single preference or- der on objects of the domain. Syntactically, this limitation translates to a context- agnostic notion of defeasible subsumption, which is quite restrictive when it comes to modelling different nuances of defeasibility. Our point of departure in our recent proposal allows for different orderings on the interpretation of roles. This yields a notion of contextual defeasible subsumption, where the context is informed by a role. In the present paper, we extend this work to also provide a proof-theoretic counterpart and associated results. We define a (naïve) tableau- based algorithm for checking preferential consistency of contextual defeasible knowledge bases, a central piece in the definition of other forms of contextual defeasible reasoning over ontologies, notably contextual rational closure.

@{247,
  author = {Katarina Britz and Ivan Varzinczak},
  title = {Preferential tableaux for contextual defeasible ALC},
  abstract = {In recent work, we addressed an important limitation in previous ex- tensions of description logics to represent defeasible knowledge, namely the re- striction in the semantics of defeasible concept inclusion to a single preference or- der on objects of the domain. Syntactically, this limitation translates to a context- agnostic notion of defeasible subsumption, which is quite restrictive when it comes to modelling different nuances of defeasibility. Our point of departure in our recent proposal allows for different orderings on the interpretation of roles. This yields a notion of contextual defeasible subsumption, where the context is informed by a role. In the present paper, we extend this work to also provide a proof-theoretic counterpart and associated results. We define a (naïve) tableau- based algorithm for checking preferential consistency of contextual defeasible knowledge bases, a central piece in the definition of other forms of contextual defeasible reasoning over ontologies, notably contextual rational closure.},
  year = {2019},
  journal = {28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX)},
  pages = {39-57},
  month = {03/09-05/09},
  publisher = {Springer LNAI no. 11714},
  isbn = {ISBN 978-3-030-29026-9},
  url = {https://www.springer.com/gp/book/9783030290252},
}

Britz, K. ., & Varzinczak, I. . (2019). Contextual rational closure for defeasible ALC. Annals of Mathematics and Artificial Intelligence, 87(1-2). http://doi.org/10.1007/s10472-019-09658-2

Abstract BibTex Entry BibTeX Download PDF

AMAI-FoIKS-SI.pdf

Description logics have been extended in a number of ways to support defeasible reason- ing in the KLM tradition. Such features include preferential or rational defeasible concept inclusion, and defeasible roles in complex concept descriptions. Semantically, defeasible subsumption is obtained by means of a preference order on objects, while defeasible roles are obtained by adding a preference order to role interpretations. In this paper, we address an important limitation in defeasible extensions of description logics, namely the restriction in the semantics of defeasible concept inclusion to a single preference order on objects. We do this by inducing a modular preference order on objects from each modular preference order on roles, and using these to relativise defeasible subsumption. This yields a notion of contextualised rational defeasible subsumption, with contexts described by roles. We also provide a semantic construction for rational closure and a method for its computation, and present a correspondence result between the two.

@article{246,
  author = {Katarina Britz and Ivan Varzinczak},
  title = {Contextual rational closure for defeasible ALC},
  abstract = {Description logics have been extended in a number of ways to support defeasible reason- ing in the KLM tradition. Such features include preferential or rational defeasible concept inclusion, and defeasible roles in complex concept descriptions. Semantically, defeasible subsumption is obtained by means of a preference order on objects, while defeasible roles are obtained by adding a preference order to role interpretations. In this paper, we address an important limitation in defeasible extensions of description logics, namely the restriction in the semantics of defeasible concept inclusion to a single preference order on objects. We do this by inducing a modular preference order on objects from each modular preference order on roles, and using these to relativise defeasible subsumption. This yields a notion of contextualised rational defeasible subsumption, with contexts described by roles. We also provide a semantic construction for rational closure and a method for its computation, and present a correspondence result between the two.},
  year = {2019},
  journal = {Annals of Mathematics and Artificial Intelligence},
  volume = {87},
  pages = {83-108},
  issue = {1-2},
  isbn = {ISSN: 1012-2443},
  url = {https://link.springer.com/article/10.1007/s10472-019-09658-2},
  doi = {10.1007/s10472-019-09658-2},
}

