18 research outputs found
Perfect IFG-formulas
IFG logic is a variant of the independence-friendly logic of Hintikka and
Sandu. We answer the question: ``Which IFG-formulas are equivalent to ordinary
first-order formulas?'' We use the answer to show that the ordinary cylindric
set algebra over a structure can be embedded into a reduct of the IFG-cylindric
set algebra over the structure.Comment: 7 pages. Submitted to Logica Universalis. See also
http://math.colgate.edu/~amann
The Doxastic Interpretation of Team Semantics
We advance a doxastic interpretation for many of the logical connectives
considered in Dependence Logic and in its extensions, and we argue that Team
Semantics is a natural framework for reasoning about beliefs and belief
updates
Characterizing downwards closed, strongly first order, relativizable dependencies
In Team Semantics, a dependency notion is strongly first order if every
sentence of the logic obtained by adding the corresponding atoms to First Order
Logic is equivalent to some first order sentence. In this work it is shown that
all nontrivial dependency atoms that are strongly first order, downwards
closed, and relativizable (in the sense that the relativizations of the
corresponding atoms with respect to some unary predicate are expressible in
terms of them) are definable in terms of constancy atoms.
Additionally, it is shown that any strongly first order dependency is safe
for any family of downwards closed dependencies, in the sense that every
sentence of the logic obtained by adding to First Order Logic both the strongly
first order dependency and the downwards closed dependencies is equivalent to
some sentence of the logic obtained by adding only the downwards closed
dependencies
Independence-friendly cylindric set algebras
Independence-friendly logic is a conservative extension of first-order logic
that has the same expressive power as existential second-order logic. In her
Ph.D. thesis, Dechesne introduces a variant of independence-friendly logic
called IFG logic. We attempt to algebraize IFG logic in the same way that
Boolean algebra is the algebra of propositional logic and cylindric algebra is
the algebra of first-order logic.
We define independence-friendly cylindric set algebras and prove two main
results. First, every independence-friendly cylindric set algebra over a
structure has an underlying Kleene algebra. Moreover, the class of such
underlying Kleene algebras generates the variety of all Kleene algebras. Hence
the equational theory of the class of Kleene algebras that underly an
independence-friendly cylindric set algebra is finitely axiomatizable. Second,
every one-dimensional independence-friendly cylindric set algebra over a
structure has an underlying monadic Kleene algebra. However, the class of such
underlying monadic Kleene algebras does not generate the variety of all monadic
Kleene algebras. Finally, we offer a conjecture about which subvariety of
monadic Kleene algebras the class of such monadic Kleene algebras does
generate.Comment: 42 pages. Submitted to the Logic Journal of the IGPL. See also
http://math.colgate.edu/~amann
Inclusion and Exclusion Dependencies in Team Semantics: On Some Logics of Imperfect Information
We introduce some new logics of imperfect information by adding atomic
formulas corresponding to inclusion and exclusion dependencies to the language
of first order logic. The properties of these logics and their relationships
with other logics of imperfect information are then studied. Furthermore, a
game theoretic semantics for these logics is developed. As a corollary of these
results, we characterize the expressive power of independence logic, thus
answering an open problem posed in (Gr\"adel and V\"a\"an\"anen, 2010)