21,833 research outputs found
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
Automated Reasoning over Deontic Action Logics with Finite Vocabularies
In this paper we investigate further the tableaux system for a deontic action
logic we presented in previous work. This tableaux system uses atoms (of a
given boolean algebra of action terms) as labels of formulae, this allows us to
embrace parallel execution of actions and action complement, two action
operators that may present difficulties in their treatment. One of the
restrictions of this logic is that it uses vocabularies with a finite number of
actions. In this article we prove that this restriction does not affect the
coherence of the deduction system; in other words, we prove that the system is
complete with respect to language extension. We also study the computational
complexity of this extended deductive framework and we prove that the
complexity of this system is in PSPACE, which is an improvement with respect to
related systems.Comment: In Proceedings LAFM 2013, arXiv:1401.056
A Logic for Reasoning about Group Norms
We present a number of modal logics to reason about group norms. As a preliminary
step, we discuss the ontological status of the group to which the norms are
applied, by adapting the classification made by Christian List of collective attitudes
into aggregated, common, and corporate attitudes. Accordingly, we shall introduce
modality to capture aggregated, common, and corporate group norms. We investigate
then the principles for reasoning about those types of modalities. Finally, we discuss
the relationship between group norms and types of collective responsibility
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
Non-normal modalities in variants of Linear Logic
This article presents modal versions of resource-conscious logics. We
concentrate on extensions of variants of Linear Logic with one minimal
non-normal modality. In earlier work, where we investigated agency in
multi-agent systems, we have shown that the results scale up to logics with
multiple non-minimal modalities. Here, we start with the language of
propositional intuitionistic Linear Logic without the additive disjunction, to
which we add a modality. We provide an interpretation of this language on a
class of Kripke resource models extended with a neighbourhood function: modal
Kripke resource models. We propose a Hilbert-style axiomatization and a
Gentzen-style sequent calculus. We show that the proof theories are sound and
complete with respect to the class of modal Kripke resource models. We show
that the sequent calculus admits cut elimination and that proof-search is in
PSPACE. We then show how to extend the results when non-commutative connectives
are added to the language. Finally, we put the logical framework to use by
instantiating it as logics of agency. In particular, we propose a logic to
reason about the resource-sensitive use of artefacts and illustrate it with a
variety of examples
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