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The act of persuasion, a key component in rhetoric argumentation, may be viewed as a dynamics modifier. We extend Dung's frameworks with acts of persuasion among agents, and consider interactions among attack, persuasion and defence that have been largely unheeded so far. We characterise basic notions of admissibilities in this framework, and show a way of enriching them through, effectively, CTL (computation tree logic) encoding, which also permits importation of the theoretical results known to the logic into our argumentation frameworks. Our aim is to complement the growing interest in coordination of static and dynamic argumentation.

Abstract. We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b, 4, and 5. This includes the constructive variants of the standard modal logics K4, S4, and S5. We use for our presentation the formalism of nested sequents and give a syntactic proof of cut elimination.

Cut elimination in sequent calculus is indispensable in bounding the number of distinct formulas to appear during a backward proof search. A usual approach to prove cut admissibility is permutation of derivation trees. Extra care must be taken, however, when contraction appears as an explicit inference rule. In G1i for example, a simple-minded permutation strategy comes short around contraction interacting directly with cut formulas, which entails irreducibility of the derivation height of Cut instances. One of the practices employed to overcome this issue is the use of MultiCut (the "mix" rule) which takes into account the effect of contraction within. A more recent substructural logic BI inherits the characteristics of the intuitionistic logic but also those of multiplicative linear logic (without exponentials). Following Pym's original work, the cut admissibility in LBI (the original BI sequent calculus) is supposed to hold with the same tweak. However, there is a critical issue in the approach: MultiCut does not take care of the effect of structural contraction that LBI permits. In this paper, we show a proper proof of the LBI cut admissibility based on another derivable rule BI-MultiCut.

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