Knowledge Representation and Reasoning Research Publications

2020

Kaliski A, Meyer T. Quo Vadis KLM-style Defeasible Reasoning? In: First Southern African Conference for Artificial Intelligence Research. Virtual: SACAIR2020; 2020. https://2020.sacair.org.za/wp-content/uploads/2021/02/SACAIR_Proceedings-MainBook_Finv4_compressed.pdf?_ga=2.116601743.849395099.1621802506-572599210.1621419278.

The field of defeasible reasoning has a variety of frameworks, all of which are constructed with the view of codifying the patterns of common-sense reasoning inherent to human reasoning. One of these frameworks was first described by Kraus, Lehmann and Magidor, and is accordingly referred to as the KLM framework. Initially defined in propositional logic, it has since been imported into description and modal logics, and implemented into many defeasible reasoning engines. However, there are many ways in which this framework may be advanced theoretically, and many opportunities for it to be applied. This paper covers some of the most prominent areas of future work and possible applications of this framework, with the intention that anyone who has recently familiarized themselves with this approach may then have an understanding of the kind of work in which they could engage.

@{414,
  author = {Adam Kaliski and Thomas Meyer},
  title = {Quo Vadis KLM-style Defeasible Reasoning?},
  abstract = {The field of defeasible reasoning has a variety of frameworks, all of which are constructed with the view of codifying the patterns of common-sense reasoning inherent to human reasoning. One of these frameworks was first described by Kraus, Lehmann and Magidor, and is accordingly referred to as the KLM framework. Initially defined in propositional logic, it has since been imported into description and modal logics, and implemented into many defeasible reasoning engines. However, there are many ways in which this framework may be advanced theoretically, and many opportunities for it to be applied. This paper covers some of the most prominent areas of future work and possible applications of this framework, with the intention that anyone who has recently familiarized themselves with this approach may then have an understanding of the kind of work in which they could engage.},
  year = {2020},
  journal = {First Southern African Conference for Artificial Intelligence Research},
  pages = {231-246},
  month = {22/02/2021},
  publisher = {SACAIR2020},
  address = {Virtual},
  isbn = {978-0-620-89373-2},
  url = {https://2020.sacair.org.za/wp-content/uploads/2021/02/SACAIR_Proceedings-MainBook_Finv4_compressed.pdf?_ga=2.116601743.849395099.1621802506-572599210.1621419278},
}
Paterson-Jones G, Meyer T. A Boolean Extension of KLM-style Conditional Reasoning. In: First Southern African Conference for AI Research (SACAIR 2020). Virtual: Springer; 2020. doi:https://doi.org/10.1007/978-3-030-66151-9_15.

Propositional KLM-style defeasible reasoning involves extending propositional logic with a new logical connective that can express defeasible (or conditional) implications, with semantics given by ordered structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique. In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.

@{413,
  author = {Guy Paterson-Jones and Thomas Meyer},
  title = {A Boolean Extension of KLM-style Conditional Reasoning},
  abstract = {Propositional KLM-style defeasible reasoning involves extending propositional logic with a new logical connective that can express defeasible (or conditional) implications, with semantics given by ordered structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique. In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.},
  year = {2020},
  journal = {First Southern African Conference for AI Research (SACAIR 2020)},
  pages = {236-252},
  month = {22/02/2021},
  publisher = {Springer},
  address = {Virtual},
  isbn = {978-3-030-66151-9},
  url = {https://link.springer.com/book/10.1007/978-3-030-66151-9},
  doi = {https://doi.org/10.1007/978-3-030-66151-9_15},
}
Baker C, Denny C, Frend P, Meyer T. Cognitive Defeasible Reasoning: the Extent to which Forms of Defeasible Reasoning Correspond with Human Reasoning. In: First Southern African Conference for AI Research (SACAIR 2020). Virtual : Springer; 2020. doi:https://doi.org/10.1007/978-3-030-66151-9_13.

