Merlin Göttlinger

Merlin Humml, Lutz Schröder, Dirk Pattinson

Alternating-time temporal logic (ATL) and its extensions, including the alternating-time $μ$-calculus (AMC), serve the specification of the strategic abilities of coalitions of agents in concurrent game structures. The key ingredient of the logic are path quantifiers specifying that some coalition of agents has a joint strategy to enforce a given goal. This basic setup has been extended to let some of the agents (revocably) commit to using certain named strategies, as in ATL with explicit strategies (ATLES). In the present work, we extend ATLES with fixpoint operators and strategy disjunction, arriving at the alternating-time $μ$-calculus with disjunctive explicit strategies (AMCDES), which allows for a more flexible formulation of temporal properties (e.g. fairness) and, through strategy disjunction, a form of controlled nondeterminism in commitments. Our main result is an ExpTime upper bound for satisfiability checking (which is thus ExpTime-complete). We also prove upper bounds QP (quasipolynomial time) and NP $\cap$ coNP for model checking under fixed interpretations of explicit strategies, and NP under open interpretation. Our key technical tool is a treatment of the AMCDES within the generic framework of coalgebraic logic, which in particular reduces the analysis of most reasoning tasks to the treatment of a very simple one-step logic featuring only propositional operators and next-step operators without nesting; we give a new model construction principle for this one-step logic that relies on a set-valued variant of first-order resolution.

Merlin Göttlinger, Lutz Schröder

The Aristotelian trichotomy distinguishes three aspects of argumentation: Logos, Ethos, and Pathos. Even rich argumentation representations like the Argument Interchange Format (AIF) are only concerned with capturing the Logos aspect. Inference Anchoring Theory (IAT) adds the possibility to represent ethical requirements on the illocutionary force edges linking locutions to illocutions, thereby allowing to capture some aspects of ethos. With the recent extensions AIF+ and Social Argument Interchange Format (S-AIF), which embed dialogue and speakers into the AIF argumentation representation, the basis for representing all three aspects identified by Aristotle was formed. In the present work, we develop the Trichotomic Argument Interchange Format (T-AIF), building on the idea from S-AIF of adding the speakers to the argumentation graph. We capture Logos in the usual known from AIF+, Ethos in form of weighted edges between actors representing trust, and Pathos via weighted edges from actors to illocutions representing their level of commitment to the propositions. This extended structured argumentation representation opens up new possibilities of defining semantic properties on this rich graph in order to characterize and profile the reasoning patterns of the participating actors.