Abstracts.202X.TS

Team semantics for dependence logic

by TBD

Abstract

TBD

Notes

• The partially ordered/branching/Henkin quantifier

  ( ∀x ∃y ∀u ∃v ) φ ( x , y , u , v , z‾ ) ⟺ ∃f ∃g ∀x ∀u φ ( x , f ( x ) , u , g ( u ) , z‾ )

  can be expressed using a dependence atom as

  ( ∀x ∃y ∀u ∃v ) φ ( x , y , u , v , z‾ ) ⟺ ∀x ∃y ∀u ∃v ( = ( z‾ , u , v ) ∧ φ ( x , f ( x ) , u , g ( u ) , z‾ ) )

• Dependence logic has the same expressive power as existential second order logic.

References

1. Jouko Väänänen. 2007. Dependence Logic — A New Approach to Independence Friendly Logic.
2. Leon Henkin. 1961. Some Remarks on Infinitely Long Formulas.
3. Juha Kontinen and Jouko Väänänen. 2009. On Definability in Dependence Logic.