267 research outputs found
Team Semantics and Recursive Enumerability
It is well known that dependence logic captures the complexity class NP, and
it has recently been shown that inclusion logic captures P on ordered models.
These results demonstrate that team semantics offers interesting new
possibilities for descriptive complexity theory. In order to properly
understand the connection between team semantics and descriptive complexity, we
introduce an extension D* of dependence logic that can define exactly all
recursively enumerable classes of finite models. Thus D* provides an approach
to computation alternative to Turing machines. The essential novel feature in
D* is an operator that can extend the domain of the considered model by a
finite number of fresh elements. Due to the close relationship between
generalized quantifiers and oracles, we also investigate generalized
quantifiers in team semantics. We show that monotone quantifiers of type (1)
can be canonically eliminated from quantifier extensions of first-order logic
by introducing corresponding generalized dependence atoms
Upwards Closed Dependencies in Team Semantics
We prove that adding upwards closed first-order dependency atoms to
first-order logic with team semantics does not increase its expressive power
(with respect to sentences), and that the same remains true if we also add
constancy atoms. As a consequence, the negations of functional dependence,
conditional independence, inclusion and exclusion atoms can all be added to
first-order logic without increasing its expressive power.
Furthermore, we define a class of bounded upwards closed dependencies and we
prove that unbounded dependencies cannot be defined in terms of bounded ones.Comment: In Proceedings GandALF 2013, arXiv:1307.416
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
Decidability of predicate logics with team semantics
We study the complexity of predicate logics based on team semantics. We show
that the satisfiability problems of two-variable independence logic and
inclusion logic are both NEXPTIME-complete. Furthermore, we show that the
validity problem of two-variable dependence logic is undecidable, thereby
solving an open problem from the team semantics literature. We also briefly
analyse the complexity of the Bernays-Sch\"onfinkel-Ramsey prefix classes of
dependence logic.Comment: Extended version of a MFCS 2016 article. Changes on the earlier arXiv
version: title changed, added the result on validity of two-variable
dependence logic, restructurin
Probabilistic Team Semantics
Team semantics is a semantical framework for the study of dependence and independence concepts ubiquitous in many areas such as databases and statistics. In recent works team semantics has been generalised to accommodate also multisets and probabilistic dependencies. In this article we study a variant of probabilistic team semantics and relate this framework to a Tarskian two-sorted logic. We also show that very simple quantifier-free formulae of our logic give rise to backslashmathrm NP NP -hard model checking problems.Peer reviewe
Continuous Team Semantics
Peer reviewe
Continuous Team Semantics
We study logics with team semantics in computable metric spaces. We show how to define approximate versions of the usual independence/dependence atoms. For restricted classes of formulae, we show that we can assume w.l.o.g.~that teams are closed sets. This then allows us to import techniques from computable analysis to study the complexity of formula satisfaction and model checking
Continuous Team Semantics
We study logics with team semantics in computable metric spaces. We show how to define approximate versions of the usual independence/dependence atoms. For restricted classes of formulae, we show that we can assume w.l.o.g.~that teams are closed sets. This then allows us to import techniques from computable analysis to study the complexity of formula satisfaction and model checking
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