However, reallife implications are causal and temporal. Errors in safetycritical systems such as embedded controllers may have drastic consequences and can even endanger human life. Mixedinteger linear programming was proposed to generate trajectories for. Paper presented at the fourth conference on logic and the foundations of the theory of games and decisions. Ltl linear temporal logic is based on lineartime perspective. Temporal logic and model checking model mathematical structure extracted from hardware or software temporal logic provides a language for specifying functional properties model checking checks whether a given property holds of a model model checking is a kind of static veri. Since then, hybrid logic with the \\mathtt\downarrow\ binder has been extensively studied, see for example the paper areces, blackburn, and marx 2001 on modeltheoretic aspects of this logic. Seshia abstractwe present a mathematical programmingbased method for model predictive control of cyberphysical systems. We encode stl speci cations as mixed integerlinear constraints on the variables of a discretetime model of the system and environment dynamics, and solve a counterexample guided series of optimization problems to yield a satisfying control. In the linear view, at each moment in time there is a single successor moment.
Detecting temporal logic predicates on the happenedbefore model alper sen and vijay k. Linear temporal logic and linear dynamic logic on finite traces. The agenda introduction basic modal logic normal systems of modal logic metatheorems of normal systems variants of modal logic conclusion. The specification is a formula of syntactically cosafe linear temporal logic scltl, which can be satisfied in finite time. We give an efficient procedure for verifying that a finitestate concurrent system meets a specification. The core of temporal logic model checking is the reachability problem, which is not expressible in rstorder logic fol. In this paper, we use a model predictive approach to control discrete time. Model checking ii temporal logic model checking cmu school of.
Temporal logic and model checking algorithms are often used for checking system properties in various environments. Temporallogic 11 in classical logic, the predicate p in if p. The particular model of time is captured by a temporal accessibility relation between worlds. Tlm, achieves this through periodically recording contextual changes, interim assessment, and. In a linear temporal logic, operators are provided for. In this paper we present a new temporal logic suitable to express and automatically verify properties of. Know what a logic model is, and how it can be useful to your daily program operations identify the key components of a logic model. Pdf techniques for temporal logic model checking david. In the next section we discuss some of the most wellknown mathemat ical modellings of time. Temporal logic flavors linear temporal logic ltl computation tree logic ctl, ctl properties expressed over a tree of all possible executions ctl gives more expressiveness than ltl ctl is a subset of ctl that is easier to verify than arbitrary ctl.
Understand the intuition behind computation tree logic ctl the specification logic used e. In the past, symmetry has been exploited in computing. Learningbased model predictive control under signal. Temporal logic and model checking model mathematical structure extracted from hardware or software temporal logic provides a language for specifying functional properties. Research article fuzzy temporal logic based railway passenger flow forecast model feidou, 1,2 liminjia, 3 liwang, 1,3 jiexu, 3 andyakunhuang 1 school of trac and transportation, beijing jiaotong university, beijing, china. Temporal notions have historically close relationships with logical ones. Classical logic is good for describing static structures. In practice, finite state concurrent systems often exhibit considerable symmetry. These are the structures the formal languages of temporal logic. The alternative model, entitled the temporal logic model. Notes on games in temporal logic by ian hodkinson, including a formal description of firstorder temporal logic. Pat is a powerful free model checker, ltl checker, simulator and refinement checker for csp and its extensions with shared variable, arrays, wide range of fairness.
In this paper, we use a model predictive approach to control discrete time linear systems with additive bounded disturbances subject to. Ltl model checkers follow the automatatheoretic approach 5, in which the. Alexandre donze signal temporal logic eecs29498 spring 2014 2 52. The model checker works for any multivalued logic whose truth values form a quasiboolean lattice.
We give an efficient procedure for verifying that a. In particular, we show that symmetry can frequently be used to reduce the size of the state space that must be explored during model checking. Local descent for temporal logic falsification of cyberphysical systems pdf, extended tech report. In contrast, delay expressions that use temporal logic based on the implicit event tick depend on the step size used by the simulink solver. We investigate techniques for reducing the complexity of temporal logic model checking in the presence of symmetry. Robust temporal logic model predictive control sadra sadraddini and calin belta abstractcontrol synthesis from temporal logic speci. To incorporate dynamic environments, it is assumed that the reference trajectories are only available over a finite horizon and a model predictive control mpc approach is employed. Detecting temporal logic predicates on the happenedbefore. In 8th haifa verification conference hvc2012, volume 7857 of lecture notes in computer science lncs, pages 243259, springerverlag, 2012. Alternatingtime temporal logic 675 of the state independently of the other players, and turnbased asynchronous in each step, only one player has a choice of moves, and that player is chosen by a fair scheduler. We can say that the modalities in temporal logic are time abstract linear temporal logic ltl that is an infinite sequence of states where each point in time has a unique successor, based on a. The primary focus of this paper is on model checking using linear temporal logic ltl specifications. Logic and computation group research school of computer science australian national university. Temporal logics tl is a convenient formalism for specifying and verifying properties of reactive systems.
The term temporal logic has been broadly used to cover all approaches to reasoning about time and temporal information, as well as their formal representation, within a logical framework, and also more narrowly to refer specifically to the modallogic type of approach introduced around 1960 by arthur prior under the name tense logic and subsequently developed further by many logicians and. Automatic verification of finitestate concurrent systems. Twenty ve years ago, pnueli identi ed temporal logic as a very convenient formal language in which to state, and reason about, the behavioral properties of parallel programs and more generallyreactivesystemspnu77. Temporal logic objectives understand why temporal logic can be a useful formalism for specifying properties of concurrentreactive systems. In this section, we provide a brief overview on temporal logic model checking and alloy.
