Matching μ-Logic

We address the problem of learning temporal properties from the branching-time behavior of systems. Existing research in this field has mostly focused on learning linear temporal properties specified using popular logics, such as Linear Temporal Logic (LTL) and Signal Temporal Logic (STL). Branching-time logics such as Computation Tree Logic (CTL) and Alternating-time Temporal Logic (ATL), despite being extensively used in specifying and verifying distributed and multi-agent systems, have not received adequate attention. Thus, in this paper, we investigate the problem of learning CTL and ATL formulas from examples of system behavior. As input to the learning problems, we rely on the typical representations of branching behavior as Kripke structures and concurrent game structures, respectively. Given a sample of structures, we learn concise formulas by encoding the learning problem into a satisfiability problem, most notably by symbolically encoding both the search for prospective formulas and their fixed-point based model checking algorithms. We also study the decision problem of checking the existence of prospective ATL formulas for a given sample. We implement our algorithms in a Python prototype and have evaluated them to extract several common CTL and ATL formulas used in practical applications.

In this thesis, we introduce and examine four new temporal logic formalisms that can be used as specification languages for the automated verification of the reliability of hardware and software designs with respect to a desired behavior. The work is organized in two parts. In the first one, we reason about two logics for computations, GCTL* and MCTL*, which are useful to describe a correct execution of monolithic closed systems. In the second one, instead, we focus on two logics for strategies, SL and mATL*, which are useful to formalize several interesting properties about interactive plays in multi-entities systems modeled as multi-agent games. In the “Logics for Computations” part, we first study the immersion of the idea of graded quantifications into the temporal-logic framework. In first order logic, existential and universal quantifiers express the concepts of the existence of at least one individual object satisfying a formula, or that all individual objects satisfy a formula. In other logics, these quantifiers have been generalized to express that, for a given non-negative integer n, at least n or all but n individuals satisfy a particular formula. Here, we consider GCTL, a temporal logic with graded path quantifiers, which allows to describe properties like “there exist at least n different classes of computational fluxes in which a system reaches a predetermined state”, where the classes over paths are computed by means of a predetermined equivalence relation. More precisely, we uniformly extend the classic concept of graded quantifiers from states to paths, through the use of a concept of path equivalence with respect to a given path formula. About this logic, in particular, we study the expressiveness and succinctness relationships with respect to GµCalculus and the complexity of the satisfiability problem, which results to be ExpTime-Complete. This research is partially based on the works [BMM09] “Graded Computation Tree Logic” and [BMM10] “Graded Computation Tree Logic with Binary Coding” published, respectively, in the proceedings of the “IEEE Symposium on Logic in Computer Science, 2009” and “EACSL Annual Conference on Computer Science Logic, 2010”. Preliminary results can be also found in [Mog07]. Furthermore, we consider special quantifiers over substructures, which allow to select, using parametric criteria, small critical parts of a system to be successively verified. In literature, there are some attempts to define a logic that allows to modify the underlying structure under exam and then to verify on it some assigned property. However, as far as we know, none of them is able to select minimal submodels of a given property describing the criteria on which then execute the verification process. Here, we base our work on the search of a new operator that merges the concept of quantifiers on structures with that one derived by a generalization of the concept of pruning. The results of this work, is a class of three different extensions of CTL* with minimal model quantifiers, which we name MCTL*. Regarding these logics, we study several reductions among them, as well as the satisfiability problem that we prove to be highly undecidability, i.e., Σ_1^1-Hard, for two out of the three cases. This research is partially based on the work [MM09] “Branching-Time Temporal Logics with Minimal Model Quantifiers” published in the proceedings of the “International Conference on Developments in Language Theory, 2009”. In the “Logics for Strategies” part, we first study the problem of defining a new specification language through which it is possible to express several important properties of multi-entities systems that are neither expressible using classical monolithic temporal logics, such as CTL*, nor using two-agent-teams temporal logics, such as ATL*. In literature, we can found some proposal of logics that try to achieve this goal, but unfortunately, none of them succeeds completely on all the aspects. Among them, one of the most important attempts is CHP-SL, a logics in which one can use variables over strategies. However, this logic has a deep weakness, since it does not allow to describe games with more than two players and even two-players concurrent games. Here, we introduce SL, a logic with a syntax similar in some aspects to the first order logic, in which the strategies of the agent building the game are treated as first order objects on which we can quantify. This logic generalizes CHP-SL, by allowing the specification of the correct behavior of multi-agent concurrent games. In SL, for example, we are able to express very complex but useful Nash equilibria that are not expressible with CHP-SL. We enlighten that Nash equilibrium is one of the most important concepts in game theory. For the introduced logic, we solve two problems left open in the work on CHP-SL. Precisely, we show that the related model-checking problem is 2ExpTime-Complete, thus not harder of the same problem for several subsumed logics, while we prove that its satisfiability problem is highly undecidable, i.e., Σ_1^1-Hard. This research is partially based on the work [MMV10a] “Reasoning About Strategies” published in the proceedings of the “IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, 2010”. Finally, we consider the concept of relentful strategic reasoning, i.e., a formalism that expresses the ability of a strategy to be used not only to achieve a first given goal, but also to change its final goal in dependence of the history of the play. In the context of planning, memoryful quantification, i.e., quantification over computations that does not lose information about the past along the time, is one of the principal way to express the fact that a system is able to achieve a desired result, and shift to a different goal if some event happens. However, this kind of quantification was not considered before in the context of multi-agent planning. Here, we introduce mATL*, a fusion of the classic alternating temporal logic ATL* with memoryful quantification, with the aim of covering the previous idea. About this logics, we prove that, although it is equivalent to ATL*, it is exponentially more succinct. Nevertheless, we prove that both the model-checking and the satisfiability problems remain 2ExpTime-Complete, as for ATL*. This research is partially based on the work [MMV10b] “Relentful Strategic Reasoning in Alternating-Time Temporal Logic” published in the proceedings of the “International Conference on Logic for Programming Artificial Intelligence and Reasoning, 2010”.

