2,280 research outputs found
Hybrid Branching-Time Logics
Hybrid branching-time logics are introduced as extensions of CTL-like logics
with state variables and the downarrow-binder. Following recent work in the
linear framework, only logics with a single variable are considered. The
expressive power and the complexity of satisfiability of the resulting logics
is investigated.
As main result, the satisfiability problem for the hybrid versions of several
branching-time logics is proved to be 2EXPTIME-complete. These branching-time
logics range from strict fragments of CTL to extensions of CTL that can talk
about the past and express fairness-properties. The complexity gap relative to
CTL is explained by a corresponding succinctness result.
To prove the upper bound, the automata-theoretic approach to branching-time
logics is extended to hybrid logics, showing that non-emptiness of alternating
one-pebble Buchi tree automata is 2EXPTIME-complete.Comment: An extended abstract of this paper was presented at the International
Workshop on Hybrid Logics (HyLo 2007
On the Expressive Power of Hybrid Branching-Time Logics
Hybrid branching-time logics are a powerful extension of branching-time logics like CTL, CTL^* or even the modal mu-calculus through the addition of binders, jumps and variable tests. Their expressiveness is not restricted by bisimulation-invariance anymore. Hence, they do not retain the tree model property, and the finite model property is equally lost. Their satisfiability problems are typically undecidable, their model checking problems (on finite models) are decidable with complexities ranging from polynomial to non-elementary time. In this paper we study the expressive power of such hybrid branching-time logics beyond some earlier results about their invariance under hybrid bisimulations. In particular, we aim to extend the hierarchy of non-hybrid branching-time logics CTL, CTL^+, CTL^* and the modal mu-calculus to their hybrid extensions. We show that most separation results can be transferred to the hybrid world, even though the required techniques become a bit more involved. We also present some collapse results for restricted classes of models that are especially worth investigating, namely linear, tree-shaped and finite models
On the Hybrid Extension of CTL and CTL+
The paper studies the expressivity, relative succinctness and complexity of
satisfiability for hybrid extensions of the branching-time logics CTL and CTL+
by variables. Previous complexity results show that only fragments with one
variable do have elementary complexity. It is shown that H1CTL+ and H1CTL, the
hybrid extensions with one variable of CTL+ and CTL, respectively, are
expressively equivalent but H1CTL+ is exponentially more succinct than H1CTL.
On the other hand, HCTL+, the hybrid extension of CTL with arbitrarily many
variables does not capture CTL*, as it even cannot express the simple CTL*
property EGFp. The satisfiability problem for H1CTL+ is complete for triply
exponential time, this remains true for quite weak fragments and quite strong
extensions of the logic
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
On Bisimulations for Description Logics
We study bisimulations for useful description logics. The simplest among the
considered logics is (a variant of PDL). The others
extend that logic with inverse roles, nominals, quantified number restrictions,
the universal role, and/or the concept constructor for expressing the local
reflexivity of a role. They also allow role axioms. We give results about
invariance of concepts, TBoxes and ABoxes, preservation of RBoxes and knowledge
bases, and the Hennessy-Milner property w.r.t. bisimulations in the considered
description logics. Using the invariance results we compare the expressiveness
of the considered description logics w.r.t. concepts, TBoxes and ABoxes. Our
results about separating the expressiveness of description logics are naturally
extended to the case when instead of we have any sublogic
of that extends . We also provide results
on the largest auto-bisimulations and quotient interpretations w.r.t. such
equivalence relations. Such results are useful for minimizing interpretations
and concept learning in description logics. To deal with minimizing
interpretations for the case when the considered logic allows quantified number
restrictions and/or the constructor for the local reflexivity of a role, we
introduce a new notion called QS-interpretation, which is needed for obtaining
expected results. By adapting Hopcroft's automaton minimization algorithm and
the Paige-Tarjan algorithm, we give efficient algorithms for computing the
partition corresponding to the largest auto-bisimulation of a finite
interpretation.Comment: 42 page
Towards Understanding Reasoning Complexity in Practice
Although the computational complexity of the logic underlying the standard OWL 2 for the Web Ontology Language (OWL) appears discouraging for real applications, several contributions have shown that reasoning with OWL ontologies is feasible in practice. It turns out that reasoning in practice is often far less complex than is suggested by the established theoretical complexity bound, which reflects the worstcase scenario. State-of-the reasoners like FACT++, HERMIT, PELLET and RACER have demonstrated that, even with fairly expressive fragments of OWL 2, acceptable performances can be achieved. However, it is still not well understood why reasoning is feasible in practice and it is rather unclear how to study this problem. In this paper, we suggest first steps that in our opinion could lead to a better understanding of practical complexity. We also provide and discuss some initial empirical results with HERMIT on prominent ontologie
Interval vs. Point Temporal Logic Model Checking: an Expressiveness Comparison
Model checking is a powerful method widely explored in formal verification to check the (state-transition) model of a system against desired properties of its behaviour. Classically, properties are expressed by formulas of a temporal logic, such as LTL, CTL, and CTL*. These logics are "point-wise" interpreted, as they describe how the system evolves state-by-state. On the contrary, Halpern and Shoham\u27s interval temporal logic (HS) is "interval-wise" interpreted, thus allowing one to naturally express properties of computation stretches, spanning a sequence of states, or properties involving temporal aggregations, which are inherently "interval-based".
In this paper, we study the expressiveness of HS in model checking, in comparison with that of the standard logics LTL, CTL, and CTL*. To this end, we consider HS endowed with three semantic variants: the state-based semantics, introduced by Montanari et al., which allows branching in the past and in the future, the linear-past semantics, allowing branching only in the future, and the linear semantics, disallowing branching. These variants are compared, as for their expressiveness, among themselves and to standard temporal logics, getting a complete picture. In particular, HS with linear (resp., linear-past) semantics is proved to be equivalent to LTL (resp., finitary CTL*)
A Team Based Variant of CTL
We introduce two variants of computation tree logic CTL based on team
semantics: an asynchronous one and a synchronous one. For both variants we
investigate the computational complexity of the satisfiability as well as the
model checking problem. The satisfiability problem is shown to be
EXPTIME-complete. Here it does not matter which of the two semantics are
considered. For model checking we prove a PSPACE-completeness for the
synchronous case, and show P-completeness for the asynchronous case.
Furthermore we prove several interesting fundamental properties of both
semantics.Comment: TIME 2015 conference version, modified title and motiviatio
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