As a by-product, complexity results for several existing merging operators are derived as well.
Several merging operators are presented, which are based on different formalizations of this background knowledge, ranging from purely qualitative approaches, related to possibilistic logic, to quantitative approaches with a probabilistic flavor.
A model-theoretic characterization of the postulates and specific merging operators are given in Lin and Mendelzon (1999).
In general, merging operators are not strategy-proof when Hamming distance is used, whereas they are strategy-proof when the drastic distance is employed.
This postulate expresses a principle already imposed on belief revision operators (of which, as we shall see, merging operators are extensions), that is, the principle of irrelevance of syntax, which says that the result of a merging operator depends only on the semantical content of the merged bases and not on their syntactical expression.
In particular, merging operators can be seen as a generalization of revision operators (Konieczny and Pino Pérez 2002).
Grégoire and Konieczny (2006) go further and claim that belief merging operators can be used to aggregate other types of information than knowledge and beliefs, such as goals, observations, and norms.
In those situations in which we can assume that there is a fact of the matter (for example, a defendant has—or has not committed a murder), which each agent has a (noisy) opinion about, the truth-tracking properties of belief merging operators can be investigated (Hartmann et al. 2010; Hartmann and Sprenger 2012; Cevolani 2014).
Both syntactic and semantic characterizations are provided for each merging operator, and the computational complexity is analyzed.