Dynamic linear time temporal logic

: The question of whether branching-time temporal logic or linear-time temporal logic is best for reasoning about concurrent programs is one of the most controversial issues in logics of programs. Concurrent programs are usually modelled by labelled state-transition graphs in which some state is designated as the initial state. For historical reasons such graphs are called Kripke structures. In linear temporal logic operators are provided for describing events along a single time path (i.e., along a single path in a Kripke structure). In a branching-time logic the temporal operators quantify over the futures that are possible from a given state (i.e., over the possible paths that lead from a state). It is well known that the two types of temporal logic have different expressive powers. Linear temporal logic, for example, can express certain fairness properties that cannot be expressed in branching-time temporal logic. On the other hand, certain practical decision problems like model checking are easier for branching-time temporal logic than for linear temporal logic. This paper provides further insight on which type of logic is best. It is shown that if two finite Kripke structures can be distinguished by some formula that contains both branching-time and linear-time operators, then the structures can be distinguished by a formula that contains only branching time operators. Specifically, we show that if two finite Kripke structures can be distinguished by some formula of the logic CTL (i.e., if there is some CTL formula that is true in one but not in the other), then they can be distinguished by some formula of the logic CTL.

Recent studies show that Information Centric is one of the best ways to help Internet users find useful messages among a myriad of information. With the help of a publisher/subscriber structure, users could use this Information Centric System to subscribe to messages they have interest or from the ones their friends have recommended. However, with the increasing usage of smart phones and computers, one user could need several IP addresses and the scale of the network could increase dramatically. How to guarantee that a publisher/subscriber structure based system continues to work well becomes an important problem. This paper provides a suitable way of checking the configuration of a publisher/subscriber system network by using Linear-time Temporal Logic (LTL) and Computation Tree Logic (CTL). In order to apply this kind of model checking methods to a large network, a necessary model checking code generator is provided in this paper.

