Logics with Multiteam Semantics

Team semantics is the mathematical basis of modern logics dependence and independence. In contrast to classical Tarski semantics, a formula evaluated not for single assignment values free variables, but on set such assignments, called team. appropriate purely logical understanding dependency notions, where only presence or absence data matters, being based sets, it does take into account multiple occurrences values. It therefore insufficient in scenarios multiplicities matter, particular reasoning about probabilities statistical independencies. Therefore, an extension from teams multiteams (i.e. multisets assignments) has been proposed by several authors. this paper we aim at systematic development independence multiteam semantics. We study atomic properties finite discuss meaning operators extend dependencies full-fledged setting. explore expressive power wide spectrum different compare them second-order logic with team many cases results resemble what known there are also interesting differences. While combination inclusion exclusion leads full both existential logic, definable any that downwards closed union thus strictly more powerful than inclusion-exclusion logic. relationship specific class metafinite structures. turns out can be characterised precise sense Presburger fragment capturing independence, need go beyond add some form multiplication. Finally, consider weights reals formulae means topological properties.