Britz, K. ., Casini, G. ., Meyer, T. ., & Varzinczak, I. . (2019). A KLM Perspective on Defeasible Reasoning for Description Logics. In Description Logic, Theory Combination, and All That. Switzerland: Springer. http://doi.org/https://doi.org/10.1007/978-3-030-22102-7 _ 7

Abstract BibTex Entry BibTeX Download PDF

2019-Festschrift-Paper_0.pdf

In this paper we present an approach to defeasible reasoning for the description logic ALC. The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case. We consider versions of a preferential semantics for two forms of defeasible subsumption, and link these semantic constructions formally to KLM-style syntactic properties via representation results. In addition to showing that the semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. With the semantics of the defeasible version of ALC in place, we turn to the investigation of an appropriate form of defeasible entailment for this enriched version of ALC. This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case. Importantly, the algorithm relies completely on classical entailment checks and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of the underlying classical ALC. Before concluding, we take a brief tour of some existing work on defeasible extensions of ALC that go beyond defeasible subsumption.

@inbook{240,
  author = {Katarina Britz and Giovanni Casini and Tommie Meyer and Ivan Varzinczak},
  title = {A KLM Perspective on Defeasible Reasoning for Description Logics},
  abstract = {In this paper we present an approach to defeasible reasoning for the description logic ALC. The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case. We consider versions of a preferential semantics for two forms of defeasible subsumption, and link these semantic constructions formally to KLM-style syntactic properties via representation results. In addition to showing that the semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. With the semantics of the defeasible version of ALC in place, we turn to the investigation of an appropriate form of defeasible entailment for this enriched version of ALC. This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case. Importantly, the algorithm relies completely on classical entailment checks and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of the underlying classical ALC. Before concluding, we take a brief tour of some existing work on defeasible extensions of ALC that go beyond defeasible subsumption.},
  year = {2019},
  journal = {Description Logic, Theory Combination, and All That},
  pages = {147–173},
  publisher = {Springer},
  address = {Switzerland},
  isbn = {978-3-030-22101-0},
  url = {https://link.springer.com/book/10.1007%2F978-3-030-22102-7},
  doi = {https://doi.org/10.1007/978-3-030-22102-7 _ 7},
}

Du Toit, T. ., Berndt, J. ., Britz, K. ., & Fischer, B. . (2019). ConceptCloud 2.0: Visualisation and exploration of geolocation-rich semi-structured data sets. ICFCA 2019 Conference and Workshops. CEUR-WS. Retrieved from http://ceur-ws.org/Vol-2378/ (Original work published 2019)

Abstract BibTex Entry BibTeX Download PDF

ICFCA-shortAT11.pdf

ConceptCloud is a flexible interactive tool for exploring, vi- sualising, and analysing semi-structured data sets. It uses a combination of an intuitive tag cloud visualisation with an underlying concept lattice to provide a formal structure for navigation through a data set. Con- ceptCloud 2.0 extends the tool with an integrated map view to exploit the geolocation aspect of data. The tool’s implementation of exploratory search does not require prior knowledge of the structure of the data or compromise on scalability, and provides seamless navigation through the tag cloud and the map viewer.

@misc{227,
  author = {Tiaan Du Toit and Joshua Berndt and Katarina Britz and Bernd Fischer},
  title = {ConceptCloud 2.0: Visualisation and exploration of geolocation-rich semi-structured data sets},
  abstract = {ConceptCloud is a flexible interactive tool for exploring, vi- sualising, and analysing semi-structured data sets. It uses a combination of an intuitive tag cloud visualisation with an underlying concept lattice to provide a formal structure for navigation through a data set. Con- ceptCloud 2.0 extends the tool with an integrated map view to exploit the geolocation aspect of data. The tool’s implementation of exploratory search does not require prior knowledge of the structure of the data or compromise on scalability, and provides seamless navigation through the tag cloud and the map viewer.},
  year = {2019},
  journal = {ICFCA 2019 Conference and Workshops},
  month = {06/2019},
  publisher = {CEUR-WS},
  isbn = {1613-0073},
  url = {http://ceur-ws.org/Vol-2378/},
}

2018

Harmse, H. ., Britz, K. ., & Gerber, A. . (2018). Informative Armstrong RDF datasets for n-ary relations. In Formal Ontology in Information Systems: 10th International Conference, Cape Town, South Africa. IOS Press.

