Relating first-order monadic omega-logic, propositional linear-time temporal logic, propositional generalized definitional reflection logic and propositional infinitary logic

2017 ◽  
Vol 27 (7) ◽  
pp. 2271-2301
Author(s):  
Norihiro Kamide
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Infinitary Logic ◽  
First Order ◽  
Linear Time Temporal Logic

scholarly journals Dynamic Linear Time Temporal Logic

1997 ◽  
Vol 4 (8) ◽  
Author(s):  
Jesper G. Henriksen ◽  
P. S. Thiagarajan
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Dynamic Logic ◽  
Order Theory ◽  
Simple Extension ◽  
Propositional Dynamic Logic ◽  
First Order ◽  
Time Semantics ◽  
Linear Time Temporal Logic ◽  
Obvious Manner

A simple extension of the propositional temporal logic of linear<br />time is proposed. The extension consists of strengthening the until<br />operator by indexing it with the regular programs of propositional<br />dynamic logic (PDL). It is shown that DLTL, the resulting logic, is<br />expressively equivalent to S1S, the monadic second-order theory<br />of omega-sequences. In fact a sublogic of DLTL which corresponds<br />to propositional dynamic logic with a linear time semantics is<br />already as expressive as S1S. We pin down in an obvious manner<br />the sublogic of DLTL which correponds to the first order fragment<br />of S1S. We show that DLTL has an exponential time decision<br />procedure. We also obtain an axiomatization of DLTL. Finally,<br />we point to some natural extensions of the approach presented<br />here for bringing together propositional dynamic and temporal<br />logics in a linear time setting.

scholarly journals Temporal logic programs with variables

2016 ◽  
Vol 17 (2) ◽  
pp. 226-243 ◽  
Author(s):  
FELICIDAD AGUADO ◽  
PEDRO CABALAR ◽  
GILBERTO PÉREZ ◽  
CONCEPCIÓN VIDAL ◽  
MARTÍN DIÉGUEZ
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Logic Program ◽  
Answer Set Programming ◽  
Logic Programs ◽  
First Order ◽  
Linear Time Temporal Logic ◽  
Definition Of ◽  
Stable Models ◽  
Answer Set

AbstractIn this note, we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic, an extension of Answer Set Programming for dealing with linear-time modal operators. To this aim, we provide a definition of a first-order version of Temporal Equilibrium Logic that shares the syntax of first-order Linear-time Temporal Logic but has different semantics, selecting some Linear-time Temporal Logic models we call temporal stable models. Then, we consider a subclass of theories (called splittable temporal logic programs) that are close to usual logic programs but allowing a restricted use of temporal operators. In this setting, we provide a syntactic definition of safe variables that suffices to show the property of domain independence – that is, addition of arbitrary elements in the universe does not vary the set of temporal stable models. Finally, we present a method for computing the derivable facts by constructing a non-temporal logic program with variables that is fed to a standard Answer Set Programming grounder. The information provided by the grounder is then used to generate a subset of ground temporal rules which is equivalent to (and generally smaller than) the full program instantiation.

scholarly journals An Expressively Complete Linear Time Temporal Logic for Mazurkiewicz Traces

1996 ◽  
Vol 3 (62) ◽  
Author(s):  
P. S. Thiagarajan ◽  
Igor Walukiewicz
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Order Reduction ◽  
Expressive Power ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Reduction Methods ◽  
Linear Time Temporal Logic ◽  
Mazurkiewicz Traces

<p>A basic result concerning LTL, the propositional temporal logic of linear time, is that it is expressively complete; it is equal in expressive power to the first order theory of sequences. We present here a smooth extension of this result to the class of partial orders known as Mazurkiewicz traces. These partial orders arise in a variety of contexts in concurrency theory and they provide the conceptual basis for many of the partial order reduction methods that have been developed in connection with LTL-specifications.</p><p>We show that LTrL, our linear time temporal logic, is equal in expressive power to the first order theory of traces when interpreted over (finite and) infinite traces. This result fills a prominent gap in the existing logical theory of infinite traces. LTrL also provides a syntactic characterisation of the so-called trace consistent (robust) LTL-specifications. These are specifications expressed as LTL formulas that do not distinguish between different linearisations of the same trace and hence are amenable to partial order reduction methods.</p>

