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2023
Journal article
Open Access
Situated conditional reasoning
Casini G., Meyer T., Varzinczak I.
Conditionals are useful for modelling many forms of everyday human reasoning but are not always sufficiently expressive to represent the information we want to reason about. In this paper, we make a case for a form of situated conditional. By 'situated', we mean that there is a context, based on an agent's beliefs and expectations, that works as background information in evaluating a conditional, and we allow such a context to vary. These conditionals are able to distinguish, for example, between expectations and counterfactuals. Formally, they are shown to generalise the conditional setting in the style of Kraus, Lehmann, and Magidor. We show that situated conditionals can be described in terms of a set of rationality postulates. We then propose an intuitive semantics for these conditionals and present a representation result which shows that our semantic construction corresponds exactly to the description in terms of postulates. With the semantics in place, we define a form of entailment for situated conditional knowledge bases, which we refer to as minimal closure. Finally, we proceed to show that it is possible to reduce the computation of minimal closure to a series of propositional entailment and satisfiability checks. While this is also the case for rational closure, it is somewhat surprising that the result carries over to minimal closure.Source: Artificial intelligence (Gen. ed.) 319 (2023). doi:10.1016/j.artint.2023.103917
DOI: 10.1016/j.artint.2023.103917
DOI: 10.48550/arxiv.2109.01552
Project(s): TAILOR
Metrics:
Casini G., Meyer T., Varzinczak I.
Conditionals are useful for modelling many forms of everyday human reasoning but are not always sufficiently expressive to represent the information we want to reason about. In this paper, we make a case for a form of situated conditional. By 'situated', we mean that there is a context, based on an agent's beliefs and expectations, that works as background information in evaluating a conditional, and we allow such a context to vary. These conditionals are able to distinguish, for example, between expectations and counterfactuals. Formally, they are shown to generalise the conditional setting in the style of Kraus, Lehmann, and Magidor. We show that situated conditionals can be described in terms of a set of rationality postulates. We then propose an intuitive semantics for these conditionals and present a representation result which shows that our semantic construction corresponds exactly to the description in terms of postulates. With the semantics in place, we define a form of entailment for situated conditional knowledge bases, which we refer to as minimal closure. Finally, we proceed to show that it is possible to reduce the computation of minimal closure to a series of propositional entailment and satisfiability checks. While this is also the case for rational closure, it is somewhat surprising that the result carries over to minimal closure.Source: Artificial intelligence (Gen. ed.) 319 (2023). doi:10.1016/j.artint.2023.103917
DOI: 10.1016/j.artint.2023.103917
DOI: 10.48550/arxiv.2109.01552
Project(s): TAILOR
Metrics:
See at:
arXiv.org e-Print Archive 
| ISTI Repository | Artificial Intelligence 
| doi.org | www.sciencedirect.com | CNR ExploRA
2023
Conference article
Open Access
Revising typical beliefs: one revision to rule them all
Heyninck J., Casini G., Meyer T., Straccia U.
Propositional Typicality Logic (PTL) extends propositional logic with a connective $\bullet$ expressing the most typical (alias normal or conventional) situations in which a given sentence holds. As such, it generalises e.g. preferential logics that formalise reasoning with conditionals such as "birds typically fly". In this paper we study the revision of sets of PTL sentences. We first show why it is necessary to extend the PTL language with a possibility operator and then define the revision of PTL sentences syntactically and characterise it semantically. We show that this allows us to represent a wide variety of existing revision methods, such as propositional revision and revision of epistemic states. Furthermore, we provide several examples showing why our approach is innovative. In more detail, we study the revision of a set of conditionals under preferential closure and the addition and contraction of possible worlds from an epistemic state.Source: KR2023 - International Conference on Principles of Knowledge Representation and Reasoning, pp. 355–364, Rhodes, Greece, 2-8/09/2023
DOI: 10.24963/kr.2023/35
Project(s): TAILOR
Metrics:
Heyninck J., Casini G., Meyer T., Straccia U.
Propositional Typicality Logic (PTL) extends propositional logic with a connective $\bullet$ expressing the most typical (alias normal or conventional) situations in which a given sentence holds. As such, it generalises e.g. preferential logics that formalise reasoning with conditionals such as "birds typically fly". In this paper we study the revision of sets of PTL sentences. We first show why it is necessary to extend the PTL language with a possibility operator and then define the revision of PTL sentences syntactically and characterise it semantically. We show that this allows us to represent a wide variety of existing revision methods, such as propositional revision and revision of epistemic states. Furthermore, we provide several examples showing why our approach is innovative. In more detail, we study the revision of a set of conditionals under preferential closure and the addition and contraction of possible worlds from an epistemic state.Source: KR2023 - International Conference on Principles of Knowledge Representation and Reasoning, pp. 355–364, Rhodes, Greece, 2-8/09/2023
DOI: 10.24963/kr.2023/35
Project(s): TAILOR
Metrics:
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ISTI Repository | proceedings.kr.org | CNR ExploRA
2023
Contribution to conference
Open Access
Preface for the first Workshop on AI-driven heterogeneous data management: Completing, merging, handling inconsistencies and query-answering (ENIGMA-2023)
Benferhat S., Casini G., Meyer T., Tettamanzi A. G. B.
Proceedings of 1st Workshop on AI-driven heterogeneous data management: Completing, merging, handling inconsistencies and query-answering, co-located with 20th International Conference on Principles of Knowledge Representation and Reasoning (KR 2023).Source: Aachen: CEUR-WS.org, 2023
Benferhat S., Casini G., Meyer T., Tettamanzi A. G. B.
