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Belief revision and belief update are approaches to represent and reason with knowledge in artificial intelligence. Previous empirical studies have shown that human reasoning is consistent with non-monotonic logic and postulates of defeasible reasoning, belief revision and belief update. We extended previous work, which tested natural language translations of the postulates of defeasible reasoning, belief revision and belief update with human reasoners via surveys, in three respects.
Firstly, we only tested postulates of belief revision and belief update, taking the position that belief change aligns more with human reasoning than non-monotonic defeasible reasoning. Secondly, we decomposed the postulates of revision and update into material implication statements of the form “If x is the case, then y is the case”, each containing a premise
and a conclusion, and then translated the premises and conclusions into natural language. Thirdly, we asked human participants to judge each component of the postulate for plausibility. In our analysis, we measured the strength of the association between the premises and the conclusion of each postulate. We used Possibility theory to determine whether the postulates hold with our participants in general. Our results showed that our participants’ reasoning is consistent with postulates of belief
revision and belief update when judging the premises and conclusion of the postulate separately.

@{427,
  author = {Clayton Baker, Tommie Meyer},
  title = {Belief Change in Human Reasoning: An Empirical Investigation on MTurk},
  abstract = {Belief revision and belief update are approaches to represent and reason with knowledge in artificial intelligence. Previous empirical studies have shown that human reasoning is consistent with non-monotonic logic and postulates of defeasible reasoning, belief revision and belief update. We extended previous work, which tested natural language translations of the postulates of defeasible reasoning, belief revision and belief update with human reasoners via surveys, in three respects.
Firstly, we only tested postulates of belief revision and belief update, taking the position that belief change aligns more with human reasoning than non-monotonic defeasible reasoning. Secondly, we decomposed the postulates of revision and update into material implication statements of the form “If x is the case, then y is the case”, each containing a premise
and a conclusion, and then translated the premises and conclusions into natural language. Thirdly, we asked human participants to judge each component of the postulate for plausibility. In our analysis, we measured the strength of the association between the premises and the conclusion of each postulate. We used Possibility theory to determine whether the postulates hold with our participants in general. Our results showed that our participants’ reasoning is consistent with postulates of belief
revision and belief update when judging the premises and conclusion of the postulate separately.},
  year = {2022},
  journal = {Second Southern African Conference for AI Research (SACAIR 2022)},
  pages = {218-234},
  month = {06/12/2021-10/12/2021},
  publisher = {SACAIR 2021 Organising Committee},
  address = {Online},
  isbn = {978-0-620-94410-6},
  url = {https://2021.sacair.org.za/proceedings/},
}

Explanation services are a crucial aspect of symbolic reasoning systems but they have not been explored in detail for defeasible formalisms such as KLM. We evaluate prior work on the topic with a focus on KLM propositional logic and find that a form of defeasible explanation initially described for Rational Closure which we term weak justification can be adapted to Relevant and Lexicographic Closure as well as described in terms of intuitive properties derived from the KLM postulates. We also consider how a more general definition of defeasible explanation known as strong explanation applies to KLM and propose an algorithm that enumerates these justifications for Rational Closure.

@inbook{426,
  author = {Lloyd Everett, Emily Morris, Tommie Meyer},
  title = {Explanation for KLM-Style Defeasible Reasoning},
  abstract = {Explanation services are a crucial aspect of symbolic reasoning systems but they have not been explored in detail for defeasible formalisms such as KLM. We evaluate prior work on the topic with a focus on KLM propositional logic and find that a form of defeasible explanation initially described for Rational Closure which we term weak justification can be adapted to Relevant and Lexicographic Closure as well as described in terms of intuitive properties derived from the KLM postulates. We also consider how a more general definition of defeasible explanation known as strong explanation applies to KLM and propose an algorithm that enumerates these justifications for Rational Closure.},
  year = {2022},
  journal = {Artificial Intelligence Research. SACAIR 2021.},
  edition = {1551},
  publisher = {Springer},
  address = {Cham},
  isbn = {978-3-030-95069-9},
  url = {https://link.springer.com/book/10.1007/978-3-030-95070-5},
  doi = {10.1007/978-3-030-95070-5_13},
}

We extend the expressivity of classical conditional reasoning by introducing context as a new parameter. The enriched
conditional logic generalises the defeasible conditional setting in the style of Kraus, Lehmann, and Magidor, and allows for a refined semantics that is able to distinguish, for example, between expectations and counterfactuals. In this paper we introduce the language for the enriched logic and define an appropriate semantic framework for it. We analyse which properties generally associated with conditional reasoning are still satisfied by the new semantic framework, provide a suitable representation result, and define an entailment relation based on Lehmann and Magidor’s generally-accepted notion of Rational Closure.

@{430,
  author = {Giovanni Casini, Tommie Meyer, Ivan Varzinczak},
  title = {Contextual Conditional Reasoning},
  abstract = {We extend the expressivity of classical conditional reasoning by introducing context as a new parameter. The enriched
conditional logic generalises the defeasible conditional setting in the style of Kraus, Lehmann, and Magidor, and allows for a refined semantics that is able to distinguish, for example, between expectations and counterfactuals. In this paper we introduce the language for the enriched logic and define an appropriate semantic framework for it. We analyse which properties generally associated with conditional reasoning are still satisfied by the new semantic framework, provide a suitable representation result, and define an entailment relation based on Lehmann and Magidor’s generally-accepted notion of Rational Closure.},
  year = {2021},
  journal = {35th AAAI Conference on Artificial Intelligence},
  pages = {6254-6261},
  month = {02/02/2021-09/02/2021},
  publisher = {AAAI Press},
  address = {Online},
}

We extend the KLM approach to defeasible reasoning to be applicable to a restricted version of first-order logic. We describe defeasibility for this logic using a set of rationality postulates, provide an appropriate semantics for it, and present a representation result that characterises the semantic description of defeasibility in terms of the rationality postulates. Based on this theoretical core, we then propose a version of defeasible entailment that is inspired by Rational Closure as it is defined for defeasible propositional logic and defeasible description logics. We show that this form of defeasible entailment is rational in the sense that it adheres to our rationality postulates. The work in this paper is the first step towards our ultimate goal of introducing KLM-style defeasible reasoning into the family of Datalog+/- ontology languages.

@{429,
  author = {Giovanni Casini, Tommie Meyer, Guy Paterson-Jones},
  title = {KLM-Style Defeasibility for Restricted First-Order Logic},
  abstract = {We extend the KLM approach to defeasible reasoning to be applicable to a restricted version of first-order logic. We describe defeasibility for this logic using a set of rationality postulates, provide an appropriate semantics for it, and present a representation result that characterises the semantic description of defeasibility in terms of the rationality postulates. Based on this theoretical core, we then propose a version of defeasible entailment that is inspired by Rational Closure as it is defined for defeasible propositional logic and defeasible description logics. We show that this form of defeasible entailment is rational in the sense that it adheres to our rationality postulates. The work in this paper is the first step towards our ultimate goal of introducing KLM-style defeasible reasoning into the family of Datalog+/- ontology languages.},
  year = {2021},
  journal = {19th International Workshop on Non-Monotonic Reasoning},
  pages = {184-193},
  month = {03/11/2021-05/11/2021},
  address = {Online},
  url = {https://drive.google.com/open?id=1WSIl3TOrXBhaWhckWN4NLXoD9AVFKp5R},
}

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, Giovanni Casini, Tommie Meyer, Kody Moodley, Uli Sattler, 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},
}