Abstract BibTex Entry BibTeX Download PDF

FOIS_2018_paper_12.pdf

The W3C standardized Semantic Web languages enable users to capture data without a schema in a manner which is intuitive to them. The challenge is that for the data to be useful, it should be possible to query the data and to query it efficiently, which necessitates a schema. Understanding the structure of data is thus important to both users and storage implementers: the structure of the data gives insight to users in how to query the data while storage implementers can use the structure to optimize queries. In this paper we propose that data mining routines can be used to infer candidate n-ary relations with related uniqueness- and null-free constraints, which can be used to construct an informative Armstrong RDF dataset. The benefit of an informative Armstrong RDF dataset is that it provides example data based on the original data which is a fraction of the size of the original data, while capturing the constraints of the original data faithfully. A case study on a DBPedia person dataset showed that the associated informative Armstrong RDF dataset contained 0.00003% of the statements of the original DBPedia dataset.

@{188,
  author = {Henriette Harmse and Katarina Britz and Aurona Gerber},
  title = {Informative Armstrong RDF datasets for n-ary relations},
  abstract = {The W3C standardized Semantic Web languages enable users to capture data without a schema in a manner which is intuitive to them. The challenge is that for the data to be useful, it should be possible to query the data and to query it efficiently, which necessitates a schema. Understanding the structure of data is thus important to both users and storage implementers: the structure of the data gives insight to users in how to query the data while storage implementers can use the structure to optimize queries. In this paper we propose that data mining routines can be used to infer candidate n-ary relations with related uniqueness- and null-free constraints, which can be used to construct an informative Armstrong RDF dataset. The benefit of an informative Armstrong RDF dataset is that it provides example data based on the original data which is a fraction of the size of the original data, while capturing the constraints of the original data faithfully. A case study on a DBPedia person dataset showed that the associated informative Armstrong RDF dataset contained 0.00003% of the statements of the original DBPedia dataset.},
  year = {2018},
  journal = {Formal Ontology in   Information Systems: 10th International Conference, Cape Town, South Africa},
  pages = {187-198},
  month = {17/09-21/09},
  publisher = {IOS Press},
}

Britz, K. ., & Varzinczak, I. . (2018). Context and rationality in defeasible subsumption. In Foundations of Information and Knowledge Systems: 10th International Symposium FoIKS 2018, Budapest, Hungary. Springer.

Abstract BibTex Entry BibTeX Download PDF

FoIKS-RationalContext.pdf

Description logics have been extended in a number of ways to support defeasible reasoning in the KLM tradition. Such features include preferential or rational defeasible concept subsumption, and defeasible roles in complex concept descriptions. Semantically, defeasible subsumption is obtained by means of a preference order on objects, while defeasible roles are obtained by adding a preference order to role interpretations. In this paper, we address an important limitation in defeasible extensions of description logics, namely the restriction in the semantics of defeasible concept subsumption to a single preference order on objects. We do this by inducing a modular preference order on objects from each preference order on roles, and use these to relativise defeasible subsumption. This yields a notion of contextualised rational defeasible subsumption, with contexts described by roles. We also provide a semantic construction for and a method for the computation of contextual rational closure, and present a correspondence result between the two.

@{187,
  author = {Katarina Britz and Ivan Varzinczak},
  title = {Context and rationality in defeasible subsumption},
  abstract = {Description logics have been extended in a number of ways to support defeasible reasoning in the KLM tradition. Such features include preferential or rational defeasible concept subsumption, and defeasible roles in complex concept descriptions. Semantically, defeasible subsumption is obtained by means of a preference order on objects, while defeasible roles are obtained by adding a preference order to role interpretations. In this paper, we address an important limitation in defeasible extensions of description logics, namely the restriction in the semantics of defeasible concept subsumption to a single preference order on objects. We do this by inducing a modular preference order on objects from each preference order on roles, and use these to relativise defeasible subsumption. This yields a notion of contextualised rational defeasible subsumption, with contexts described by roles. We also provide a semantic construction for and a method for the computation of contextual rational closure, and present a correspondence result between the two.},
  year = {2018},
  journal = {Foundations of Information and Knowledge Systems: 10th International Symposium FoIKS 2018, Budapest, Hungary},
  pages = {114-132},
  month = {14/05-18/05},
  publisher = {Springer},
}

