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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
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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
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ceur-ws.org | ISTI Repository | CNR ExploRA