948 research outputs found
Satisfiability for relation-changing logics
Relation-changing modal logics (RC for short) are extensions of the basic modal logic with dynamic operators that modify the accessibility relation of a model during the evaluation of a formula. These languages are equipped with dynamic modalities that are able e.g. to delete, add and swap edges in the model, both locally and globally. We study the satisfiability problem for some of these logics.We first show that they can be translated into hybrid logic. As a result, we can transfer some results from hybrid logics to RC. We discuss in particular decidability for some fragments. We then show that satisfiability is, in general, undecidable for all the languages introduced, via translations from memory logics.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; ArgentinaFil: Fervari, Raul Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; ArgentinaFil: Hoffmann, Guillaume Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Martel, Mauricio. Universitat Bremen; Alemani
Relation-Changing Logics as Fragments of Hybrid Logics
Relation-changing modal logics are extensions of the basic modal logic that
allow changes to the accessibility relation of a model during the evaluation of
a formula. In particular, they are equipped with dynamic modalities that are
able to delete, add, and swap edges in the model, both locally and globally. We
provide translations from these logics to hybrid logic along with an
implementation. In general, these logics are undecidable, but we use our
translations to identify decidable fragments. We also compare the expressive
power of relation-changing modal logics with hybrid logics.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
A decidable weakening of Compass Logic based on cone-shaped cardinal directions
We introduce a modal logic, called Cone Logic, whose formulas describe
properties of points in the plane and spatial relationships between them.
Points are labelled by proposition letters and spatial relations are induced by
the four cone-shaped cardinal directions. Cone Logic can be seen as a weakening
of Venema's Compass Logic. We prove that, unlike Compass Logic and other
projection-based spatial logics, its satisfiability problem is decidable
(precisely, PSPACE-complete). We also show that it is expressive enough to
capture meaningful interval temporal logics - in particular, the interval
temporal logic of Allen's relations "Begins", "During", and "Later", and their
transposes
On the uniform one-dimensional fragment
The uniform one-dimensional fragment of first-order logic, U1, is a recently
introduced formalism that extends two-variable logic in a natural way to
contexts with relations of all arities. We survey properties of U1 and
investigate its relationship to description logics designed to accommodate
higher arity relations, with particular attention given to DLR_reg. We also
define a description logic version of a variant of U1 and prove a range of new
results concerning the expressivity of U1 and related logics
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
Separability in the Ambient Logic
The \it{Ambient Logic} (AL) has been proposed for expressing properties of
process mobility in the calculus of Mobile Ambients (MA), and as a basis for
query languages on semistructured data. We study some basic questions
concerning the discriminating power of AL, focusing on the equivalence on
processes induced by the logic . As underlying calculi besides MA we
consider a subcalculus in which an image-finiteness condition holds and that we
prove to be Turing complete. Synchronous variants of these calculi are studied
as well. In these calculi, we provide two operational characterisations of
: a coinductive one (as a form of bisimilarity) and an inductive one
(based on structual properties of processes). After showing to be stricly
finer than barbed congruence, we establish axiomatisations of on the
subcalculus of MA (both the asynchronous and the synchronous version), enabling
us to relate to structural congruence. We also present some
(un)decidability results that are related to the above separation properties
for AL: the undecidability of on MA and its decidability on the
subcalculus.Comment: logical methods in computer science, 44 page
To Be Announced
In this survey we review dynamic epistemic logics with modalities for
quantification over information change. Of such logics we present complete
axiomatizations, focussing on axioms involving the interaction between
knowledge and such quantifiers, we report on their relative expressivity, on
decidability and on the complexity of model checking and satisfiability, and on
applications. We focus on open problems and new directions for research
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