The Handling of Loops in Talmudic Logic, with Application to Odd and Even Loops in Argumentation

Abraham, Michaël; Gabbay, Dov M.; Schild, Uri J.

doi:10.29007/gkg6

Cited by 6 publications

(15 citation statements)

References 16 publications

(26 reference statements)

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“…σ (F ≡ σ s G) coincides with syntactic equivalence, i.e. F = G. 1 The result as stated here requires A(F ) = A(G), since we do not impose any prerequisites on the given semantics σ. However, in case A(F ) = A(G) implies F ≡ σ s G (as it is the case for all semantics studied in terms of strong equivalence so far, see also Lemma 5.3), the result is even stronger saying that succinctness holds, if and only if, strong and syntactic equivalence coincide.…”

Section: Lemma 54 For Any Afsmentioning

confidence: 85%

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The cf2 argumentation semantics revisited

Gaggl¹,

Woltran²

2012

Journal of Logic and Computation

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Abstract.Abstract argumentation frameworks nowadays provide the most popular formalization of argumentation on a conceptual level. Numerous semantics for this paradigm have been proposed, whereby the cf2 semantics has shown to solve particular problems concerned with odd-length cycles in such frameworks. Due to the complicated definition of this semantics it has somehow been neglected in the literature. In this article, we introduce an alternative characterization of the cf2 semantics which, roughly speaking, avoids the recursive computation of sub-frameworks. This facilitates further investigation steps, like a complete complexity analysis. Furthermore, we show how the notion of strong equivalence can be characterized in terms of the cf2 semantics. In contrast to other semantics, it turns out that for the cf2 semantics strong equivalence coincides with syntactical equivalence. We make this particular behavior more explicit by defining a new property for argumentation semantics, called the succinctness property. If a semantics σ satisfies the succinctness property, then for every framework F , all its attacks contribute to the evaluation of at least one framework F containing F . We finally characterize strong equivalence also for the stage and the naive semantics. Together with known results these characterizations imply that none of the prominent semantics for abstract argumentation, except the cf2 semantics, satisfies the succinctness property.

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Section: Lemma 54 For Any Afsmentioning

confidence: 85%

“…1 Theorem 5.8 An argumentation semantics σ satisfies the succinctness property iff for any AFs F , G with A(F ) = A(G) it holds that strong equivalence between F and G wrt. σ (F ≡ σ s G) coincides with syntactic equivalence, i.e.…”

Section: Lemma 54 For Any Afsmentioning

confidence: 99%

The cf2 argumentation semantics revisited

Gaggl¹,

Woltran²

2012

Journal of Logic and Computation

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“…This paper offers a time stamping model, where each argument is time stamped when it is available. The model is similar but not the same as the ones used in Abraham et al (2011a) and Barringer et al (2005). In all cases, the change is in the meta-level.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…In Barringer et al (2005), the change in time was of strength of argument and this can influence the argument's attack capabilities and (Abraham et al 2011a) the time stamping was used to resolve loops.…”

Section: Introduction and Orientationmentioning

confidence: 99%

Modal and temporal argumentation networks

Barringer

Gabbay

Woods³

2012

Argument & Computation

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The traditional Dung networks depict arguments as atomic and study the relationships of attack between them. This can be generalised in two ways. One is to consider various forms of attack, support, feedback, etc. Another is to add content to nodes and put there not just atomic arguments but more structure, e.g. proofs in some logic or simply just formulas from a richer language. This paper offers to use temporal and modal language formulas to represent arguments in the nodes of a network. The suitable semantics for such networks is Kripke semantics. We also introduce a new key concept of usability of an argument. This is the beginning of a continuing research for adding contents to the nodes of an argumentation network. This research will allow us to address notions like 'what does it exactly mean for a node to attack another' or 'what does it mean for a network to be consistent' or 'can we give proper proof rules to manipulate networks', and more.

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“…The Shkop principle says that she cannot take the action. See our paper (Abraham et al 2012) about the Shkop principle.…”

Section: Comparison With the Literaturementioning

confidence: 96%

Contrary to time conditionals in Talmudic logic

2012

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We consider conditionals of the form A ) B where A depends on the future and B on the present and past. We examine models for such conditional arising in Talmudic legal cases. We call such conditionals contrary to time conditionals.Three main aspects will be investigated:1. Inverse causality from future to past, where a future condition can influence a legal event in the past (this is a man made causality). 2. Comparison with similar features in modern law. 3. New types of temporal logics arising from modelling the Talmudic examples.We shall see that we need a new temporal logic,which we call Talmudic temporal logic with linear open advancing future and parallel changing past, based on two parameters for time.

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The Handling of Loops in Talmudic Logic, with Application to Odd and Even Loops in Argumentation

Cited by 6 publications

References 16 publications

The cf2 argumentation semantics revisited

The cf2 argumentation semantics revisited

Modal and temporal argumentation networks

Contrary to time conditionals in Talmudic logic

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