Verifying linear time temporal logic properties of concurrent Ada programs with quasar

2004 ◽  
Vol XXIV (1) ◽  
pp. 17-24 ◽  
Author(s):  
S. Evangelista ◽  
C. Kaiser ◽  
J. F. Pradat-Peyre ◽  
P. Rousseau
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Linear Time Temporal Logic

Vehicle route-sequence planning using temporal logic

2002 ◽  
Vol 16 (1) ◽  
pp. 31-38
Author(s):  
KIAM TIAN SEOW ◽  
MICHEL PASQUIER
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Simple Procedure ◽  
Precedence Constraints ◽  
Sequence Planning ◽  
Vehicle Route ◽  
Passenger Travel ◽  
State Formula ◽  
Linear Time Temporal Logic ◽  
Service Task

This paper proposes a new logical framework for vehicle route-sequence planning of passenger travel requests. Each request is a fetch-and-send service task associated with two request-locations, namely, a source and a destination. The proposed framework is developed using propositional linear time temporal logic of Manna and Pnueli. The novelty lies in the use of the formal language for both the specification and theorem-proving analysis of precedence constraints among the location visits that are inherent in route sequences. In the framework, legal route sequences—each of which visits every request location once and only once in the precedence order of fetch-and-send associated with every such request—is formalized and justified, forming a basis upon which the link between a basic precedence constraint and the corresponding canonical forbidden-state formula is formally established. Over a given base route plan, a simple procedure to generate a feasible subplan based on a specification of the forbidden-state canonical form is also given. An example demonstrates how temporal logic analysis and the proposed procedure can be applied to select a final (feasible) subplan based on additional precedence constraints.

Ein Ansatz zur formalen Verifikation von Schaltungsbeschreibungen in SystemC (An Approach for Formal Verification of Circuits in SystemC)

2003 ◽  
Vol 45 (4) ◽  
Author(s):  
Daniel Große ◽  
Rolf Drechsler
Keyword(s):  
Formal Verification ◽  
Temporal Logic ◽  
Linear Time ◽  
Linear Time Temporal Logic

ZusammenfassungDer vorgestellte Ansatz ermöglicht es, für SystemC-Schaltkreisbeschreibungen, die über einer gegebenen Gatterbibliothek definiert sind, Eigenschaften zu beweisen (engl. property checking). Als Spezifikationssprache wird LTL (linear time temporal logic) verwendet. Für den Beweis einer LTL-Eigenschaft kann die Erfüllbarkeit einer Booleschen Funktion betrachtet werden, die aus der Eigenschaft und der Schaltkreisbeschreibung mittels symbolischer Methoden konstruiert wird. Im Gegensatz zu simulationsbasierten Ansätzen kann dabei Vollständigkeit gewährleistet werden. Anhand einer Fallstudie eines skalierbaren Arbiters wird die Effizienz des Beweisverfahrens untersucht.

scholarly journals Verifying Fault-Tolerance in Probabilistic Swarm Systems

2020 ◽  
Author(s):  
Alessio Lomuscio ◽  
Edoardo Pirovano
Keyword(s):  
Fault Tolerance ◽  
Temporal Logic ◽  
Decision Problem ◽  
Swarm Robotics ◽  
Linear Time ◽  
Experimental Results ◽  
Robotic Swarms ◽  
Linear Time Temporal Logic ◽  
Probabilistic Nature

We present a method for reasoning about fault-tolerance in unbounded robotic swarms. We introduce a novel semantics that accounts for the probabilistic nature of both the swarm and possible malfunctions, as well as the unbounded nature of swarm systems. We define and interpret a variant of probabilistic linear-time temporal logic on the resulting executions, including those arising from faulty behaviour by some of the agents in the swarm. We specify the decision problem of parameterised fault-tolerance, which concerns determining whether a probabilistic specification holds under possibly faulty behaviour. We outline a verification procedure that we implement and use to study a foraging protocol from swarm robotics, and report the experimental results obtained.

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