Games and spacessemantics of a modal probabilistic logic

Resumo

In this work we make a study of the different semantics for a modal probabilistic system. In the first part of the work, we compare two model-based semantics: relational and neighbourhood semantics. Nearly all the works in the field of probabilistic modal logic fall within the first label. We defend that neighbourhood semantics is more suitable for probabilistic modal logic, particularly for subjective probability logic. The main reasons of this are the following: - Neighbourhood semantics allows to distinguish between lack of probabilistic belief and the complementary probabilistic belief in the opposite proposition. - In neighbourhood semantics we can equate the composition of the doxastic and the probabilistic operator with the subjective probabilistic operator. - Relational models can be seen as isomorphic to a certain subset of neighbourhood models. - It is more adequate for future developments. For example, non-standard probabilistic believers or situations in which we distinguish between explicit and implicit belieg. In the second part of the work we choose to develop two dynamical semantics. We develop variations of dialogical games and semantic tableaux for probability modal logic for the probabilistic modal operator, establishing the corresponding rules for dealing with probabilies. We find the following remarkable results: • Being a non-normal modal operator, we can extablish a connection between the model-theoretical semantics for probability and the rules for our dynamical systems. • There is a connection between probabilistic semantic tableaux and dialogical games, so they can be seen in parallel.