Raciocínios sob incerteza: combinando lógica epistêmica e probabilidade

Abstract

In the usual epistemic logic it is possible to represent the agents' knowledge. However, it is not possible to represent the cases in which the agents cannot assert something with certainty, but have good reasons to accept certain propositions to the detriment of others. To increase the range of language in this sense, it is necessary to enrich the epistemic logic with probability. With probability, in epistemic logics it will be possible to assign a numerical value (or another qualitative element) to sets of worlds, creating, in turn, a kind of authority among the propositions. From this ordering, even in uncertain conditions, making more rational choices and representing them is possible. This conjugation between two types of logic guarantees language an expanded capacity to deal with reflection in a deductive way (richer and more expressive formalism). This research aims to analyze and show how features of epistemic logic and probability can be associated with representing reasonings under uncertainty. For that, an investigation is made into the epistemic logic (syntax, semantics and limits in the reach of the representation). In addition, it explores the relationship between the concepts of probability and epistemic uncertainty. Finally, we discuss how the combination between epistemic logic and probability has been made by Joseph Halpern in his Reasoning about uncertainty (2003). The methodology used here is the usual bibliographical research in the relevant literature.