SLA-Driven modeling and verifying cloud systems: A Bigraphical reactive systems-based approach

The dynamic description logic DDL provides formalism for describing dynamic system in the semantic Web environment Model checking is a formal verification method based on state transition system. In this paper, we bring dynamic description logic into model checking. Firstly, state transition systems considered in model checking are modeled as complex actions in dynamic description logic. Secondly, a kind of temporal description logic DL-CTL is introduced to specify temporal properties on state transition systems, where DL-CTL is a DL-based extension of propositional branch-time temporal logic CTL. Finally, verification algorithm is presented with the help of reasoning mechanisms provided by description logic.

Specifying and verifying interaction protocols in a temporal action logic

The introduction of Past Operators enables to produce more natural formulation of a wide class of properties of reactive systems, compared to traditional pure future temporal logics. For this reason, past temporal logics are gaining increasing interest in several application areas, ranging from Requirement Engineering to Formal Verification and Model Checking. We show how SAT-based Bounded Model Checking techniques can be extended to deal with Linear Temporal Logics with Past Operators (PLTL). Though apparently simple, this task turns out to be absolutely non-trivial when tackled in its full generality. We discuss a bounded semantics for PLTL, we show that it is correct (and complete), and propose an encoding scheme able to cope with PLTL formulas. Finally, we implement the encoding in NuSMV, and present a first experimental evaluation of the approach.

In 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.

Summary form only given. We briefly present a rule-based framework, called EAGLE, shown to be capable of defining and implementing finite trace monitoring logics, including future and past time temporal logic, extended regular expressions, real-time and metric temporal logics (MTL), interval logics, forms of quantified temporal logics, and so on. In this paper we focus on a linear temporal logic (LTL) specialisation of EAGLE. For an initial formula of size m, we establish upper bounds of O(m/sup 2/2/sup m/logm) and O(m/sup 4/2/sup 2m/log/sup 2/m) for the space and time complexity, respectively, of single step evaluation over an input trace. EAGLE has been successfully used, in both LTL and metric LTL forms, to test a real-time controller of an experimental NASA planetary rover.

Unified temporal logic

As an important complex problem, the temporal logic model checking problem is still far from being fully resolved under the circumstance of DNA computing, especially Computation Tree Logic (CTL), Interval Temporal Logic (ITL), and Projection Temporal Logic (PTL), because there is still a lack of approaches for DNA model checking. To address this challenge, a model checking method is proposed for checking the basic formulas in the above three temporal logic types with DNA molecules. First, one-type single-stranded DNA molecules are employed to encode the Finite State Automaton (FSA) model of the given basic formula so that a sticker automaton is obtained. On the other hand, other single-stranded DNA molecules are employed to encode the given system model so that the input strings of the sticker automaton are obtained. Next, a series of biochemical reactions are conducted between the above two types of single-stranded DNA molecules. It can then be decided whether the system satisfies the formula or not. As a result, we have developed a DNA-based approach for checking all the basic formulas of CTL, ITL, and PTL. The simulated results demonstrate the effectiveness of the new method.

This paper shows the relation between linear temporal logic and theory of languages of concurrent processes. To this purpose, we give an algebraic correspondence between temporal logic systems and some non deterministic sequential machines. This correspondence lies on an effective method which composes machines as temporal operators. So we can synthetise processes from temporal logic formulas and solve logic problems by algorithms applied to machines.KeywordsTemporal LogicLinear Temporal LogicTemporal Logic FormulaNous AllonsBranch Time Temporal LogicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Most works that extend workflow validation beyond syntactical checking consider constraints on the sequence of messages exchanged between services. However, these constraints are expressed only in terms of message names and abstract away their actual data content. Using the context of the User-controlled Lightpath initiative (UCLP) hosted by the CANARIE consortium, we provide examples of real- world "data-aware" web service constraints where the sequence of messages and their content are interdependent. We present CTL-FO <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> , an extension over Computation Tree Logic that includes first-order quantification on state variables in addition to temporal operators. We show how CTL- FO <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> is adequate for expressing data-aware constraints, give a complete model checking algorithm for CTL-FO <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> and establish its complexity to be PSPACE-complete. This makes using CTL-FO <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> for validating workflow properties no harder than using the Linear Temporal Logic (LTL) already used by some web service tools. Finally, we show how the modelling of data-aware properties is an increase in expressiveness that cannot be efficiently simulated by these tools.