When I was working on the model of argumentation referred to above, Tony Hunter and Philippe Besnard started to look at paraconsistent logics. But these typically end up supporting conclusions that are somewhat counter intuitive. So they moved towards the preferred solution in the argumentation community of working with consistent subsets as the basis for an argument.
In the case where we have on un-attacked argument for A and another against A then it is hard (not possible?) to find a rational way of preferring one or other outcome. Most models of argumentation allow a mechanism of undercutting, where a further argument can contradict a proposition in the support of an argument. That in turn can be attacked ...
So without any notion of weighting of propositions, one is able to give a notion of preference of conclusions on the basis of preferring arguments where all their defeaters can themselves be attacked.
In cases where ordinal or cardinal weights are allowed, then finer grained preferences can be supported.
Going back to an earlier part of the discussion - it is possible to allow reinforcement between arguments if weights are supported. But you do need to account for any dependencies between the arguments (so there is no double counting). Our "probabilistic valuation" did just this (see section 5.3 of the paper Alexandros cited). In cases where you are unsure of the relationship between sources of evidence, the possibilistic approach of just weighting support for a proposition by its strongest argument (use of "max" for aggregating strengths of arguments) is appropriately cautious.

When I was working on the model of argumentation referred to above, Tony Hunter and Philippe Besnard started to look at paraconsistent logics. But these typically end up supporting conclusions that are somewhat counter intuitive. So they moved towards the preferred solution in the argumentation community of working with consistent subsets as the basis for an argument. In the case where we have on un-attacked argument for A and another against A then it is hard (not possible?) to find a rational way of preferring one or other outcome. Most models of argumentation allow a mechanism of undercutting, where a further argument can contradict a proposition in the support of an argument. That in turn can be attacked ... So without any notion of weighting of propositions, one is able to give a notion of preference of conclusions on the basis of preferring arguments where all their defeaters can themselves be attacked. In cases where ordinal or cardinal weights are allowed, then finer grained preferences can be supported. Going back to an earlier part of the discussion - it is possible to allow reinforcement between arguments if weights are supported. But you do need to account for any dependencies between the arguments (so there is no double counting). Our "probabilistic valuation" did just this (see section 5.3 of the paper Alexandros cited). In cases where you are unsure of the relationship between sources of evidence, the possibilistic approach of just weighting support for a proposition by its strongest argument (use of "max" for aggregating strengths of arguments) is appropriately cautious.