195 research outputs found
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
The Lattice of Congruences of a Finite Line Frame
Let be a finite Kripke frame. A
congruence of is a bisimulation of that is also an
equivalence relation on F. The set of all congruences of is a
lattice under the inclusion ordering. In this article we investigate this
lattice in the case that is a finite line frame. We give concrete
descriptions of the join and meet of two congruences with a nontrivial upper
bound. Through these descriptions we show that for every nontrivial congruence
, the interval embeds into the lattice of
divisors of a suitable positive integer. We also prove that any two congruences
with a nontrivial upper bound permute.Comment: 31 pages, 11 figures. Expanded intro, conclusions rewritten. New,
less geometrical, proofs of Lemma 19 and (former) Lemma 3
Unsorted Functional Translations
AbstractIn this article we first show how the functional and the optimized functional translation from modal logic to many-sorted first-order logic can be naturally extended to the hybrid language H(@,↓). The translation is correct not only when reasoning over the class of all models, but for any first-order definable class. We then show that sorts can be safely removed (i.e., without affecting the satisfiability status of the formula) for frame classes that can be defined in the basic modal language, and show a counterexample for a frame class defined using nominals
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
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
On the logic for utopia
In this study we propose the standard modal logic KD43 as the logle governing expressions about Utopia. We define a formal construction corresponding to Utopian expressions In ordlnary language that we name utopian eonditionals.
They possess the singular properties of admitting Strengthening of the Antecedent whlle possibly defeating the rule of Modus Ponens. Perhaps the most interesting aspect of this work is that, as far as the authors know, this is the first time a category of expressions in the ordinary language corresponding to these two singular properties is provided.Eje: 2do. Workshop sobre aspectos teóricos de la inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI
Hybrid type theory: a quartet in four movements
This paper sings a song -a song created by bringing together the work of four great names in the history of logic: Hans Reichenbach, Arthur Prior, Richard Montague, and Leon Henkin. Although the work of the first three of these authors have previously been combined, adding the ideas of Leon Henkin is the addition required to make the combination work at the logical level. But the present paper does not focus on the underlying technicalities (these can be found in Areces, Blackburn, Huertas, and Manzano [to appear]) rather it focusses on the underlying instruments, and the way they work together. We hope the reader will be tempted to sing along
From boxes to worlds
In this paper we show an innovative way to represent graphic designs 01 systems and to verify design properties. The graphic designs are thought as models of an extended modal logic; and the methods used to verify properties are developed from techniques typical of classic modal logic, extended to cover the differences in the underlying formalism. We present the procedures orlogical tools to derive the modal model associated to a given design, the filtration of models and the construction 01 modal descriptions.
A higher level of abstraction is obtained in this way, and it lets us reason over designs in a strictly formal manner. The power of formal provability is also achieved.
We use a working example to show how our tools help to veri1y properties 01 design like the detection of cycles (self loops).Eje: Diseño de softwareRed de Universidades con Carreras en Informática (RedUNCI
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