Harmse, H. ., Britz, K. ., & Gerber, A. . (2018). Generating Armstrong ABoxes for ALC TBoxes. In Theoretical Aspects of Computing: 15th International Colloquium, Stellenbosch, South Africa. Springer.

Abstract BibTex Entry BibTeX Download PDF

ICTACpaper_19.pdf

A challenge in ontology engineering is the mismatch in ex- pertise between the ontology engineer and domain expert, which often leads to important constraints not being specified. Domain experts often only focus on specifying constraints that should hold and not on specify- ing constraints that could possibly be violated. In an attempt to bridge this gap we propose the use of “perfect test data”. The generated test data is perfect in that it satisfies all the constraints of an application domain that are required, including ensuring that the test data violates constraints that can be violated. In the context of Description Logic on- tologies we call this test data an “Armstrong ABox”, a notion derived from Armstrong relations in relational database theory. In this paper we detail the theoretical development of Armstrong ABoxes for ALC TBoxes as well as an algorithm for generating such Armstrong ABoxes. The proposed algorithm is based, via the ontology completion algorithm of Baader et al., on attribute exploration in formal concept analysis.

@{186,
  author = {Henriette Harmse and Katarina Britz and Aurona Gerber},
  title = {Generating Armstrong ABoxes for ALC TBoxes},
  abstract = {A challenge in ontology engineering is the mismatch in ex- pertise between the ontology engineer and domain expert, which often leads to important constraints not being specified. Domain experts often only focus on specifying constraints that should hold and not on specify- ing constraints that could possibly be violated. In an attempt to bridge this gap we propose the use of “perfect test data”. The generated test data is perfect in that it satisfies all the constraints of an application domain that are required, including ensuring that the test data violates constraints that can be violated. In the context of Description Logic on- tologies we call this test data an “Armstrong ABox”, a notion derived from Armstrong relations in relational database theory. In this paper we detail the theoretical development of Armstrong ABoxes for ALC TBoxes as well as an algorithm for generating such Armstrong ABoxes. The proposed algorithm is based, via the ontology completion algorithm of Baader et al., on attribute exploration in formal concept analysis.},
  year = {2018},
  journal = {Theoretical Aspects of   Computing: 15th International Colloquium, Stellenbosch, South Africa},
  pages = {211-230},
  month = {16/10-19/10},
  publisher = {Springer},
}

Berndt, J. ., Fischer, B. ., & Britz, K. . (2018). Scaling the ConceptCloud browser to large semi-structured data sets. In 14th African Conference on Research in Computer Science and Applied Mathematics, Stellenbosch, South Africa, Proceedings. HAL archives-ouvertes. Retrieved from https://hal.inria.fr/hal-01881376

Abstract BibTex Entry BibTeX Download PDF

Cari2018CRSubmissionID40.pdf

Semi-structured data sets such as product reviews or event log data are simultaneously becoming more widely used and growing ever larger. This paper describes ConceptCloud, a flexible interactive browser for semi-structured datasets, with a focus on the recent trend of implementing server-based architectures to accommodate ever growing datasets. ConceptCloud makes use of an intuitive tag cloud visualization viewer in combination with an underlying concept lattice to provide a formal structure for navigation through datasets without prior knowledge of the structure of the data or compromising scalability. This is achieved by implementing architectural changes to increase the system’s resource efficiency.

