Speaker: Fan Yang (Utrecht University)
Date and Time: Thursday, December 15th 2022, 16:30-18:00
Venue: ILLC seminar room F1.15 in Science Park 107 and online.
Title: Generalizing propositional team semantics
Abstract. In this talk, we discuss a generalization of the standard team semantics in the propositional logic context. Team semantics was introduced by Hodges (1997) and later advanced by Väänänen (2007) in dependence logic. Propositional dependence logic (studied in (Yang & Väänänen 2016)) is an extension of (classical) propositional logic with a new type of atomic formulas, called dependence atoms, to express the (functional) dependencies between propositions. The key idea of team semantics is that such dependency properties can only make sense in multitudes. A formula in such a logic is thus evaluated on a set of valuations or possible worlds (called teams). Dependence atoms correspond exactly to functional dependencies studied in database theory; in particular, these atoms satisfy Armstrong’s Axioms (1974), which completely axiomatize the implication problem of functional dependencies. The same type of team semantics was also independently adopted in inquisitive logic (Ciardelli & Roelofsen 2011).
Essentially, team semantics is defined over an underlying powerset (Kripke) frame of the teams, which also forms a bounded join-semilattice. Several authors ((Puncochar 2016 & 2017),(Holliday 2020),(Dmitrieva 2021),(Bezhanishvili & Yang 2022)) have recently defined different generalizations of the standard team semantics by modifying this powerset structure from different perspectives. In this talk, we propose a new definition of team semantics that tries to combine the approaches of (Puncochar 2017),(Dmitrieva 2021),(Bezhanishvili & Yang 2022) and also preserve the key original idea of Hodges (1997). We define a team (Kripke) frame simply as an arbitrary bounded join-semilattice satisfying certain conditions. The semantics for connectives and constants are generalized in a natural manner. The dependence atoms in this generalized setting still satisfy Armstrong’s Axioms of functional dependencies.