Giovanni Casini

2021

Casini, G. ., Meyer, T. ., & Varzinczak, I. . (2021). Contextual Conditional Reasoning. In 35th AAAI Conference on Artificial Intelligence. Online: AAAI Press. (Original work published 2021)

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AAAI-8192.CasiniG.pdf

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 and Tommie Meyer and 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},
}

Casini, G. ., Meyer, T. ., & Paterson-Jones, G. . (2021). KLM-Style Defeasibility for Restricted First-Order Logic. In 19th International Workshop on Non-Monotonic Reasoning. Online. Retrieved from https://drive.google.com/open?id=1WSIl3TOrXBhaWhckWN4NLXoD9AVFKp5R (Original work published 2021)

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nmr2021.pdf

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 and Tommie Meyer and 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},
}

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

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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},
}

Paterson-Jones, G. ., Casini, G. ., & Meyer, T. . (2020). BKLM - An expressive logic for defeasible reasoning. 18th International Workshop on Non-Monotonic Reasoning. (Original work published 2020)

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WorkshopNotes.pdf

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 Tommie 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 = {12/09/2020-24/09/2020},
}

Casini, G. ., Meyer, T. ., & Varzinczak, I. . (2020). Rational Defeasible Belief Change. In 17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020). Virtual: IJCAI. http://doi.org/10.24963/kr.2020/22 (Original work published 2020)

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kr2020-0022-casini-et-al.pdf

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 Tommie 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},
}

2019

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

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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},
}

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

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2019-JELIA-Casini-ea.pdf

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 Tommie 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},
}

Casini, G. ., Meyer, T. ., & Varzinczak, I. . (2019). Simple Conditionals with Constrained Right Weakening. In International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence. http://doi.org/10.24963/ijcai.2019/226

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0226.pdf

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 Tommie 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},
}

Casini, G. ., Harrison, M. ., Meyer, T. ., & Swan, R. . (2019). Arbitrary Ranking of Defeasible Subsumption. 32nd International Work- shop on Description Logics. Retrieved from http://ceur-ws.org/Vol-2373/paper-9.pdf (Original work published 2019)

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paper-9.pdf

In this paper we propose an algorithm that generalises existing procedures for the implementation of defeasible reasoning in the framework of Description Logics (DLs). One of the well-known approaches to defeasible reasoning, the so-called KLM approach, is based on con- structing specific rankings of defeasible information, and using these rankings to determine priorities in case of conflicting information. Here we propose a procedure that allows us to input any possible ranking of the defeasible concept inclusions contained in the knowledge base. We analyse and investigate the forms of defeasible reasoning obtained when conclusions drawn are obtained using these rankings.

@misc{222,
  author = {Giovanni Casini and Michael Harrison and Tommie Meyer and Reid Swan},
  title = {Arbitrary Ranking of Defeasible Subsumption},
  abstract = {In this paper we propose an algorithm that generalises existing procedures for the implementation of defeasible reasoning in the framework of Description Logics (DLs). One of the well-known approaches to defeasible reasoning, the so-called KLM approach, is based on con- structing specific rankings of defeasible information, and using these rankings to determine priorities in case of conflicting information. Here we propose a procedure that allows us to input any possible ranking of the defeasible concept inclusions contained in the knowledge base. We analyse and investigate the forms of defeasible reasoning obtained when conclusions drawn are obtained using these rankings.},
  year = {2019},
  journal = {32nd International Work- shop on Description Logics},
  month = {06/2019},
  url = {http://ceur-ws.org/Vol-2373/paper-9.pdf},
}

Casini, G. ., Straccia, U. ., & Meyer, T. . (2019). A polynomial Time Subsumption Algorithm for Nominal Safe ELO⊥ under Rational Closure. Information Sciences, 501. http://doi.org/https://doi.org/10.1016/j.ins.2018.09.037

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Inf. Sci. 2019 Casini.pdf

Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO⊥, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO⊥ under RC that relies entirely on a series of classical, monotonic EL⊥ subsumption tests. Therefore, any existing classical monotonic EL⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability.