@{185,
  author = {Joshua Berndt and Bernd Fischer and Katarina Britz},
  title = {Scaling the ConceptCloud browser to large semi-structured data sets},
  abstract = {Semi-structured data sets such as product reviews or event log data are simultaneously becoming more widely used and growing ever larger. This paper describes ConceptCloud, a flexible interactive browser for semi-structured datasets, with a focus on the recent trend of implementing server-based architectures to accommodate ever growing datasets. ConceptCloud makes use of an intuitive tag cloud visualization viewer in combination with an underlying concept lattice to provide a formal structure for navigation through datasets without prior knowledge of the structure of the data or compromising scalability. This is achieved by implementing architectural changes to increase the system’s resource efficiency.},
  year = {2018},
  journal = {14th African Conference on Research in   Computer Science and Applied Mathematics, Stellenbosch, South Africa, Proceedings},
  pages = {276- 283},
  month = {14/10-16/10},
  publisher = {HAL archives-ouvertes},
  url = {https://hal.inria.fr/hal-01881376},
}

Britz, K. ., & Varzinczak, I. . (2018). Preferential accessibility and preferred worlds. Journal of Logic, Language and Information, 27(2). Retrieved from https://doi.org/10.1007/s10849-017-9264-0

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JoLLI-PrefModal.pdf

Modal accounts of normality in non-monotonic reasoning traditionally have an underlying semantics based on a notion of preference amongst worlds. In this paper, we motivate and investigate an alternative semantics, based on ordered accessibility relations in Kripke frames. The underlying intuition is that some world tuples may be seen as more normal, while others may be seen as more exceptional. We show that this delivers an elegant and intuitive semantic construction, which gives a new perspective on defeasible necessity. Technically, the revisited logic does not change the expressive power of our previously defined preferential modalities. This conclusion follows from an analysis of both semantic constructions via a generalisation of bisimulations to the preferential case. Reasoners based on the previous semantics therefore also suffice for reasoning over the new semantics. We complete the picture by investigating different notions of defeasible conditionals in modal logic that can also be captured within our framework.\footnote{A preliminary version of the work reported in this paper was presented at the Workshop on Nonmonotonic Reasoning.

@article{183,
  author = {Katarina Britz and Ivan Varzinczak},
  title = {Preferential accessibility and preferred worlds},
  abstract = {Modal accounts of normality in non-monotonic reasoning traditionally have an underlying semantics based on a notion of preference amongst worlds. In this paper, we motivate and investigate an alternative semantics, based on ordered accessibility relations in Kripke frames. The underlying intuition is that some world tuples may be seen as more normal, while others may be seen as more exceptional. We show that this delivers an elegant and intuitive semantic construction, which gives a new perspective on defeasible necessity. Technically, the revisited logic does not change the expressive power of our previously defined preferential modalities. This conclusion follows from an analysis of both semantic constructions via a generalisation of bisimulations to the preferential case. Reasoners based on the previous semantics therefore also suffice for reasoning over the new semantics. We complete the picture by investigating different notions of defeasible conditionals in modal logic that can also be captured within our framework.\footnote{A preliminary version of the work reported in this paper was presented at the Workshop on Nonmonotonic Reasoning.},
  year = {2018},
  journal = {Journal of Logic, Language and Information},
  volume = {27},
  pages = {133-155},
  issue = {2},
  publisher = {Springer},
  url = {https://doi.org/10.1007/s10849-017-9264-0},
}

Britz, K. ., & Varzinczak, I. . (2018). From KLM-Style Conditionals to Defeasible Modalities, and Back. Journal of Applied Non-Classical Logics, 28(1). Retrieved from https://doi.org/10.1080/11663081.2017.1397325

Abstract BibTex Entry BibTeX Download PDF

JANCL-DefModalities.pdf

We investigate an aspect of defeasibility that has somewhat been overlooked by the non-monotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal operators with which to formalise the notion of defeasible necessity and distinct possibility, and that can be used to represent expected effects, refutable knowledge, and so on. We show how KLM-style conditionals can smoothly be integrated with our richer language. We also propose a tableau calculus which is sound and complete with respect to our modal preferential semantics, and of which the computational complexity remains in the same class as that of the underlying classical modal logic.

