Emerson E. A., and J. Srinivasan (1989) Branching time temporal logic, Linear Time, Branching Time and Partial Order, Proceedings of Logics and Models for Concurrency, Springer-Verlag, pp. 123--172.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....has been spent trying to extend CTL (because it lacks expressive power, most notably for fairness properties) without losing the e cient model checking algorithms that CTL permits . 4.2. 1 A selection of branching time logics Several natural fragments of CTL # have been identi ed and named [ES89, Eme90] Below we consider: an extension of CTL, introduced in [EH86] and where Boolean combinations (not nesting) of temporal modalities are allowed under the scope of a path quanti er. e.g. CTL allows formulae like A(aUb cUd) There exists a translation from CTL to CTL [EH85] ....

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, volume 354 of Lect. Notes in Comp. Sci., pages 123172. Springer, 1989.

....for each observable action. It simply suffices to investigate the computation tree of the labelled transition graph under consideration up to depth jOEj, where jOEj denotes the size of OE defined in the usual way by counting the number of operators. The Logics EF, EG and UB The logic EF [50] is obtained from HennessyMilner logic by adding the operator EFOE, meaning there exists a path such that eventually OE holds . This addition increases the expressive power of the logic significantly, as it becomes possible to reason about paths of arbitrary length. In fact, it already suffices ....

E.A. Emerson and Srinivasan. Branching time temporal logic. In J.W. de Bakker, W.-P. de ROever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, LNCS 354, pages 123--172. Springer, 1989.

....for reasoning about non deterministic, concurrent and reactive programs. Since then, a number of linear and branching time temporal logical systems have been put forward with this purpose, some of the most popular ones of the latter type being UB, CTL, CTL and variations of them (see (Emerson and Srinivasan, 1989; Emerson, 1990) Penczek, 1995) and (Stirling, 1992) for surveys on these) Since CTL subsumes the others, it will be the one in the focus of this paper, though the results will accordingly apply to the others as well. Besides the computational interpretation, branching time logics have ....

....outlined here was introduced and axiomatized in (Goranko, 1994) 2.2. Computation Tree Logics The full branching time computation tree logic CTL was introduced in (Emerson and Halpern, 1983) Here we o er a very brief summary of the syntax and semantics of CTL , referring the reader to (Emerson and Srinivasan, 1989), Emerson, 1990) or (Penczek, 1995) for more detail. 2.2.1. Syntax The language of CTL is a propositional language with a set of atomic propositions (propositional variables) AP, temporal operators X (nexttime) and U (until) and path quanti ers, 8 meaning for all paths , and its dual 9, ....

Emerson E.A. & J. Srinivasan, Branching Time Temporal Logic, in: Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, J de Bakker, W.-P. de Roever, G. Rosenberg (eds.), LNCS 354, Springer-Verlag, 1989, 123-172.

....change the extensional part. Vice versa, a proposal for expressing actions as updates was given in [14] 9. 2 Temporal Logics for BDI agents Temporal aspects are addressed in BDI agents (Belief, Desire, Intention; see, e.g. 81] by means of an extension of the branching time temporal logic CTL [65]. This approach is based on a possible worlds model, represented by a time tree with a single past and a branching time future. Branches in the time tree represent the different choices available to the agent at each given point of time, as to which action to be performed. A set of ....

E. Emerson and J. Srinivasan. Branching Time Temporal Logic. In J. D. Bakker, W. D. Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop (REX Workshop'88), volume 354 of Lecture Notes in Computer Science (LNCS), pages 123--172. Springer Verlag, 1988.

....specifications for Computational Tree Logic, CTL [18] a propositional branching time temporal logic, and for other four related temporal logics. The first is a custom extension of 58 CTL, called CLT e [67, 66] We will also show how model checking algorithms can be generated for the logics CTL [25, 24] and the real time temporal logic RTCTL [28] as well as a symbolic model checking algorithm for CTL [9] 5.1 Computational Tree Logic Formally, a model M is a tuple M = hS; E; P : AP 2 S i, where S is a finite set of states (also called nodes) S = fs 1 ; s 2 ; s m g, and E is a ....

....j= f 2 and 8j; 0 j i; p j j= f . The theory behind model checkers for CTL is well understood, to the best of our knowledge and others [16] no one else has implemented a CTL model checking algorithm. One reason for this is the fact that a CTL model checking algorithm is a P SPACE algorithm [25]. 74 Algebraically, the syntax algebra of CTL is a heterogeneous algebra in which the carrier sets are the state formulas SF and path formulas PF with operations corresponding to the rules given above. There are distinct logical and : operators for state formulas and path formulas, as indicated ....

E. Allen Emerson and Jai Srinivasan. Branching time temporal logic. In J. W. de Bakker, W. P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, number 354 in Lecture Notes in Computer Science, pages 123--172, New York, 1988.

