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Hierarchies in independence logic ∗
"... We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the socalled lax semantics for these logics, we relate these fragments of inclusion ..."
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We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the socalled lax semantics for these logics, we relate these fragments of inclusion and independence logic to familiar sublogics of existential secondorder logic. We also show that, with respect to the stronger strict semantics, inclusion logic is equivalent to existential secondorder logic.
Expressivity and Complexity of Dependence Logic
"... In this article we review recent results on expressivity and complexity of firstorder, modal, and propositional dependence logic and some of its variants like independence and inclusion logic. Dependence logic was introduced by Jouko Väänänen in [51]. On the syntactic side, it extends usual firs ..."
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In this article we review recent results on expressivity and complexity of firstorder, modal, and propositional dependence logic and some of its variants like independence and inclusion logic. Dependence logic was introduced by Jouko Väänänen in [51]. On the syntactic side, it extends usual firstorder logic by so
from the Jenny and Antti Wihuri Foundation.
, 2015
"... © The Author(s) 2015. This article is published with open access at Springerlink.com Abstract We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants ..."
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© The Author(s) 2015. This article is published with open access at Springerlink.com Abstract We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants of dependence logic, possibly extended with generalized quantifiers and generalized atoms, under the same umbrella framework. The semantics is based on pairs of teams, or double teams. We also devise a gametheoretic semantics equivalent to the double team semantics. We make use of the double team semantics by defining a logic DC2 which canonically fuses together twovariable dependence logic D2 and twovariable logic with counting quantifiers FOC2. We establish that the satisfiability and finite satisfiability problems of DC2 are complete for NEXPTIME.
Relating paths in transition systems: the fall of the modal mucalculus?
"... Abstract. We revisit Janin and Walukiewicz’s classic result on the expressive completeness of the modal mucalculus w.r.t. MSO, when transition systems are equipped with a binary relation over paths. We obtain two natural extensions of MSO and the mucalculus: MSO with path relation and the jumping ..."
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Abstract. We revisit Janin and Walukiewicz’s classic result on the expressive completeness of the modal mucalculus w.r.t. MSO, when transition systems are equipped with a binary relation over paths. We obtain two natural extensions of MSO and the mucalculus: MSO with path relation and the jumping mucalculus. While “boundedmemory ” binary relations bring about no extra expressivity to either of the two logics, “unboundedmemory ” binary relations make the bisimulationinvariant fragment of MSO with path relation more expressive than the jumping mucalculus: the existence of winning strategies in games with imperfectinformation inhabits the gap. 1
On Extensions and Variants of Dependence Logic — A study of intuitionistic connectives in the team semantics setting
"... To be presented for public examination ..."
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