Classical logic forms the basis of knowledge representation and reasoning in AI. In the real world, however, classical logic alone is insufficient to describe the reasoning behaviour of human beings. It lacks the flexibility so characteristically required of reasoning under uncertainty, reasoning under incomplete information and reasoning with new information, as humans must. In response, non-classical extensions to propositional logic have been formulated, to provide non-monotonicity. It has been shown in previous studies that human reasoning exhibits non-monotonicity. This work is the product of merging three independent studies, each one focusing on a different formalism for non-monotonic reasoning: KLM defeasible reasoning, AGM belief revision and KM belief update. We investigate, for each of the postulates propounded to characterise these logic forms, the extent to which they have correspondence with human reasoners. We do this via three respective experiments and present each of the postulates in concrete and abstract form. We discuss related work, our experiment design, testing and evaluation, and report on the results from our experiments. We find evidence to believe that 1 out of 5 KLM defeasible reasoning postulates, 3 out of 8 AGM belief revision postulates and 4 out of 8 KM belief update postulates conform in both the concrete and abstract case. For each experiment, we performed an additional investigation. In the experiments of KLM defeasible reasoning and AGM belief revision, we analyse the explanations given by participants to determine whether the postulates have a normative or descriptive relationship with human reasoning. We find evidence that suggests, overall, KLM defeasible reasoning has a normative relationship with human reasoning while AGM belief revision has a descriptive relationship with human reasoning. In the experiment of KM belief update, we discuss counter-examples to the KM postulates.

@{412,
  author = {Clayton Baker and Claire Denny and Paul Frend and Thomas Meyer},
  title = {Cognitive Defeasible Reasoning: the Extent to which Forms of Defeasible Reasoning Correspond with Human Reasoning},
  abstract = {Classical logic forms the basis of knowledge representation and reasoning in AI. In the real world, however, classical logic alone is insufficient to describe the reasoning behaviour of human beings. It lacks the flexibility so characteristically required of reasoning under uncertainty, reasoning under incomplete information and reasoning with new information, as humans must. In response, non-classical extensions to propositional logic have been formulated, to provide non-monotonicity. It has been shown in previous studies that human reasoning exhibits non-monotonicity. This work is the product of merging three independent studies, each one focusing on a different formalism for non-monotonic reasoning: KLM defeasible reasoning, AGM belief revision and KM belief update. We investigate, for each of the postulates propounded to characterise these logic forms, the extent to which they have correspondence with human reasoners. We do this via three respective experiments and present each of the postulates in concrete and abstract form. We discuss related work, our experiment design, testing and evaluation, and report on the results from our experiments. We find evidence to believe that 1 out of 5 KLM defeasible reasoning postulates, 3 out of 8 AGM belief revision postulates and 4 out of 8 KM belief update postulates conform in both the concrete and abstract case. For each experiment, we performed an additional investigation. In the experiments of KLM defeasible reasoning and AGM belief revision, we analyse the explanations given by participants to determine whether the postulates have a normative or descriptive relationship with human reasoning. We find evidence that suggests, overall, KLM defeasible reasoning has a normative relationship with human reasoning while AGM belief revision has a descriptive relationship with human reasoning. In the experiment of KM belief update, we discuss counter-examples to the KM postulates.},
  year = {2020},
  journal = {First Southern African Conference for AI Research (SACAIR 2020)},
  pages = {199-219},
  month = {22/02/2021},
  publisher = {Springer},
  address = {Virtual},
  isbn = {978-3-030-66151-9},
  url = {https://link.springer.com/book/10.1007/978-3-030-66151-9},
  doi = {https://doi.org/10.1007/978-3-030-66151-9_13},
}
Harrison M, Meyer T. DDLV: A System for rational preferential reasoning for datalog. South African Computer Journal. 2020;32(2). doi:https://doi.org/10.18489/sacj.v32i2.850.

Datalog is a powerful language that can be used to represent explicit knowledge and compute inferences in knowledge bases. Datalog cannot, however, represent or reason about contradictory rules. This is a limitation as contradictions are often present in domains that contain exceptions. In this paper, we extend Datalog to represent contradictory and defeasible information. We define an approach to efficiently reason about contradictory information in Datalog and show that it satisfies the KLM requirements for a rational consequence relation. We introduce DDLV, a defeasible Datalog reasoning system that implements this approach. Finally, we evaluate the performance of DDLV.

@article{411,
  author = {Michael Harrison and Thomas Meyer},
  title = {DDLV: A System for rational preferential reasoning for datalog},
  abstract = {Datalog is a powerful language that can be used to represent explicit knowledge and compute inferences in knowledge bases. Datalog cannot, however, represent or reason about contradictory rules. This is a limitation as contradictions are often present in domains that contain exceptions. In this paper, we extend Datalog to represent contradictory and defeasible information. We define an approach to efficiently reason about contradictory information in Datalog and show that it satisfies the KLM requirements for a rational consequence relation. We introduce DDLV, a defeasible Datalog reasoning system that implements this approach. Finally, we evaluate the performance of DDLV.},
  year = {2020},
  journal = {South African Computer Journal},
  volume = {32},
  pages = {184-217},
  issue = {2},
  publisher = {SACJ},
  address = {Online},
  isbn = {ISSN 2313-7835},
  doi = {https://doi.org/10.18489/sacj.v32i2.850},
}
Chingoma J, Meyer T. Defeasibility applied to Forrester’s paradox. South African Computer Journal. 2020;32(2). doi:https://doi.org/10.18489/sacj.v32i2.848.

