scholarly journals Weak Completeness Theorem for Propositional Linear Time Temporal Logic

2012 ◽  
Vol 20 (3) ◽  
pp. 227-234
Author(s):  
Mariusz Giero
Keyword(s):  
Temporal Logic ◽  
Classical Logic ◽  
Linear Time ◽  
Completeness Theorem ◽  
Weak Completeness ◽  
Finite Set ◽  
Temporal Model ◽  
Linear Time Temporal Logic

Summary We prove weak (finite set of premises) completeness theorem for extended propositional linear time temporal logic with irreflexive version of until-operator. We base it on the proof of completeness for basic propositional linear time temporal logic given in [20] which roughly follows the idea of the Henkin-Hasenjaeger method for classical logic. We show that a temporal model exists for every formula which negation is not derivable (Satisfiability Theorem). The contrapositive of that theorem leads to derivability of every valid formula. We build a tree of consistent and complete PNPs which is used to construct the model.

scholarly journals A Product Version of Dynamic Linear Time Temporal Logic

1997 ◽  
Vol 4 (9) ◽  
Author(s):  
Jesper G. Henriksen ◽  
P. S. Thiagarajan
Keyword(s):  
Temporal Logic ◽  
Decision Procedure ◽  
Linear Time ◽  
Dynamic Logic ◽  
Two Dimensions ◽  
Sequential Programs ◽  
Propositional Dynamic Logic ◽  
The Core ◽  
Finite Set ◽  
Linear Time Temporal Logic

We present here a linear time temporal logic which simultaneously extends LTL, the propositional temporal logic of linear time, along two dimensions. Firstly, the until operator is strengthened by indexing it with the regular programs of propositional dynamic logic (PDL). Secondly, the core formulas of the logic are decorated with names of sequential agents drawn from fixed finite set. The resulting logic has a natural semantics in terms of the runs of a distributed program consisting of a finite set of sequential programs that communicate by performing common actions together. We show that our logic, denoted DLTL, admits an exponential time decision procedure. We also show that DLTL is expressively equivalent to the so called regular product languages.

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.

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.

Natural Deduction Calculus for Linear-Time Temporal Logic

2006 ◽  
pp. 56-68 ◽  
Author(s):  
Alexander Bolotov ◽  
Artie Basukoski ◽  
Oleg Grigoriev ◽  
Vasilyi Shangin
Keyword(s):  
Temporal Logic ◽  
Natural Deduction ◽  
Linear Time ◽  
Linear Time Temporal Logic
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