....among the system and the designer based on temporal logic than petri nets invariants. The temporal logic formulas we will use consist of progress conditions specifying relations among states, and exclusion conditions specifying that certain states cannot be present (or absent) at the same time [5, 7]. The temporal logic operators we use are 2, 3, r. Informally, 2 means always ( it is always true that Delta Delta Delta ) 3 means eventually ( now or at some point in the future it will be true that Delta Delta Delta ) and r means next time ( at any next point in time it will be ....

E.A. Emerson and J. Srinivasan. Branching time temporal logic. In J.W. Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, volume 354 of Lecture Notes in COmputer Science. Springer-Verlag, 1988.

....Temporal Logics; Automated Verification. This research has been partly supported by the Netherlands grant NWO NF 3 62 500 and a grant from The Wolfson Research Awards Scheme in The United Kingdom. 158 On temporal logics on trace systems 159 1 Introduction Linear time [1] and branching time [2] temporal logics are usually applied for specifying and proving properties of concurrent systems and programs. Lately, several attempts have been made to use also logics interpreted over partial order structures [3 14] The main motivation for defining these logics was to express properties ....

: Emerson, E.A., Srinivasan, J., Branching Time Temporal Logic, LNCS 354, 1988.

....be interspersed before and after each a i . Modal logic expresses properties of processes as their behaviour unfolds through transitions. Temporal logic, on the other hand, ascribes properties to processes by expressing features of some or all of their runs. For surveys of temporal logic see [31, 49, 64]. In fact there is not a clear demarcation because modal operators can also be viewed as temporal operators, which express next : E 0 j= K] Phi iff for all E 0 runs E 0 a1 Gamma E 1 a2 Gamma : if a 1 2 K then E 1 j= Phi: E 0 j= hKi Phi iff for some E 0 run E 0 a1 Gamma E 1 ....

Emerson, E, and Srinivasan, J. (1989). Branching time temporal logic. Lecture Notes in Computer Science, 354, 123-284.

....[RG95, KGR96, Bra87] agents are supposed to be rational and have, as said in [RG95] mental attitudes of Belief, Desire, and Intention (BDI) representing, respectively, the information, motivational, and deliberative states of the agent. Such agents have been formalized using temporal logics [EJ89] together with modal operators for beliefs, desires and intentions [RG91, CH90] We see two connections between these approaches and our approach; ffl The formulation of agent behavior using the temporal logic CTL and its extensions [Sin94, RG91] represents worlds as time trees. These time ....

E. A. Emerson and J.Srinivasan. Branching time temporal logic. In J.W. de Bakker, W. P. de Roever, and G. Roezenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer-Verlag, Berlin, 1989. 52

....particular for reasoning about non deterministic, concurrent and reactive programs. Since then, a number of linear and branching time temporal logical systems have been put forward with this purpose, some of the most popular ones of the latter type being UB, CTL, CTL and variations of them (see [ES 89, Eme 90] Pen 95] and [Sti 92] for surveys on these) The logic CTL will be in the focus of this paper, though the results will accordingly apply to all others subsumed by it, as well. Besides the computational interpretation, branching time logics have important philosophical and purely ....

....languages with pointers (binders) without universal modality have been axiomatized. 4 1. 2 Computation Tree Logics The full branching time computation tree logic CTL was introduced in [EmH 83] Here we offer a very brief summary of the syntax and semantics of CTL , referring the reader to [ES 89] Eme 90] or [Pen 95] for more detail. 1.2.1 Syntax The language of CTL is a propositional language with a set of atomic propositions (propositional variables) AP, temporal operators X (nexttime) and U (until) and path quantifiers, 8 meaning for all paths , and its dual 9, meaning for ....

Emerson E.A. & J. Srinivasan, Branching Time Temporal Logic, in: Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, J de Bakker, W.-P. de Roever, G. Rosenberg (eds.), LNCS 354, Springer-Verlag, 1989, 123-172.

....logics, and , meaning necessity and possibility, are interpreted as always and eventually respectively in temporal logics. Different temporal logics have been developed for differing underlying orderings of events and so for example, may be linear [Pnu77, Pnu81, MP92] or branching [BAMP81, CE81, ES88] discrete or dense [BG85, BKP86] or may be based on intervals [HMM83, Mos83, SMSV83] However, here we will consider linear, discrete temporal logics, unless we state otherwise. Models of propositional temporal logic can be represented as a sequence of states indexed by the natural numbers. Each ....

....system can still be applied. 126 Application to Branching Time Throughout the thesis we have considered linear time temporal logics and models of such logics have been a series of states. If we relax the forwards linearity constraint to consider branching time temporal logics [Lam80, EH86, ES88] models will have a tree like structure that branches into the future (if the backwards linearity constraint is maintained) Thus, the syntax of branching time logics have operators related to paths, 8, for all paths and 9, there exists a path, and operators relating to states, g and U ....

