First-order Linear Temporal Logic Research Articles

Temporal prophecy for proving temporal properties of infinite-state systems

Various verification techniques for temporal properties transform temporal verification to safety verification. For infinite-state systems, these transformations are inherently imprecise. That is, for some instances, the temporal property holds, but the resulting safety property does not. This paper introduces a mechanism for tackling this imprecision. This mechanism, which we call temporal prophecy, is inspired by prophecy variables. Temporal prophecy refines an infinite-state system using first-order linear temporal logic formulas, via a suitable tableau construction. For a specific liveness-to-safety transformation based on first-order logic, we show that using temporal prophecy strictly increases the precision. Furthermore, temporal prophecy leads to robustness of the proof method, which is manifested by a cut elimination theorem. We integrate our approach into the Ivy deductive verification system, and show that it can handle challenging temporal verification examples.

A decidable and expressive fragment of Many-Sorted First-Order Linear Temporal Logic

First-Order Linear Temporal Logic (FOLTL) and its Many-Sorted variant (MSFOLTL) are well-suited to specify infinite-state systems. However, the satisfiability of (MS)FOLTL is not even semi-decidable, thus preventing automated verification. In this paper, we exhibit various fragments of increasing scope that provide a pertinent basis for the abstract specification of infinite-state systems. We show that these fragments enjoy the Bounded Domain Property (any satisfiable (MS)FOLTL formula has a model with a finite, bounded FO domains), which provides a basis for complete, automated verification by reduction to LTL satisfiability. Finally, we present a simple case study illustrating the applicability and limitations of our results.

Workflow Nets With Tables and Their Soundness

Workflow nets and their extensions with data flows, e.g., workflow nets with data and colored workflow nets, can well model the business processes of workflow systems, and their soundness guarantees that systems have neither deadlock nor livelock. However, some design requirements related to the changes of data values within multiple business cases are not reflected by these models, and thus, some errors of the modeled systems cannot be detected by them. In this article, we propose workflow nets with tables (WFT-nets) to model workflow systems that are closely related to the database (i.e., different users, records, and attributes). We define the firing rule of WFT-nets via data refinements in order to avoid infinite states caused by unbounded data. We use first-order linear temporal logic to represent the design requirements of records and attributes’ values and then define the soundness of WFT-nets. We construct an algorithm to verify soundness. A tool is developed, and a group of experiments are done to illustrate the effectiveness of our methods.

Verification for commitment-based web service protocols

We propose a model for a class of web services which are powered by relational databases and annotated by social commitment. Our model can be viewed as an extension of WSDL specification where schemas of service operations specify not only input-output signatures but also data constraints, control-flow constraints, state/output/effect rules. The data-aware temporal properties about interactions between services and users are specified in Linear Temporal First-Order Logic with Social Commitment (LTL-FOSC). We have proved it is possible to use existing tools (e.g. WAVE) originally designed for verification of web applications to verify such properties.

Automatic Verification of Data-centric Web Service Specifications

Amodel are proposed for modeling data-centric Web services which are powered by relational databases and interact with users according to logical formulas specifying input constraints, control-flow constraints and state/output/action rules. The Linear Temporal First-Order Logic (LTL-FO) formulas over inputs, states, outputs and actions are used to express the properties to be verified.We have proven that automatic verification of LTL-FO properties of data-centric Web services under input-bounded constraints is decidable by reducing Web services to data-centric Web applications. Thus, we can verify Web service specifications using existing verifier designed for Web applications.

Monodic temporal logic with quantified propositional variables

We extend the monodic fragment of first-order linear temporal logic to include right-linear grammar operators and quantification of propositional variables. Unlike propositional temporal logic, the use of grammar operators in first-order temporal logic is not equivalent to general propositional quantification, as the latter admit satisfiable formulae without countable models. We consider the decision problem for fragments where propositional quantification occurs outside of quantification of individual variables and temporal (grammar) operators. We show that if externally quantified propositions inside temporal operators occur within positive occurrences of universal quantifiers for individual variables, then validity for all propositional prefix classes is recursively enumerable and decidable in the two-variable case. Without this condition we show that, even with very severe restrictions on the first-order part of the logic, no non-trivial prefix class is recursively enumerable.

On Formalism of Continuous Knowledge Discovery and Temporal Granularity

The accessibility and abundance of data today makes knowledge discovery a matter of considerable importance and necessity. The process to discover continuously knowledge in evolving business domain is a challenge issue. A continuous knowledge discovery process is introduced for inducing the local first-order rules and global evolutional rules, to trace dynamic evolution patterns firstly. The definitions of main notions (event, sequence pattern, temporal rule) are proposed in a formal way, based on first-order linear temporal logic and temporal granularity. The measures of support and confidence about ranged degree of truth of a formula are established. The formalism defines the valuation on a linear state structure with time granules. By defining transition operation between temporal types, it is proved that only the independent information for unspanned-granule may be transferred without loss among different granularities. Otherwise, an aggregation mechanism was proposed to state sequence.

