Sequent-based logical argumentation

Arieli, Ofer; Straßer, Christian

doi:10.1080/19462166.2014.1002536

Cited by 39 publications

(74 citation statements)

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“…Logic-based argumentation is closest to our setting from Section 2. Systems can be found in, for instance, [2,5]. 3 The core logic L is a finitary Tarskian logic with an adequate consequence relation ⊢ ⊆ ℘ fin (L) × L. Given a set S ⊆ L, the set of arguments defined by Arg ⊢ (S) consists of all (Γ, γ) where Γ ⊢ γ and Γ ⊆ S just like in Def.…”

Section: Systems Of Structured Argumentationmentioning

confidence: 99%

“…We studied the properties Non-Interference, Crash Resistance, and Cumulativity. In future work we plan to incorporate priorities (e.g., [1,11,18]) and to extend our study to other meta-theoretic properties, such as other properties of non-monotonic inference ( [16]) and rationality postulates ( [8]).…”

Section: Semantic Relevancementioning

confidence: 99%

“…Structured argumentation has been studied in various settings such as ASPIC [19,20], ABA [7,21], and logic-based argumentation [2,5,6]. These frameworks share the underlying idea that arguments are to have a logical structure and attacks between them are at least partially determined by logical considerations.…”

Section: Introductionmentioning

confidence: 99%

“…A similar property is Basic Relevance [3, Definition 3.1] 2. |∼ is non-trivial if there are always two sets of formulas with the same atoms but different conclusions (see[9]).…”

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confidence: 99%

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Relevance in Structured Argumentation

Borg

Straßer

2018

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

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We study properties related to relevance in non-monotonic consequence relations obtained by systems of structured argumentation. Relevance desiderata concern the robustness of a consequence relation under the addition of irrelevant information. For an account of what (ir)relevance amounts to we use syntactic and semantic considerations. Syntactic criteria have been proposed in the domain of relevance logic and were recently used in argumentation theory under the names of non-interference and crashresistance. The basic idea is that the conclusions of a given argumentative theory should be robust under adding information that shares no propositional variables with the original database. Some semantic relevance criteria are known from non-monotonic logic. For instance, cautious monotony states that if we obtain certain conclusions from an argumentation theory, we may expect to still obtain the same conclusions if we add some of them to the given database. In this paper we investigate properties of structured argumentation systems that warrant relevance desiderata.Our attack form is sometimes called premise-attack [20] or directed undercut [6]. In Section 4 we will show that by adjusting · and · adequately we are able to accommodate many other attack forms defined in the literature.Definition 4 (Attack Diagram). Given a setting AF ⊢ (S), its attack diagram is the directed graph with the set of nodes Arg ⊢ (S) and edges between a and b iff a attacks b.Definition 5 (Dung Semantics, [12]). Where AF ⊢ (S) is a setting and A ⊆ Arg ⊢ (S) we define: A is conflict-free iff there are no a, b ∈ A such that a attacks b. A defends a ∈ Arg ⊢ (S) iff for each attacker b ∈ Arg ⊢ (S) of a there is a c ∈ A that attacks b. A is admissible iff it is conflict-free and it defends every a ∈ A. A is complete iff it is admissible and it contains every a ∈ Arg ⊢ (S) it defends. A is preferred iff it is ⊆-maximal complete. A is grounded iff it is ⊆-minimal complete. A is stable iff it is admissible and for all a ∈ Arg ⊢ (S) \ A there is a b ∈ A that attacks a.We denote the set of all admissible [complete, preferred, stable] sets A (also called "extensions") by Adm(AF ⊢ (S)) [Cmp(AF ⊢ (S)), Prf(AF ⊢ (S)), Stb(AF ⊢ (S))] and the grounded set by Grd(AF ⊢ (S)).Definition 6 (Consequence Relations). Where Sem ∈ {Grd, Prf, Stb}, and given a setting AF ⊢ we define:Where the setting AF ⊢ is clear from the context we will simply write |∼ Sem to avoid clutter.Remark 2. For reasons of space we restrict our focus in this paper on skeptical consequence as defined in Definition 6. Note that |∼ AF ⊢ Cmp coincides with |∼ AF ⊢ Grd .3 The Relevance Properties Syntactic RelevanceA syntactical relevance property that has been proposed in the context of structured argumentation is noninterference [9]. Let us call two sets of formulas syntactically disjoint if no atom that occurs in a formula

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Section: Systems Of Structured Argumentationmentioning

confidence: 99%

Section: Semantic Relevancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…A similar property is Basic Relevance [3, Definition 3.1] 2. |∼ is non-trivial if there are always two sets of formulas with the same atoms but different conclusions (see[9]).…”

mentioning

confidence: 99%

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Relevance in Structured Argumentation

Borg

Straßer

2018

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

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“…In a sense this logic models a reasoning process that uses the inference rules of CL in a cautious way akin to the approach advocated by Vickers, though the logic is inconsistency tolerant. Another example is the consequence relations phrased in terms of deductive argumentation frameworks (see Besnard and Hunter 2009;Arieli and Straßer 2014). Underlying is the idea that the (defeasible) reasoning of an agent (e.g.…”

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confidence: 99%