@article{182,
  author = {Katarina Britz and Ivan Varzinczak},
  title = {From KLM-Style Conditionals to Defeasible Modalities, and Back},
  abstract = {We investigate an aspect of defeasibility that has somewhat been overlooked by the non-monotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal operators with which to formalise the notion of defeasible necessity and distinct possibility, and that can be used to represent expected effects, refutable knowledge, and so on. We show how KLM-style conditionals can smoothly be integrated with our richer language. We also propose a tableau calculus which is sound and complete with respect to our modal preferential semantics, and of which the computational complexity remains in the same class as that of the underlying classical modal logic.},
  year = {2018},
  journal = {Journal of Applied Non-Classical Logics},
  volume = {28},
  pages = {92-121},
  issue = {1},
  publisher = {Taylor &amp; Francis},
  url = {https://doi.org/10.1080/11663081.2017.1397325},
}

2017

Britz, K. ., & Varzinczak, I. . (2017). Context-based defeasible subsumption for dSROIQ. In 13th International Symposium on Commonsense Reasoning.

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ComSen2017.pdf

The description logic dSROIQ is a decidable extension of SROIQ that supports defeasible reasoning in the KLM tradition. It features a parameterised preference order on binary relations in a domain of interpretation, which allows for the use of defeasible roles in complex concepts, as well as in defeasible concept and role subsumption, and in defeasible role assertions. In this paper, we address an important limitation both in dSROIQ and in other defeasible extensions of description logics, namely the restriction in the semantics of defeasible concept subsumption to a single preference order on objects. We do this by inducing preference orders on objects from preference orders on roles, and use these to relativise defeasible subsumption. This yields a notion of contextualised defeasible subsumption, with contexts described by roles.

@{169,
  author = {Katarina Britz and Ivan Varzinczak},
  title = {Context-based defeasible subsumption for dSROIQ},
  abstract = {The description logic dSROIQ is a decidable extension of SROIQ that supports defeasible reasoning in the KLM tradition. It features a parameterised preference order on binary relations in a domain of interpretation, which allows for the use of defeasible roles in complex concepts, as well as in defeasible concept and role subsumption, and in defeasible role assertions. In this paper, we address an important limitation both in dSROIQ and in other defeasible extensions of description logics, namely the restriction in the semantics of defeasible concept subsumption to a single preference order on objects. We do this by inducing preference orders on objects from preference orders on roles, and use these to relativise defeasible subsumption. This yields a notion of contextualised defeasible subsumption, with contexts described by roles.},
  year = {2017},
  journal = {13th International Symposium on Commonsense Reasoning},
  month = {06/11-08/11},
}

Britz, K. ., & Varzinczak, I. . (2017). Towards defeasible SROIQ. Retrieved from http://ceur-ws.org/Vol-1879/

Abstract BibTex Entry BibTeX Download PDF

DL-dSROIQ.pdf

We present a decidable extension of the Description Logic SROIQ that supports defeasible reasoning in the KLM tradition, and extends it through the introduction of defeasible roles. The semantics of the resulting DL dSROIQ extends the classical semantics with a parameterised preference order on binary relations in a domain of interpretation. This allows for the use of defeasible roles in complex concepts, as well as in defeasible concept and role subsumption, and in defeasible role assertions. Reasoning over dSROIQ ontologies is made possible by a translation of entailment to concept satisfiability relative to an RBox only. A tableau algorithm then decides on consistency of dSROIQ-concepts in the preferential semantics.

@misc{168,
  author = {Katarina Britz and Ivan Varzinczak},
  title = {Towards defeasible SROIQ},
  abstract = {We present a decidable extension of the Description Logic SROIQ that supports defeasible reasoning in the KLM tradition, and extends it through the introduction of defeasible roles. The semantics of the resulting DL dSROIQ extends the classical semantics with a parameterised preference order on binary relations in a domain of interpretation. This allows for the use of defeasible roles in complex concepts, as well as in defeasible concept and role subsumption, and in defeasible role assertions.  Reasoning over dSROIQ ontologies is made possible by a translation of entailment to concept satisfiability relative to an RBox only. A tableau algorithm then decides on consistency of dSROIQ-concepts in the preferential semantics.},
  year = {2017},
  isbn = {ISSN 1613-0073},
  url = {http://ceur-ws.org/Vol-1879/},
}