Abstract
In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the known weaknesses of logical argumentation frameworks and to prove several desirable properties of the entailments that are induced by the extended (hypersequent-based) frameworks. It also allows us to incorporate as the deductive base of our formalism some well-known logics (like the intermediate logic LC, the modal logic S5, and the relevance logic RM), which lack cut-free sequent calculi, and so are not adequate for standard sequent-based argumentation. We show that hypersequent-based argumentation yields robust defeasible variants of these logics, with many desirable properties.
Highlights
Argumentation theory has been described as “a core study within artificial intelligence” [27]
Logical argumentation is a branch of argumentation theory in which arguments have a specific structure. This includes rule-based argumentation, such as the ASPIC+ framework [71], assumption-based argumentation (ABA) systems [34], defeasible logic programming (DeLP) systems [52], and methods that are based on Tarskian logics, like Besnard and Hunter’s approach [31], in which classical logic is the deductive base
We consider general entailment relations that are obtained by the hypersequential argumentation-based approach, and show how the following ingredients affect their properties: (1) the set of assumptions at hand; (2) the core logic and itssequent calculus, according to which arguments are introduced; (3) the interplay among arguments, namely: how an argument challenges another argument; and (4) considerations that are related to the semantics of the argumentation framework
Summary
Argumentation theory has been described as “a core study within artificial intelligence” [27]. This includes rule-based argumentation, such as the ASPIC+ framework [71], assumption-based argumentation (ABA) systems [34], defeasible logic programming (DeLP) systems [52], and methods that are based on Tarskian logics, like Besnard and Hunter’s approach [31], in which classical logic is the deductive base (the so-called core logic) The latter method was generalized in [9] to sequent-based argumentation, where Gentzen’s sequents [53], extensively used in proof theory, are Presented by Jacek Malinowski; Received February 27, 2019. We consider general entailment relations that are obtained by the hypersequential argumentation-based approach, and show how the following ingredients affect their properties: (1) the set of assumptions (premises) at hand; (2) the core logic and its (hyper)sequent calculus, according to which arguments are introduced; (3) the interplay among arguments, namely: how an argument challenges another argument; and (4) considerations that are related to the semantics of the argumentation framework (in particular, what set of arguments should be taken into account when inferences are made).
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