Team semantics and dependence logic
In the traditional so-called Tarski’s Truth Definition the semantics of first order logic is defined with respect to an assignment of values to the free variables.  A richer family of semantic concepts can be modelled if semantics is defined with respect to a set (a ""team"") of such assignments. This is what is called team semantics, a term coined by the PI in his 2007 monograph, and used ever since to describe this highly non-trivial modification of Tarskian semantics. Team semantics was introduced around the same time in inquisitive logic under the name state semantics. Examples of semantic concepts available in team semantics but not in traditional Tarski semantics are the concepts of dependence and independence. The PI introduced what he called dependence logic around these concepts. It appears that teams appear naturally in several areas of sciences and humanities which has made it possible to apply dependence logic and its variants to these areas. Now is the right moment to move from dependence logic to a broader explication of team semantics. This is what the TEAMDEP project proposes to do. In the TEAMDEP project we take team semantics to a new level by focusing on its hard axiomatizability questions and to its applications to the foundations of quantum mechanics and to the multiverse of set theory.