16,448 research outputs found
Limitations of the Program Memory and the Expressive Power of Dynamic Logics
AbstractFor a dynamic logic L we study dynamic logics Ln for which programs allowed in formulas cannot use more than n variables. We prove that there exists a structure A of a finite signature such that for a wide class of dynamic logics L and for every natural number n the logic Ln+1 is more expressive over A than Ln. This result is based on a construction of some canonical form for the formulas of Ln over a free one-generated groupoid
The Modal Logic of Stepwise Removal
We investigate the modal logic of stepwise removal of objects, both for its
intrinsic interest as a logic of quantification without replacement, and as a
pilot study to better understand the complexity jumps between dynamic epistemic
logics of model transformations and logics of freely chosen graph changes that
get registered in a growing memory. After introducing this logic
() and its corresponding removal modality, we analyze its
expressive power and prove a bisimulation characterization theorem. We then
provide a complete Hilbert-style axiomatization for the logic of stepwise
removal in a hybrid language enriched with nominals and public announcement
operators. Next, we show that model-checking for is
PSPACE-complete, while its satisfiability problem is undecidable. Lastly, we
consider an issue of fine-structure: the expressive power gained by adding the
stepwise removal modality to fragments of first-order logic
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 modal operators
We study dynamic modal operators that can change the accessibility relation of a model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to delete, add or swap an edge between pairs of elements of the domain. We define a generic framework to characterize this kind of operations. First, we investigate relation-changing modal logics as fragments of classical logics. Then, we use the new framework to get a suitable notion of bisimulation for the logics introduced, and we investigate their expressive power. Finally, we show that the complexity of the model checking problem for the particular operators introduced is PSpace-complete, and we study two subproblems of model checking: formula complexity and program complexity.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fervari, Raul Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hoffmann, Guillaume Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
On Spatial Conjunction as Second-Order Logic
Spatial conjunction is a powerful construct for reasoning about dynamically
allocated data structures, as well as concurrent, distributed and mobile
computation. While researchers have identified many uses of spatial
conjunction, its precise expressive power compared to traditional logical
constructs was not previously known. In this paper we establish the expressive
power of spatial conjunction. We construct an embedding from first-order logic
with spatial conjunction into second-order logic, and more surprisingly, an
embedding from full second order logic into first-order logic with spatial
conjunction. These embeddings show that the satisfiability of formulas in
first-order logic with spatial conjunction is equivalent to the satisfiability
of formulas in second-order logic. These results explain the great expressive
power of spatial conjunction and can be used to show that adding unrestricted
spatial conjunction to a decidable logic leads to an undecidable logic. As one
example, we show that adding unrestricted spatial conjunction to two-variable
logic leads to undecidability. On the side of decidability, the embedding into
second-order logic immediately implies the decidability of first-order logic
with a form of spatial conjunction over trees. The embedding into spatial
conjunction also has useful consequences: because a restricted form of spatial
conjunction in two-variable logic preserves decidability, we obtain that a
correspondingly restricted form of second-order quantification in two-variable
logic is decidable. The resulting language generalizes the first-order theory
of boolean algebra over sets and is useful in reasoning about the contents of
data structures in object-oriented languages.Comment: 16 page
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