Deontic logic is a logic often used to formalise scenarios in the legal domain. Within the legal domain there are many exceptions and conflicting obligations. This motivates the enrichment of deontic logic with not only the notion of defeasibility, which allows for reasoning about exceptions, but a stronger notion of typicality that is based on defeasibility. KLM-style defeasible reasoning is a logic system that employs defeasibility while Propositional Typicality Logic (PTL) is a logic that does the same for the notion of typicality. Deontic paradoxes are often used to examine logic systems as the paradoxes provide undesirable results even if the scenarios seem intuitive. Forrester’s paradox is one of the most famous of these paradoxes. This paper shows that KLM-style defeasible reasoning and PTL can be used to represent and reason with Forrester’s paradox in such a way as to block undesirable conclusions without completely sacrificing desirable deontic properties.

@article{410,
  author = {Julian Chingoma and Thomas Meyer},
  title = {Defeasibility applied to Forrester’s paradox},
  abstract = {Deontic logic is a logic often used to formalise scenarios in the legal domain. Within the legal domain there are many exceptions and conflicting obligations. This motivates the enrichment of deontic logic with not only the notion of defeasibility, which allows for reasoning about exceptions, but a stronger notion of typicality that is based on defeasibility. KLM-style defeasible reasoning is a logic system that employs defeasibility while Propositional Typicality Logic (PTL) is a logic that does the same for the notion of typicality. Deontic paradoxes are often used to examine logic systems as the paradoxes provide undesirable results even if the scenarios seem intuitive. Forrester’s paradox is one of the most famous of these paradoxes. This paper shows that KLM-style defeasible reasoning and PTL can be used to represent and reason with Forrester’s paradox in such a way as to block undesirable conclusions without completely sacrificing desirable deontic properties.},
  year = {2020},
  journal = {South African Computer Journal},
  volume = {32},
  pages = {161-183},
  issue = {2},
  publisher = {SACJ},
  address = {Online},
  isbn = {ISSN 2313-7835},
  doi = {https://doi.org/10.18489/sacj.v32i2.848},
}
Morris M, Ross T, Meyer T. Algorithmic definitions for KLM-style defeasible disjunctive Datalog. South African Computer Journal. 2020;32(2). doi:https://doi.org/10.18489/sacj.v32i2.846.

Datalog is a declarative logic programming language that uses classical logical reasoning as its basic form of reasoning. Defeasible reasoning is a form of non-classical reasoning that is able to deal with exceptions to general assertions in a formal manner. The KLM approach to defeasible reasoning is an axiomatic approach based on the concept of plausible inference. Since Datalog uses classical reasoning, it is currently not able to handle defeasible implications and exceptions. We aim to extend the expressivity of Datalog by incorporating KLM-style defeasible reasoning into classical Datalog. We present a systematic approach for extending the KLM properties and a well-known form of defeasible entailment: Rational Closure. We conclude by exploring Datalog extensions of less conservative forms of defeasible entailment: Relevant and Lexicographic Closure. We provide algorithmic definitions for these forms of defeasible entailment and prove that the definitions are LM-rational.

@article{409,
  author = {Matthew Morris and Tala Ross and Thomas Meyer},
  title = {Algorithmic definitions for KLM-style defeasible disjunctive Datalog},
  abstract = {Datalog is a declarative logic programming language that uses classical logical reasoning as its basic form of reasoning. Defeasible reasoning is a form of non-classical reasoning that is able to deal with exceptions to general assertions in a formal manner. The KLM approach to defeasible reasoning is an axiomatic approach based on the concept of plausible inference. Since Datalog uses classical reasoning, it is currently not able to handle defeasible implications and exceptions. We aim to extend the expressivity of Datalog by incorporating KLM-style defeasible reasoning into classical Datalog. We present a systematic approach for extending the KLM properties and a well-known form of defeasible entailment: Rational Closure. We conclude by exploring Datalog extensions of less conservative forms of defeasible entailment: Relevant and Lexicographic Closure. We provide algorithmic definitions for these forms of defeasible entailment and prove that the definitions are LM-rational.},
  year = {2020},
  journal = {South African Computer Journal},
  volume = {32},
  pages = {141-160},
  issue = {2},
  publisher = {SACJ},
  address = {Online},
  isbn = {ISSN 2313-7835},
  doi = {https://doi.org/10.18489/sacj.v32i2.846},
}
Wanyana T, Moodley D, Meyer T. An Ontology for Supporting Knowledge Discovery and Evolution. In: First Southern African Conference for Artificial Intelligence Research. Virtual: SACAIR2020; 2020. https://2020.sacair.org.za/wp-content/uploads/2021/02/SACAIR_Proceedings-MainBook_Finv4_compressed.pdf?_ga=2.116601743.849395099.1621802506-572599210.1621419278.

