1,940 research outputs found
Defining a Double Team Semantics for Generalized Quantifiers
In this brief technical report we sketch a semantics for fi rst-order logic with generalized quantifiers based on double teams. We also define the notion of a generalized atom. Such atoms can be used in order to define extensions of first-order logic with a team-based semantics. We then briefly discuss how our double team semantics relates to game semantics based approaches to extensions of first-order logic with generalized quantifiers
Defining a Double Team Semantics for Generalized Quantifiers
In this brief technical report we sketch a semantics for fi rst-order logic with generalized quantifiers based on double teams. We also define the notion of a generalized atom. Such atoms can be used in order to define extensions of first-order logic with a team-based semantics. We then briefly discuss how our double team semantics relates to game semantics based approaches to extensions of first-order logic with generalized quantifiers
Defining a Double Team Semantics for Generalized Quantifiers (Extended Version)
In this brief technical report we sketch a semantics for first-order logic with generalized quantifi ers based on double teams. We also defi ne the notion of a generalized atom. Such atoms can be used in order to defi ne extensions of first-order logic with a team-based semantics. We then briefly discuss how our double team semantics relates to game semantics based approaches to extensions of fi rst-order logic with generalized quantifi ers
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
Some Turing-Complete Extensions of First-Order Logic
We introduce a natural Turing-complete extension of first-order logic FO. The
extension adds two novel features to FO. The first one of these is the capacity
to add new points to models and new tuples to relations. The second one is the
possibility of recursive looping when a formula is evaluated using a semantic
game. We first define a game-theoretic semantics for the logic and then prove
that the expressive power of the logic corresponds in a canonical way to the
recognition capacity of Turing machines. Finally, we show how to incorporate
generalized quantifiers into the logic and argue for a highly natural
connection between oracles and generalized quantifiers.Comment: In Proceedings GandALF 2014, arXiv:1408.556
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
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