Some comments on history based structures

Abstract History based models, introduced by Parikh and Ramanujam, provide a natural mathematical model of social interactive situations. These models offer a “low level” description of a social situation—describing the situation in terms of events, sequences of events, and the agents‘ view of these events. A multi-agent epistemic temporal modal logic can be used to reason about these structures. A number of other models have been proposed in the literature which can be used as a semantics for such a logical language. Most notably, the interpreted systems discussed by Fagin et al. In this paper, we will discuss the differences and similarities between these two mathematical models. In particular, it is shown that these two semantics are modally equivalent. We will conclude with a discussion of a number of questions that are raised when history based models are used to reason about game-theoretic situations.

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