Knowledge Discovery and Evolution (KDE) is of interest to a broad array of researchers from both Philosophy of Science (PoS) and Artificial Intelligence (AI), in particular, Knowledge Representation and Reasoning (KR), Machine Learning and Data Mining (ML-DM) and the Agent Based Systems (ABS) communities. In PoS, Haig recently pro- posed a so-called broad theory of scientific method that uses abduction for generating theories to explain phenomena. He refers to this method of scientific inquiry as the Abductive Theory of Method (ATOM). In this paper, we analyse ATOM, align it with KR and ML-DM perspectives and propose an algorithm and an ontology for supporting agent based knowledge discovery and evolution based on ATOM. We illustrate the use of the algorithm and the ontology on a use case application for electricity consumption behaviour in residential households.

@{405,
  author = {Tezira Wanyana and Deshen Moodley and Thomas Meyer},
  title = {An Ontology for Supporting Knowledge Discovery and Evolution},
  abstract = {Knowledge Discovery and Evolution (KDE) is of interest to a broad array of researchers from both Philosophy of Science (PoS) and Artificial Intelligence (AI), in particular, Knowledge Representation and Reasoning (KR), Machine Learning and Data Mining (ML-DM) and the Agent Based Systems (ABS) communities. In PoS, Haig recently pro- posed a so-called broad theory of scientific method that uses abduction for generating theories to explain phenomena. He refers to this method of scientific inquiry as the Abductive Theory of Method (ATOM). In this paper, we analyse ATOM, align it with KR and ML-DM perspectives and propose an algorithm and an ontology for supporting agent based knowledge discovery and evolution based on ATOM. We illustrate the use of the algorithm and the ontology on a use case application for electricity consumption behaviour in residential households.},
  year = {2020},
  journal = {First Southern African Conference for Artificial Intelligence Research},
  pages = {206-221},
  month = {22/02/2021},
  publisher = {SACAIR2020},
  address = {Virtual},
  isbn = {978-0-620-89373-2},
  url = {https://2020.sacair.org.za/wp-content/uploads/2021/02/SACAIR_Proceedings-MainBook_Finv4_compressed.pdf?_ga=2.116601743.849395099.1621802506-572599210.1621419278},
}
Paterson-Jones G, Casini G, Meyer T. BKLM - An expressive logic for defeasible reasoning. 18th International Workshop on Non-Monotonic Reasoning. 2020.

Propositional KLM-style defeasible reasoning involves a core propositional logic capable of expressing defeasible (or conditional) implications. The semantics for this logic is based on Kripke-like structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique. In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.

@misc{383,
  author = {Guy Paterson-Jones and Giovanni Casini and Thomas Meyer},
  title = {BKLM - An expressive logic for defeasible reasoning},
  abstract = {Propositional KLM-style defeasible reasoning involves a core propositional logic capable of expressing defeasible (or conditional) implications. The semantics for this logic is based on Kripke-like structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique.
In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.},
  year = {2020},
  journal = {18th International Workshop on Non-Monotonic Reasoning},
  month = {12/09/2020},
}
Casini G, Meyer T, Varzinczak I. Rational Defeasible Belief Change. In: 17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020). Virtual: IJCAI; 2020. doi:10.24963/kr.2020/22.