@article{221,
  author = {Giovanni Casini and Umberto Straccia and Tommie Meyer},
  title = {A polynomial Time Subsumption Algorithm for Nominal Safe ELO⊥ under Rational Closure},
  abstract = {Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO⊥, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO⊥ under RC that relies entirely on a series of classical, monotonic EL⊥ subsumption tests. Therefore, any existing classical monotonic EL⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability.},
  year = {2019},
  journal = {Information Sciences},
  volume = {501},
  pages = {588 - 620},
  publisher = {Elsevier},
  isbn = {0020-0255},
  url = {http://www.sciencedirect.com/science/article/pii/S0020025518307436},
  doi = {https://doi.org/10.1016/j.ins.2018.09.037},
}

Booth, R. ., Casini, G. ., Meyer, T. ., & Varzinczak, I. . (2019). On rational entailment for Propositional Typicality Logic. Artificial Intelligence , 227. http://doi.org/https://doi.org/10.1016/j.artint.2019.103178

Abstract BibTex Entry BibTeX Download PDF

2019-AIJ.pdf

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence holds. The semantics of PTL is in terms of ranked models as studied in the well-known KLM approach to preferential reasoning and therefore KLM-style rational consequence relations can be embedded in PTL. In spite of the non-monotonic features introduced by the semantics adopted for the typicality operator, the obvious Tarskian definition of entailment for PTL remains monotonic and is therefore not appropriate in many contexts. Our first important result is an impossibility theorem showing that a set of proposed postulates that at first all seem appropriate for a notion of entailment with regard to typicality cannot be satisfied simultaneously. Closer inspection reveals that this result is best interpreted as an argument for advocating the development of more than one type of PTL entailment. In the spirit of this interpretation, we investigate three different (semantic) versions of entailment for PTL, each one based on the definition of rational closure as introduced by Lehmann and Magidor for KLM-style conditionals, and constructed using different notions of minimality.

@article{219,
  author = {Richard Booth and Giovanni Casini and Tommie Meyer and Ivan Varzinczak},
  title = {On rational entailment for Propositional Typicality Logic},
  abstract = {Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence holds. The semantics of PTL is in terms of ranked models as studied in the well-known KLM approach to preferential reasoning and therefore KLM-style rational consequence relations can be embedded in PTL. In spite of the non-monotonic features introduced by the semantics adopted for the typicality operator, the obvious Tarskian definition of entailment for PTL remains monotonic and is therefore not appropriate in many contexts. Our first important result is an impossibility theorem showing that a set of proposed postulates that at first all seem appropriate for a notion of entailment with regard to typicality cannot be satisfied simultaneously. Closer inspection reveals that this result is best interpreted as an argument for advocating the development of more than one type of PTL entailment. In the spirit of this interpretation, we investigate three different (semantic) versions of entailment for PTL, each one based on the definition of rational closure as introduced by Lehmann and Magidor for KLM-style conditionals, and constructed using different notions of minimality.},
  year = {2019},
  journal = {Artificial Intelligence},
  volume = {227},
  pages = {103178},
  publisher = {Elsevier},
  isbn = {0004-3702},
  url = {https://www.sciencedirect.com/science/article/abs/pii/S000437021830506X?via%3Dihub},
  doi = {https://doi.org/10.1016/j.artint.2019.103178},
}

2018

Casini, G. ., Meyer, T. ., & Varzinczak, I. . (2018). Defeasible Entailment: from Rational Closure to Lexicographic Closure and Beyond. In 7th International Workshop on Non-Monotonic Reasoning (NMR 2018). Retrieved from http://orbilu.uni.lu/bitstream/10993/37393/1/NMR2018Paper.pdf

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NMR2018Paper.pdf

In this paper we present what we believe to be the first systematic approach for extending the framework for defeasible entailment first presented by Kraus, Lehmann, and Magidor—the so-called KLM approach. Drawing on the properties for KLM, we first propose a class of basic defeasible entailment relations. We characterise this basic framework in three ways: (i) semantically, (ii) in terms of a class of properties, and (iii) in terms of ranks on statements in a knowlege base. We also provide an algorithm for computing the basic framework. These results are proved through various representation results. We then refine this framework by defining the class of rational defeasible entailment relations. This refined framework is also characterised in thee ways: semantically, in terms of a class of properties, and in terms of ranks on statements. We also provide an algorithm for computing the refined framework. Again, these results are proved through various representation results. We argue that the class of rational defeasible entailment relations—a strengthening of basic defeasible entailment which is itself a strengthening of the original KLM proposal—is worthy of the term rational in the sense that all of them can be viewed as appropriate forms of defeasible entailment. We show that the two well-known forms of defeasible entailment, rational closure and lexicographic closure, fall within our rational defeasible framework. We show 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.

