In this thesis (modal) dependence logic is investigated. It was introduced in
2007 by Jouko V\"a\"aan\"anen as an extension of first-order (resp. modal)
logic by the dependence operator =(). For first-order (resp. propositional)
variables x_1,...,x_n, =(x_1,...,x_n) intuitively states that the value of x_n
is determined by those of x_1,...,x_n-1.
We consider fragments of modal dependence logic obtained by restricting the
set of allowed modal and propositional connectives. We classify these fragments
with respect to the complexity of their satisfiability and model-checking
problems. For satisfiability we obtain complexity degrees from P over NP,
Sigma_P^2 and PSPACE up to NEXP, while for model-checking we only classify the
fragments with respect to their tractability, i.e. we either show
NP-completeness or containment in P.
We then study the extension of modal dependence logic by intuitionistic
implication. For this extension we again classify the complexity of the
model-checking problem for its fragments. Here we obtain complexity degrees
from P over NP and coNP up to PSPACE.
Finally, we analyze first-order dependence logic, independence-friendly logic
and their two-variable fragments. We prove that satisfiability for two-variable
dependence logic is NEXP-complete, whereas for two-variable
independence-friendly logic it is undecidable; and use this to prove that the
latter is also more expressive than the former.Comment: PhD thesis; 138 pages (110 main matter