Proceedings of 1st Workshop on AI-driven heterogeneous data management: Completing, merging, handling inconsistencies and query-answering, co-located with 20th International Conference on Principles of Knowledge Representation and Reasoning (KR 2023).Source: Aachen: CEUR-WS.org, 2023
See at:
ceur-ws.org | ISTI Repository | CNR ExploRA
2022
Conference article
Open Access
Situated conditionals - A brief introduction
Casini G., Meyer T., Varzinczak I.
We extend the expressivity of classical conditional reasoning by introducing situation 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. 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 RationalClosure.Source: NMR 2022 - International Workshop on Non-Monotonic Reasoning 2022, pp. 151–154, Haifa, Israel, 07-09/08/2022
Project(s): TAILOR
Casini G., Meyer T., Varzinczak I.
We extend the expressivity of classical conditional reasoning by introducing situation 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. 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 RationalClosure.Source: NMR 2022 - International Workshop on Non-Monotonic Reasoning 2022, pp. 151–154, Haifa, Israel, 07-09/08/2022
Project(s): TAILOR
See at:
ceur-ws.org | ISTI Repository | CNR ExploRA
2022
Conference article
Closed Access
KLM-style defeasibility for restricted first-order logic
Casini G., Meyer T., Paterson-Jones G., Varzinczak I.
In this paper, we extend the KLM approach to defeasible reasoning beyond the propositional setting. We do so by making it applicable to a restricted version of first-order logic. We describe defeasibility for this logic using a set of rationality postulates, provide a suitable and intuitive semantics for it, and present a representation result characterising the semantic description of defeasibility in terms of our postulates. An advantage of our semantics is that it is sufficiently general to be applicable to other restricted versions of first-order logic as well. Based on this theoretical core, we then propose a version of defeasible entailment that is inspired by the well-known notion of 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 the full set of rationality postulates.Source: RuleML+RR 2022 - International Joint Conference on Rules and Reasoning, pp. 81–94, Berlin, Germany, 26-28/09/2022
DOI: 10.1007/978-3-031-21541-4_6
Project(s): TAILOR
Metrics:
Casini G., Meyer T., Paterson-Jones G., Varzinczak I.
In this paper, we extend the KLM approach to defeasible reasoning beyond the propositional setting. We do so by making it applicable to a restricted version of first-order logic. We describe defeasibility for this logic using a set of rationality postulates, provide a suitable and intuitive semantics for it, and present a representation result characterising the semantic description of defeasibility in terms of our postulates. An advantage of our semantics is that it is sufficiently general to be applicable to other restricted versions of first-order logic as well. Based on this theoretical core, we then propose a version of defeasible entailment that is inspired by the well-known notion of 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 the full set of rationality postulates.Source: RuleML+RR 2022 - International Joint Conference on Rules and Reasoning, pp. 81–94, Berlin, Germany, 26-28/09/2022
DOI: 10.1007/978-3-031-21541-4_6
Project(s): TAILOR
Metrics:
See at:
doi.org | link.springer.com | CNR ExploRA
2021
Report
Open Access
Situated conditional reasoning
Casini G., Meyer T., Varzinczak I.
Conditionals are useful for modelling, but aren't always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive than classical conditionals, are general enough to be used in several application domains, and are able to distinguish, for example, between expectations and counterfactuals. Formally, they are shown to generalise the conditional setting in the style of Kraus, Lehmann, and Magidor. We show that situation-based conditionals can be described in terms of a set of rationality postulates. We then propose an intuitive semantics for these conditionals, and present a representation result which shows that our semantic construction corresponds exactly to the description in terms of postulates. With the semantics in place, we proceed to define a form of entailment for situated conditional knowledge bases, which we refer to as minimal closure. It is reminiscent of and, indeed, inspired by, the version of entailment for propositional conditional knowledge bases known as rational closure. Finally, we proceed to show that it is possible to reduce the computation of minimal closure to a series of propositional entailment and satisfiability checks. While this is also the case for rational closure, it is somewhat surprising that the result carries over to minimal closure.Source: ISTI Technical Report, ISTI-2021-TR/009, 2021
DOI: 10.32079/isti-tr-2021/009
Metrics:
Casini G., Meyer T., Varzinczak I.
Conditionals are useful for modelling, but aren't always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive than classical conditionals, are general enough to be used in several application domains, and are able to distinguish, for example, between expectations and counterfactuals. Formally, they are shown to generalise the conditional setting in the style of Kraus, Lehmann, and Magidor. We show that situation-based conditionals can be described in terms of a set of rationality postulates. We then propose an intuitive semantics for these conditionals, and present a representation result which shows that our semantic construction corresponds exactly to the description in terms of postulates. With the semantics in place, we proceed to define a form of entailment for situated conditional knowledge bases, which we refer to as minimal closure. It is reminiscent of and, indeed, inspired by, the version of entailment for propositional conditional knowledge bases known as rational closure. Finally, we proceed to show that it is possible to reduce the computation of minimal closure to a series of propositional entailment and satisfiability checks. While this is also the case for rational closure, it is somewhat surprising that the result carries over to minimal closure.Source: ISTI Technical Report, ISTI-2021-TR/009, 2021
DOI: 10.32079/isti-tr-2021/009
Metrics:
See at:
ISTI Repository | CNR ExploRA
2021
Conference article
Open Access
KLM-style defeasibility for restricted first-order logic
Casini G., Meyer T., Paterson-Jones G.
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.Source: NMR 2021 - 19th International Workshop on Non-Monotonic Reasoning, pp. 184–193, Online Conference, 3-5/11/2021
Casini G., Meyer T., Paterson-Jones G.
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.Source: NMR 2021 - 19th International Workshop on Non-Monotonic Reasoning, pp. 184–193, Online Conference, 3-5/11/2021
See at:
drive.google.com | ISTI Repository | CNR ExploRA