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We investigate fragments of intuitionistic propositional logic containing implication but not disjunction. These fragments are finite, but their size grows superexponentially with the number of generators. Exact models are used to characterize the fragments.

This article ~s a report on research m progress into the structure of fimte diagrams of mtuinomst~c proposmonal logic with the aid of automated reasoning systems for larger calculanons. A/ragment of a proposmonal logic is the set of formulae built up from a fimte number of proposinonal variables by means of a number of connectives of the logic, among which possibly non-standard ones like ~ or ~ which are stud~ed here. The dtagram of that fragment ~s the set of eqmvalence classes of its formulae parnally ordered by the derivability relation. N.G. de Brmjn's concept of exact model has been used to construct subdlagrams of the [p, q, A, ~, ~]-fragment.

We present DIAL, a model of group dynamics and opinion dynamics. It features dialogues, in which agents gamble about reputation points. Intra-group radicalisation of opinions appears to be an emergent phenomenon. We position this model within the theoretical literature on opinion dynamics and social influence. Moreover, we investigate the effect of argumentation on group structure by simulation experiments. We compare runs of the model with varying influence of the outcome of debates on the reputation of the agents.

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