Temporal logics may differ according to how they handle branching in the underlying computation tree. S is the start state r is a transition relation every state has a successor i is a set of interpretations specifying which propositions are true in each state. But there are no tools to aid the logician or practitioner in the experimentation with different varieties of temporal logics and model checkers. It is therefore crucially important to verify the correctness of such systems in a logically precise manner during system. Model checking is a computerassisted method for the analysis of dynamical systems that can be modeled by statetransition systems. Temporal logic model checking in alloy springerlink. These subclasses of concurrent games capture various notions of synchronous and asynchronous interaction between open systems. Temporal logic model checking as automated theorem. However, once we consider asynchronously executing agents, the semantics is given as a formula in the temporal logic of the reals tlr barringer et al. Murray1, alberto sangiovannivincentelli 2and sanjit a. For example, many early thinkers who did not distinguish logical and natural necessity from each other e. Automatic verification of finitestate concurrent systems using temporal logic specifications e. Linear time model infinite sequences of states cannot express properties over a set of different paths 16.
Introduction to modal and temporal logic c rajeev gore. Drawing from research traditions in mathematical logic. In ltl, one can encode formulae about the future of paths, e. How to create a logic model two main approaches are used to create a logic model. Control chart execution by using temporal logic matlab. Pdf model checking is a set of formal verification techniques that aim to show that a structure representing a computational system for instance, a. Ctl computational tree logic is based on a branchingtime view. Molecular model checking a temporal logic a preprint version posted on arxiv.
Our models are generalized kripke structures, where both atomic propositions and transitions between states may take any of the truth values of a given multivalued logic. Applications of temporal logic temporal logic is used in. The term temporal logic has been broadly used to cover all approaches to reasoning about time and temporal information, as well as their formal representation, within a logical framework, and also more narrowly to refer specifically to the modal logic type of approach introduced around 1960 by arthur prior under the name tense logic and subsequently developed further by many logicians and. The density of this real number model is useful in representing the asynchronous nature of each agents. Model predictive control for signal temporal logic speci. Temporal logic model predictive control sciencedirect. The main part of this paper, section 3, is devoted to a fairly detailed exposition of priors basic tense logic. Research article fuzzy temporal logic based railway. However, currently, these models must be translated to another tool to carry out full temporal logic model checking.
Ltl was first introduced as a vehicle for reasoning about concurrent programs by pnueli in 1977 4. Temporal logicsltl model checkingctl model checking temporal logic model checking thomas wahl computing laboratory, oxford university 18 feb, 2009 thomas wahl, oxford university temporal logic model checking 1. Temporal logic and model checking university of cambridge. Properties to be model checked are expressed in ctl. In the latter case, the algorithms return a negative answer accompanied by a counterexample, i. Q then q retains its truth value even after q has been derived. In logic, linear temporal logic or lineartime temporal logic ltl is a modal temporal logic with modalities referring to time. Model checking is required to decide whether a given system satis. Cadp provides generic model checkers for various temporal logic. A linear temporal logic model checking method over finite words. Temporal logic and model checking for operator precedence languages.
In other words, in classical logic the truth of a formula is static. This article proposes an alternative program logic model based on the concepts of learning organizations and systems theory. Mining parametric temporal logic properties in model based design for cyberphysical systems pdf, extended tech report bardh hoxha, adel dokhanchi and georgios fainekos international journal on software tools for technology transfer sttt, 2018. Model predictive control for signal temporal logic. The declarative and relational aspects of alloy make it a desirable language to use for highlevel modeling of transition systems. It is a fragment of the more complex ctl, which additionally allows branching time and quantifiers. Temporal logic model checking techniques are applied, in a natural way, to the analysis of the set of finite traces composing a system log. The implicit event tick is not supported when a stateflow chart in a. Exploiting symmetry in temporal logic model checking. In the branching view, it has a branching, treelike structure, where time may split into alternative course. Essentially, temporal logic extends classical propositional logic with a set of temporal operators that navigate between worlds using this accessibility relation. Deterministic compilation of temporal safety properties in explicit state model checking. Pdf temporal logic and model checking for operator.
We also provide a comparison of features of the temporal logics discussed. Seshia abstractwe present a mathematical programmingbased. Additionally, absolutetime temporal logic is supported in charts that have input events. Linear temporal logic an overview sciencedirect topics. Motivationhyperpctl syntax and semanticshyperpctl in actionhyperpctl model checkingconclusion the need for a probabilistic hyper logic existing probabilistic temporal logics such aspctlandpctl, cannot draw connection between the probability of reaching certain states in independent executions. A comprehensive study of the modeltheory of hybrid logic is the phd thesis of ten cate 2004. Reverse logic right to left asks but how questions forward logic left to right uses ifthen statements.
Thus, 1981 is considered the birth year of model checking. R elated w ork trajectory optimization or model predictive control under temporal logic specications has been considered before in the context of linear temporal logic ltl. Reactive synthesis from signal temporal logic speci. Pdf temporal logic model checking sumit k jha academia. Integrating temporal logics and model checking algorithms. Temporal logic model checking as automated theorem proving.
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