E. A. Emerson and J. Srinivasan. Branching Time Temporal Logic. Lecture Notes in Computer Science, 354:123--172, 1988.

....and Petri nets [Rei] also have transition systems asssociated with them in a natural way to explain their operational behaviours. Consequently, a variety of logics that have been proposed to reason about the behaviours of distributed systems are based on models built out of transition systems [Pnu, ES, HM]. A classic and powerful example of such logics is the propositional calculus [Koz] The transition systems that are used in such applications are, however, sequential. A (labelled) transition in these transition systems is a triple (s; a; s 0 ) denoting that the system can perform the (single) ....

Emerson, E.A., and Srinivasan, J. (1989), Branching time temporal logic, LNCS 354, 123-172.

....defined in Appendix A. Some well known temporal operators that can be introduced as abbreviations are F (finally or sometime) G (globally or always) and [a] inevitably after a) ffl F stands for U , ffl G stands for : F : ffl [a] stands for A: X a : X ) U ) 3 CTL [8] is the standard full branching time temporal logic. 5 We also use the abbreviation [a 1 ; a n ] for [a 1 ] a n ] Note that [a] means that, for all paths from the current state with an a transition as its first transition, will be true after this a transition and ....

E.A. Emerson and J. Srinivasan. Branching time temporal logic. In J.W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer Verlag, LNCS 354, 1989.

....checker without any internal changes. 1 Introduction To formulate the specification properties of a given design many different temporal logics are available, each of them with a different expressive power: Fair ) CTL [6] is a branching time logic, LTL [18] is a linear time logic and CTL [13] is a superset containing both of them. CTL itself is a subset of the calculus [17] which in addition allows to verify bisimulation and other more complex properties. In practice, however, the characteristics people mainly try to verify are simple safety properties that are expressible in all ....

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In REX workshop, volume 354 of LNCS, pages 123--172. Springer-Verlag, 1989.

....In [RG95,KGR96,Bra87] agents are supposed to be rational and have, as said in [RG95] mental attitudes of Belief, Desire, and Intention (BDI) representing, respectively, the information, motivational, and deliberative states of the agent. Such agents have been formalized using temporal logics [EJ89] together with modal operators for beliefs, desires and intentions [RG91,CH90] We see two connections between these approaches and our approach; The formulation of agent behavior using the temporal logic CTL and its extensions [Sin94,RG91] represents worlds as time trees. These time trees ....

E. A. Emerson and J.Srinivasan. Branching time temporal logic. In J.W. de Bakker, W. P. de Roever, and G. Roezenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer-Verlag, Berlin, 1989.

....be verified latter when analyzing the environment interacting with the analyzed G Net. The basic principle to be adopted is the natural partition of the state space problem and then apply an assume guarantee like paradigm to verify the behavior of the G Net system. Computation Tree Logic (CTL)[11] is employed as a query language to extract the abstraction of a G Net and to express the properties of the environment. 16 3.1 G Net Decomposition The objective to decompose a G Net is to provide a clear structural coupling among G Nets. This structural coupling imposes restrictions in the ....

E.A. Emerson and J. Srinivasan. Branching time temporal logic. In J.W. Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, volume 354 of Lecture Notes in COmputer Science. Springer-Verlag, 1988.

....syntax and semantics of one of the most powerful of these branching time logics called CTL , and point to the abundant literature for tableau methods for these logics. 5.2. 1 Syntax of Branching Temporal Logics We again concentrate on the future fragment only and follow Emerson and Srinivasan [ES88] using new modal connectives E and X in addition to U . 74 Rajeev Gor e The syntax of branching time logics is given in terms of state formulae and path formulae where state formulae are true or false at some state (world) and where path formulae are true or false of (rather than on) a ....

....if there is some model M containing some path x such that x j= P , and is valid if for every model M and every fullpath path x in M we have x j= P . As Emerson and Srinivasan note, a menagerie of branching time temporal logics can be obtained by restricting or extending these definitions [ES88]. Note that path formulae cannot be evaluated at states since there are no clauses in the definition of j= for evaluating XP or P UQ at a state. But a state formula P can be evaluated on a fullpath simply by checking if the first state of the fullpath satisfies P . Hence, if P is a state formula, ....

[Article contains additional citation context not shown here]

E. Allen Emerson and Jai Srinivasan. Branching time temporal logic. In Proc. School/Workshop on Linear Time, Branching Time and Partial Order In Logics and Models of Concurrency, The Netherlands, 1988, LNCS 354, pages 123--172, 1988.

