Title: Capturing Dual Properties in Propositional Team Semantics

Speaker: Matilda Häggblom (University of Helsinki)

Time: Apr. 7th (Tuesday), 15:10 - 18:00

Location: Room 314, Teaching Building No.2 (北京大学第二教学楼314)

Abstract:

In team semantics, we evaluate formulas with respect to a team—a set of assignments—as opposed to a single assignment. This makes it possible to meaningfully evaluate dependencies between variables, such as functional dependency: whether or not the value of variable y depends on the value of variable x. 

Propositional logic with team semantics has three core closure properties: downward closure, union closure, and the empty team property. These three properties have been studied extensively in propositional team semantics. We expand this picture by considering their duals: upward closure (if a formula is satisfied by a team, it is satisfied by all its superteams), intersection closure (whenever two teams satisfy a formula, so does their intersection), and the full team property (the maximal team satisfies all formulas). 

We introduce expressively complete logics for various combinations of these properties, such that the set-theoretical duality is reflected in the syntax and normal forms of the logics. Our two main tools are to modify the semantic clause of the disjunction and to use formulas that capture inclusion dependencies. In the process, we find some curious aspects of the logics. This includes connections to might and must modalities, and the subtle role of the empty/full team property when defining suitable semantic clauses for the disjunction.