@{200,
  author = {Giovanni Casini and Tommie Meyer and Ivan Varzinczak},
  title = {Defeasible Entailment: from Rational Closure to Lexicographic Closure and Beyond},
  abstract = {In this paper we present what we believe to be the first systematic approach for extending the framework for defeasible entailment first presented by Kraus, Lehmann, and Magidor—the so-called KLM approach. Drawing on the properties for KLM, we first propose a class of basic defeasible entailment relations. We characterise this basic framework in three ways: (i) semantically, (ii) in terms of a class of properties, and (iii) in terms of ranks on statements in a knowlege base. We also provide an algorithm for computing the basic framework. These results are proved through various representation results. We then refine this framework by defining the class of rational defeasible entailment relations. This refined framework is also characterised in thee ways: semantically, in terms of a class of properties, and in terms of ranks on statements. We also provide an algorithm for computing the refined framework. Again, these results are proved through various representation results.
We argue that the class of rational defeasible entailment relations—a strengthening of basic defeasible entailment which is itself a strengthening of the original KLM proposal—is worthy of the term rational in the sense that all of them can be viewed as appropriate forms of defeasible entailment. We show that the two well-known forms of defeasible entailment, rational closure and lexicographic closure, fall within our rational defeasible framework. We show 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 = {2018},
  journal = {7th International Workshop on Non-Monotonic Reasoning (NMR 2018)},
  pages = {109-118},
  month = {27/10-29/10},
  url = {http://orbilu.uni.lu/bitstream/10993/37393/1/NMR2018Paper.pdf},
}

Casini, G. ., Eduardo, F. ., Meyer, T. ., & Varzinczak, I. . (2018). A Semantic Perspective on Belief Change in a Preferential Non-Monotonic Framework. In 16th International Conference on Principles of Knowledge Representation and Reasoning. United States of America: AAAI Press. Retrieved from https://dblp.org/db/conf/kr/kr2018.html

Abstract BibTex Entry BibTeX Download PDF

KR_2018_paper_204.pdf

Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we investigate the integration of the two formalisms by studying belief change for a (preferential) non-monotonic framework. We show that the standard AGM approach to belief change can be transferred to a preferential non-monotonic framework in the sense that change operations can be defined on conditional knowledge bases. We take as a point of departure the results presented by Casini and Meyer (2017), and we develop and extend such results with characterisations based on semantics and entrenchment relations, showing how some of the constructions defined for propositional logic can be lifted to our preferential non-monotonic framework.

@{197,
  author = {Giovanni Casini and F. Eduardo and Tommie Meyer and Ivan Varzinczak},
  title = {A Semantic Perspective on Belief Change in a Preferential Non-Monotonic Framework},
  abstract = {Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we investigate the integration of the two formalisms by studying belief change for a (preferential) non-monotonic framework. We show that the standard AGM approach to belief change can be transferred to a preferential non-monotonic framework in the sense that change operations can be defined on conditional knowledge bases. We take as a point of departure the results presented by Casini and Meyer (2017), and we develop and extend such results with characterisations based on semantics and entrenchment relations, showing how some of the constructions defined for propositional logic can be lifted to our preferential non-monotonic framework.},
  year = {2018},
  journal = {16th International Conference on Principles of Knowledge Representation and Reasoning},
  pages = {220-229},
  month = {27/10-02/11},
  publisher = {AAAI Press},
  address = {United States of America},
  isbn = {978-1-57735-803-9},
  url = {https://dblp.org/db/conf/kr/kr2018.html},
}

2017

Casini, G. ., & Meyer, T. . (2017). Belief Change in a Preferential Non-Monotonic Framework. In International Joint Conference on Artificial Intelligence (IJCAI-17).

Abstract BibTex Entry BibTeX Download PDF

0129.pdf

Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we show that we can also integrate the two formalisms by studying belief change within a (preferential) non-monotonic framework. This integration relies heavily on the identification of the monotonic core of a non-monotonic framework. We consider belief change operators in a non-monotonic propositional setting with a view towards preserving consistency. These results can also be applied to the preservation of coherence—an important notion within the field of logic-based ontologies. We show that the standard AGM approach to belief change can be adapted to a preferential non-monotonic framework, with the definition of expansion, contraction, and revision operators, and corresponding representation results. Surprisingly, preferential AGM belief change, as defined here, can be obtained in terms of classical AGM belief change.

@{167,
  author = {Giovanni Casini and Tommie Meyer},
  title = {Belief Change in a Preferential Non-Monotonic Framework},
  abstract = {Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we show that we can also integrate the two formalisms by studying belief change within a (preferential) non-monotonic framework. This integration relies heavily on the identification of the monotonic core of a non-monotonic framework. We consider belief change operators in a non-monotonic propositional setting with a view towards preserving consistency. These results can also be applied to the preservation of coherence—an important notion within the field of logic-based ontologies. We show that the standard AGM approach to belief change can be adapted to a preferential non-monotonic framework, with the definition of expansion, contraction, and revision operators, and corresponding representation results. Surprisingly, preferential AGM belief change, as defined here, can be obtained in terms of classical AGM belief change.},
  year = {2017},
  journal = {International Joint Conference on Artificial Intelligence (IJCAI-17)},
  pages = {929-935},
  month = {19/08-25/08},
  isbn = {978-0-9992411-0-3},
}