3,534 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
Characterizing Quantifier Extensions of Dependence Logic
We characterize the expressive power of extensions of Dependence Logic and
Independence Logic by monotone generalized quantifiers in terms of quantifier
extensions of existential second-order logic.Comment: 9 page
A Simple Logic of Functional Dependence
This paper presents a simple decidable logic of functional dependence LFD,
based on an extension of classical propositional logic with dependence atoms
plus dependence quantifiers treated as modalities, within the setting of
generalized assignment semantics for first order logic. The expressive
strength, complete proof calculus and meta-properties of LFD are explored.
Various language extensions are presented as well, up to undecidable
modal-style logics for independence and dynamic logics of changing dependence
models. Finally, more concrete settings for dependence are discussed:
continuous dependence in topological models, linear dependence in vector
spaces, and temporal dependence in dynamical systems and games.Comment: 56 pages. Journal of Philosophical Logic (2021
Dependence Logic with Generalized Quantifiers: Axiomatizations
We prove two completeness results, one for the extension of dependence logic
by a monotone generalized quantifier Q with weak interpretation, weak in the
meaning that the interpretation of Q varies with the structures. The second
result considers the extension of dependence logic where Q is interpreted as
"there exists uncountable many." Both of the axiomatizations are shown to be
sound and complete for FO(Q) consequences.Comment: 17 page
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
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
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
A Fragment of Dependence Logic Capturing Polynomial Time
In this paper we study the expressive power of Horn-formulae in dependence
logic and show that they can express NP-complete problems. Therefore we define
an even smaller fragment D-Horn* and show that over finite successor structures
it captures the complexity class P of all sets decidable in polynomial time.
Furthermore we study the question which of our results can ge generalized to
the case of open formulae of D-Horn* and so-called downwards monotone
polynomial time properties of teams
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