Analyzing and Managing Role-Based Access Control Policies

Today more and more security-relevant data is stored on computer systems; security-critical business processes are mapped to their digital counterparts. This situation applies to various domains such as health care industry, digital government, and financial service institutes requiring that different security requirements must be fulfilled. Authorisation constraints can help the policy architect design and express higher-level organisational rules. Although the importance of authorisation constraints has been addressed in the literature, there does not exist a systematic way to verify and validate authorisation constraints. In this paper, we specify both non-temporal and history-based authorisation constraints in the Object Constraint Language (OCL) and first-order linear temporal logic (LTL). Based upon these specifications, we attempt to formally verify role-based access control policies with the help of a theorem prover and to validate policies with the USE system, a validation tool for OCL constraints. We also describe an authorisation engine, which supports the enforcement of authorisation constraints.

The serializability problem for a temporal logic of transaction queries

We define the logic FOTLT(n), to be a monadic monodic fragment of first-order linear temporal logic, with 2n propositions representing the read and write steps of n two-step concurrent database transactions and a time-dependent predicate representing queries giving the sets of data items accessed by those read and write steps at given points in time. The models of FOTLT(n) contain interleaved sequences of the steps of infinitely many occurrences of the n transactions accessing unlimited data over time. A property of serializability is specified for FOTLT(n) formulae. We show that the serializability problem for FOTLT(n) formulae is decidable.

Decidability of infinite-state timed CCP processes and first-order LTL

The ntcc process calculus is a timed concurrent constraint programming (ccp) model equipped with a first-order linear-temporal logic (LTL) for expressing process specifications. A typical behavioral observation in ccp is the strongest postcondition ( sp). The ntcc sp denotes the set of all infinite output sequences that a given process can exhibit. The verification problem is then whether the sequences in the sp of a given process satisfy a given ntcc LTL formula. This paper presents new positive decidability results for timed ccp as well as for LTL. In particular, we shall prove that the following problems are decidable: (1) the sp equivalence for the so-called locally-independent ntcc fragment; unlike other fragments for which similar results have been published, this fragment can specify infinite-state systems, (2) verification for locally-independent processes and negation-free first-order formulae of the ntcc LTL, (3) implication for such formulae, (4) Satisfiability for a first-order fragment of Manna and Pnueli's LTL. The purpose of the last result is to illustrate the applicability of ccp to well-established formalisms for concurrency.

A Decision Procedure for Nonperiodic Sequents of the First-Order Linear Temporal Logic

A deduction-based decision procedure is presented for the nonperiodic D-sequents of the first-order linear temporal logic. The D-sequents are obtained from D2-sequents [7], [8] by removing the periodicity condition. The deductive procedure proposed consists of decidable deductive procedures that replace infinitary and finitary induction rules for the temporal operator ``always''. The soundness and completeness of the deduction-based decision procedure proposed is proved.

Infinitary Calculus without Loop Rules for Restricted Sequents of the First-Order Linear Temporal Logic

A restricted first-order linear temporal logic with temporal operators “next” and “always” is considered. We prove that for this logic one can construct a sequential calculus without loop rules, i.e., the rules containing a duplication of the main formula in the premises of these rules. This paper continues the previous work of the author, where an infinitary calculus without loop rules on the logical level, but containing the traditional loop antecedent rule for the operator “always,” was constructed. In this paper, in order to remove this loop rule we introduce a nonlocal rule allowing us to eliminate loops in the process of the proof search. The soundness and ω>-completeness of the constructed calculus is proved.

Infinitary calculus for a restricted first-order linear temporal logic without contraction on quantified formulas

An infinitary calculus for a restricted fragment of the first-order linear temporal logic is considered. We prove that for this fragment one can construct the infinitary calculusG Lω * without contraction on predicate formulas. The calculusG Lω * possesses the following properties: (1) the succedent rule for the existential quantifier is included into the corresponding axiom; (2) the premise of the antecedent rule for the universal quantifier does not contain a duplicate of the main formula. The soundness and completness ofG Lω * are also proved.

The saturated tableaux for linear miniscoped horn-like temporal logic

A new type of tableau system is proposed for the complete class (called miniscoped Horn-like) of first-order linear temporal logic. The described system instead of induction-like postulates contains some nonlogical axioms indicating the saturation of a derivation process in this system.