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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:
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arXiv.org e-Print Archive 
| ISTI Repository | Artificial Intelligence 
| doi.org | www.sciencedirect.com | 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:
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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
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ISTI Repository | CNR ExploRA
2021
Conference article
Open Access
Conditional inference under disjunctive rationality
Booth R., Varzinczak I.
The question of conditional inference, i.e., of which conditional sentences of the form "if ? then, normally, ?" should follow from a set KB of such sentences, has been one of the classic questions of AI, with several well-known solutions proposed. Perhaps the most notable is the rational closure construction of Lehmann and Magidor, under which the set of inferred conditionals forms a rational consequence relation, i.e., satisfies all the rules of preferential reasoning, plus Rational Monotonicity. However, this last named rule is not universally accepted, and other researchers have advocated working within the larger class of disjunctive consequence relations, which satisfy the weaker requirement of Disjunctive Rationality. While there are convincing arguments that the rational closure forms the "simplest" rational consequence relation extending a given set of conditionals, the question of what is the simplest disjunctive consequence relation has not been explored. In this paper, we propose a solution to this question and explore some of its properties.Source: AAAI 2021 - 35th AAAI Conference on Artificial Intelligence, pp. 6227–6234, Online conference, 2-9/02/2021
Booth R., Varzinczak I.
The question of conditional inference, i.e., of which conditional sentences of the form "if ? then, normally, ?" should follow from a set KB of such sentences, has been one of the classic questions of AI, with several well-known solutions proposed. Perhaps the most notable is the rational closure construction of Lehmann and Magidor, under which the set of inferred conditionals forms a rational consequence relation, i.e., satisfies all the rules of preferential reasoning, plus Rational Monotonicity. However, this last named rule is not universally accepted, and other researchers have advocated working within the larger class of disjunctive consequence relations, which satisfy the weaker requirement of Disjunctive Rationality. While there are convincing arguments that the rational closure forms the "simplest" rational consequence relation extending a given set of conditionals, the question of what is the simplest disjunctive consequence relation has not been explored. In this paper, we propose a solution to this question and explore some of its properties.Source: AAAI 2021 - 35th AAAI Conference on Artificial Intelligence, pp. 6227–6234, Online conference, 2-9/02/2021
See at:
ojs.aaai.org | ISTI Repository | CNR ExploRA
2021
Conference article
Open Access
A connection method for a defeasible extension of ALC
Fernandes R., Freitas F., Varzinczak I.
In this paper, we propose a connection method `a la Bibel for an exception-tolerant extension of ALC. As for the language, we assume ALC extended with a typicality operator on concepts, which is a variant of defeasible DLs studied in the literature over the past decade and in which most of these can be embedded. We revisit the definition of matrix representation of a knowledge base and establish the conditions for a given axiom to be provable from it. In particular, we show how term substitution is dealt with and define a suitable condition of blocking in the presence of typicality operators. We show that the calculus terminates and that it is sound and complete w.r.t. a DL version of the preferential semantics widely adopted in non-monotonic reasoning.Source: DL 2021 - 34th International Workshop on Description Logics, Bratislava, Slovakia, 19-22/09/2021
Fernandes R., Freitas F., Varzinczak I.
In this paper, we propose a connection method `a la Bibel for an exception-tolerant extension of ALC. As for the language, we assume ALC extended with a typicality operator on concepts, which is a variant of defeasible DLs studied in the literature over the past decade and in which most of these can be embedded. We revisit the definition of matrix representation of a knowledge base and establish the conditions for a given axiom to be provable from it. In particular, we show how term substitution is dealt with and define a suitable condition of blocking in the presence of typicality operators. We show that the calculus terminates and that it is sound and complete w.r.t. a DL version of the preferential semantics widely adopted in non-monotonic reasoning.Source: DL 2021 - 34th International Workshop on Description Logics, Bratislava, Slovakia, 19-22/09/2021
See at:
ceur-ws.org | ISTI Repository | CNR ExploRA