1,227 research outputs found
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
Modal Logics with Hard Diamond-free Fragments
We investigate the complexity of modal satisfiability for certain
combinations of modal logics. In particular we examine four examples of
multimodal logics with dependencies and demonstrate that even if we restrict
our inputs to diamond-free formulas (in negation normal form), these logics
still have a high complexity. This result illustrates that having D as one or
more of the combined logics, as well as the interdependencies among logics can
be important sources of complexity even in the absence of diamonds and even
when at the same time in our formulas we allow only one propositional variable.
We then further investigate and characterize the complexity of the
diamond-free, 1-variable fragments of multimodal logics in a general setting.Comment: New version: improvements and corrections according to reviewers'
comments. Accepted at LFCS 201
Temporal Logic with Recursion
We introduce extensions of the standard temporal logics CTL and LTL with a recursion operator that takes propositional arguments. Unlike other proposals for modal fixpoint logics of high expressive power, we obtain logics that retain some of the appealing pragmatic advantages of CTL and LTL, yet have expressive power beyond that of the modal ?-calculus or MSO. We advocate these logics by showing how the recursion operator can be used to express interesting non-regular properties. We also study decidability and complexity issues of the standard decision problems
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
Boolean Dependence Logic and Partially-Ordered Connectives
We introduce a new variant of dependence logic called Boolean dependence
logic. In Boolean dependence logic dependence atoms are of the type
=(x_1,...,x_n,\alpha), where \alpha is a Boolean variable. Intuitively, with
Boolean dependence atoms one can express quantification of relations, while
standard dependence atoms express quantification over functions.
We compare the expressive power of Boolean dependence logic to dependence
logic and first-order logic enriched by partially-ordered connectives. We show
that the expressive power of Boolean dependence logic and dependence logic
coincide. We define natural syntactic fragments of Boolean dependence logic and
show that they coincide with the corresponding fragments of first-order logic
enriched by partially-ordered connectives with respect to expressive power. We
then show that the fragments form a strict hierarchy.Comment: 41 page
A Theory of Sampling for Continuous-time Metric Temporal Logic
This paper revisits the classical notion of sampling in the setting of
real-time temporal logics for the modeling and analysis of systems. The
relationship between the satisfiability of Metric Temporal Logic (MTL) formulas
over continuous-time models and over discrete-time models is studied. It is
shown to what extent discrete-time sequences obtained by sampling
continuous-time signals capture the semantics of MTL formulas over the two time
domains. The main results apply to "flat" formulas that do not nest temporal
operators and can be applied to the problem of reducing the verification
problem for MTL over continuous-time models to the same problem over
discrete-time, resulting in an automated partial practically-efficient
discretization technique.Comment: Revised version, 43 pages
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