We present a formal framework for modelling belief change within a non-monotonic reasoning system. Belief change and non-monotonic reasoning are two areas that are formally closely related, with recent attention being paid towards the analysis of belief change within a non-monotonic environment. In this paper we consider the classical AGM belief change operators, contraction and revision, applied to a defeasible setting in the style of Kraus, Lehmann, and Magidor. The investigation leads us to the formal characterisation of a number of classes of defeasible belief change operators. For the most interesting classes we need to consider the problem of iterated belief change, generalising the classical work of Darwiche and Pearl in the process. Our work involves belief change operators aimed at ensuring logical consistency, as well as the characterisation of analogous operators aimed at obtaining coherence—an important notion within the field of logic-based ontologies

@{382,
  author = {Giovanni Casini and Thomas Meyer and Ivan Varzinczak},
  title = {Rational Defeasible Belief Change},
  abstract = {We present a formal framework for modelling belief change within a non-monotonic reasoning system. Belief change and non-monotonic reasoning are two areas that are formally closely related, with recent attention being paid towards the analysis of belief change within a non-monotonic environment. In this paper we consider the classical AGM belief change operators, contraction and revision, applied to a defeasible setting in the style of Kraus, Lehmann, and Magidor. The investigation leads us to the formal characterisation of a number of classes of defeasible belief change operators. For the most interesting classes we need to consider the problem of iterated belief change, generalising the classical work of Darwiche and Pearl in the process. Our work involves belief change operators aimed at ensuring logical consistency, as well as the characterisation of analogous operators aimed at obtaining coherence—an important notion within the field of logic-based ontologies},
  year = {2020},
  journal = {17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020)},
  pages = {213-222},
  month = {12/09/2020},
  publisher = {IJCAI},
  address = {Virtual},
  url = {https://library.confdna.com/kr/2020/},
  doi = {10.24963/kr.2020/22},
}
Moodley D, Meyer T. Artificial Intelligence – Where it is heading and what we should do about it . 2020. https://link.springer.com/article/10.1007/s42354-020-0269-5.

Artificial Intelligence (AI) is already shaping our everyday lives. While there is enormous potential for harnessing AI to solve complex industrial and social problems and to create new and innovative products and solutions, many organisations are still grappling to understand the relevance and future impact of AI on their activities and what they should be doing about it.

@misc{381,
  author = {Deshen Moodley and Thomas Meyer},
  title = {Artificial Intelligence – Where it is heading and what we should do about it},
  abstract = {Artificial Intelligence (AI) is already shaping our everyday lives. While there is enormous potential for harnessing AI to solve complex industrial and social problems and to create new and innovative products and solutions, many organisations are still grappling to understand the relevance and future impact of AI on their activities and what they should be doing about it.},
  year = {2020},
  url = {https://link.springer.com/article/10.1007/s42354-020-0269-5},
}

2019

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

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 Thomas 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},
}
Casini G, Meyer T, Varzinczak I. Taking Defeasible Entailment Beyond Rational Closure. In: European Conference on Logics in Artificial Intelligence. Switzerland: Springer; 2019. doi:https://doi.org/10.1007/978-3-030-19570-0 _ 12.

We present a systematic approach for extending the KLM framework for defeasible entailment. We first present a class of basic defeasible entailment relations, characterise it in three distinct ways and provide a high-level algorithm for computing it. This framework is then refined, with the refined version being characterised in a similar manner. We show that the two well-known forms of defeasible entailment, rational closure and lexicographic closure, fall within our refined framework, that rational closure is the most conservative of the defeasible entailment relations within the framework (with respect to subset inclusion), but that there are forms of defeasible entailment within our framework that are more “adventurous” than lexicographic closure.

@{238,
  author = {Giovanni Casini and Thomas Meyer and Ivan Varzinczak},
  title = {Taking Defeasible Entailment Beyond Rational Closure},
  abstract = {We present a systematic approach for extending the KLM framework for defeasible entailment. We first present a class of basic defeasible entailment relations, characterise it in three distinct ways and provide a high-level algorithm for computing it. This framework is then refined, with the refined version being characterised in a similar manner. We show that the two well-known forms of defeasible entailment, rational closure and lexicographic closure, fall within our refined framework, that rational closure is the most conservative of the defeasible entailment relations within the framework (with respect to subset inclusion), but that there are forms of defeasible entailment within our framework that are more “adventurous” than lexicographic closure.},
  year = {2019},
  journal = {European Conference on Logics in Artificial Intelligence},
  pages = {182 - 197},
  month = {07/05 - 11/05},
  publisher = {Springer},
  address = {Switzerland},
  isbn = {978-3-030-19569-4},
  url = {https://link.springer.com/chapter/10.1007%2F978-3-030-19570-0_12},
  doi = {https://doi.org/10.1007/978-3-030-19570-0 _ 12},
}
Botha L, Meyer T, Peñaloza R. A Bayesian Extension of the Description Logic ALC. In: European Conference on Logics in Artificial Intelligence. Switzerland: Springer; 2019. doi:https://doi.org/10.1007/978-3-030-19570-0 _ 22.

Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension BALC of the DL ALC. We present a tableau based procedure for deciding consistency, and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain ExpTime-complete, the same as reasoning in the underlying classical ALC.

@{237,
  author = {Leonard Botha and Thomas Meyer and Rafael Peñaloza},
  title = {A Bayesian Extension of the Description Logic ALC},
  abstract = {Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension BALC of the DL ALC. We present a tableau based procedure for deciding consistency, and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain ExpTime-complete, the same as reasoning in the underlying classical ALC.},
  year = {2019},
  journal = {European Conference on Logics in Artificial Intelligence},
  pages = {339 - 354},
  month = {07/05 - 11/05},
  publisher = {Springer},
  address = {Switzerland},
  isbn = {978-3-030-19569-4},
  url = {https://link.springer.com/chapter/10.1007%2F978-3-030-19570-0_22},
  doi = {https://doi.org/10.1007/978-3-030-19570-0 _ 22},
}
Casini G, Meyer T, Varzinczak I. Simple Conditionals with Constrained Right Weakening. In: International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence; 2019. doi:10.24963/ijcai.2019/226.

In this paper we introduce and investigate a very basic semantics for conditionals that can be used to define a broad class of conditional reasoning systems. We show that it encompasses the most popular kinds of conditional reasoning developed in logic-based KR. It turns out that the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy the property of Right Weakening. We show that it can be used for the further development of an analysis of the notion of relevance in conditional reasoning.

@{226,
  author = {Giovanni Casini and Thomas Meyer and Ivan Varzinczak},
  title = {Simple Conditionals with Constrained Right Weakening},
  abstract = {In this paper we introduce and investigate a very basic semantics for conditionals that can be used to define a broad class of conditional reasoning systems. We show that it encompasses the most popular kinds of conditional reasoning developed in logic-based KR. It turns out that the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy the property of Right Weakening. We show that it can be used for the further development of an analysis of the notion of relevance in conditional reasoning.},
  year = {2019},
  journal = {International Joint Conference on Artificial Intelligence},
  pages = {1632-1638},
  month = {10/08-16/08},
  publisher = {International Joint Conferences on Artificial Intelligence},
  isbn = {978-0-9992411-4-1},
  url = {https://www.ijcai.org/Proceedings/2019/0226.pdf},
  doi = {10.24963/ijcai.2019/226},
}
Morris M, Ross T, Meyer T. Defeasible disjunctive datalog. In: Forum for Artificial Intelligence Research. CEUR; 2019. http://ceur-ws.org/Vol-2540/FAIR2019_paper_38.pdf.

Datalog is a declarative logic programming language that uses classical logical reasoning as its basic form of reasoning. Defeasible reasoning is a form of non-classical reasoning that is able to deal with exceptions to general assertions in a formal manner. The KLM approach to defeasible reasoning is an axiomatic approach based on the concept of plausible inference. Since Datalog uses classical reasoning, it is currently not able to handle defeasible implications and exceptions. We aim to extend the expressivity of Datalog by incorporating KLM-style defeasible reasoning into classical Datalog. We present a systematic approach to extending the KLM properties and a well-known form of defeasible entailment: Rational Closure. We conclude by exploring Datalog extensions of less conservative forms of defeasible entailment: Relevant and Lexicographic Closure.

@{225,
  author = {Matthew Morris and Tala Ross and Thomas Meyer},
  title = {Defeasible disjunctive datalog},
  abstract = {Datalog is a declarative logic programming language that uses classical logical reasoning as its basic form of reasoning. Defeasible reasoning is a form of non-classical reasoning that is able to deal with exceptions to general assertions in a formal manner. The KLM approach to defeasible reasoning is an axiomatic approach based on the concept of plausible inference. Since Datalog uses classical reasoning, it is currently not able to handle defeasible implications and exceptions. We aim to extend the expressivity of Datalog by incorporating KLM-style defeasible reasoning into classical Datalog. We present a systematic approach to extending the KLM properties and a well-known form of defeasible entailment: Rational Closure. We conclude by exploring Datalog extensions of less conservative forms of defeasible entailment: Relevant and Lexicographic Closure.},
  year = {2019},
  journal = {Forum for Artificial Intelligence Research},
  pages = {208-219},
  month = {03/12-06/12},
  publisher = {CEUR},
  isbn = {1613-0073},
  url = {http://ceur-ws.org/Vol-2540/FAIR2019_paper_38.pdf},
}
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