....intended as complete surveys of the field. Rather they are intended as introductions to the field for non specialists. The references should be consulted for further reading. This paper has benefitted enormously from the papers Clarke and Emerson (1981) Clarke, Emerson and Sistla (1983, 1986) and Emerson and Srinivasan (1988). Thanks also to Allen Emerson, Ryszard Janicki and Peter Lauer for comments on earlier versions of this and the following paper. 1 The system CTL The strongest system of temporal logic we will consider is CTL , which we investigate in this section. Historically, CTL was a development of a ....

Emerson, E.A., Srinivasan, A.J. (1988): Branching time temporal logic. In: Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency: School/Workshop, Noorwijkerhout, The Netherlands, May/June 1988 (ed. J.W. de Bakker, W.P. de Roever, G. Rozenberg). Lecture Notes in Computer Science, 354, Springer-Verlag.

....between the successful execution of events and their failure and label the branches accordingly. As we will see later this is critical in having an agent act on her intentions without requiring her to be successful in her attempts. We use a formalism similar to the Computation Tree Logic CTL [ Emerson and Srinivasan, 1989 ] to describe these structures. A distinction is made between path formulas and state formulas: the former are evaluated at a particular situation and the latter over a path in a time tree. We introduce two modal operators OPTIONAL and INEVITABLE which op2 inevitably eventually q inevitably ....

....p p p p p p f f f f p p p p f f f f f d1 d2 d1 d1 d2 b Belief worlds Goal worlds Intention worlds Events: d1 go to dentist 1, d2 go to dentist 2, b go shopping Facts: p pain, f tooth filled b1 g1 g2 i1 i2 Figure 4: Belief, Goal, and Intention Worlds 4 Formal Theory 4. 1 Syntax CTL [ Emerson and Srinivasan, 1989 ] is a propositional branching time logic used for reasoning about programs. We extend this logic in two different ways: first we describe a first order variant of the logic and second we extend this first order branching time logic to a possible worlds framework by introducing modal operators for ....

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer-Verlag, Berlin, 1989.

....model of rational agency should generalize to the decision theoretic viewpoint when sufficient quantitative data is available. Within such a framework, we now look at the static properties of BDI systems. The BDI systems we consider are extensions of Computation Tree Logics, CTL and CTL [ Emerson and Srinivasan, 1989 ] that have been used extensively for reasoning about concurrent programs. We extend the branching time logics to represent the mental state or belief desireintention state of an agent. These logics can then be used to reason about agents and the way in which their beliefs, desires, and actions ....

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer-Verlag, Berlin, 1989.

....[18] advocates this methodology as a good software engineering methodology. 6 We then present guidelines on how to construct correct triggers from given evolution specifications. Our approach in this paper has some relationship with research in specification and synthesis of concurrent programs [14, 15], and the formalization of the relation between reactive control and theories of actions [5] and automatic construction of reactive control from theories of action [5] In [14, 15] concurrent programs are specified using temporal formulas. They do not use aggregates. In general program synthesis ....

.... Our approach in this paper has some relationship with research in specification and synthesis of concurrent programs [14, 15] and the formalization of the relation between reactive control and theories of actions [5] and automatic construction of reactive control from theories of action [5] In [14, 15] concurrent programs are specified using temporal formulas. They do not use aggregates. In general program synthesis is harder because the allowable statements in a program are more general than allowable modifications to a database. On the other hand the approach in [5] although only considers ....

E. A. Emerson and J.Srinivasan. Branching time temporal logic. In J.W. de Bakker, W. P. de Roever, and G. Roezenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer-Verlag, Berlin, 1989.

....maps a role and a joint plan to the corresponding role plan. 3.2 Meta Language Syntax The meta language ML, used to reason about plans and their execution, needs to be expressive enough to reason about the future and the past. We use a formalism similar to Computation Tree Logic, CTL [ Emerson and Srinivasan, 1989 ] to describe the temporal structures. The temporal structure in CTL is a tree with branching futures and a single past. A distinction is made between path formulas and state formulas: the former are evaluated over a specified path in a time tree; the latter at a specified time point in a ....

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer-Verlag, Berlin, 1989.

....agent act on her inevitably eventually q inevitably always s p q r r s s s s s optionally eventually p s optionally always r s r q q Figure 1: Temporal modalities intentions without requiring her to be successful in her attempts. We use a formalism similar to Computation Tree Logic, CTL , Emerson and Srinivasan, 1989 ] to describe these structures. 1 A distinction is made between state formulas and path formulas: the former are evaluated at a specified time point in a time tree and the latter over a specified path in a time tree. We introduce two modal operators, optional and inevitable, which operate on ....

....and revised as the agent interacts with her environment. Different types of agent will have different schemes for doing this, which in turn will determine their behavioral characteristics. We consider some of these schemes and their formalization in Section 4. 3 FORMAL THEORY 3. 1 SYNTAX CTL [ Emerson and Srinivasan, 1989 ] is a propositional branching time logic used for reasoning about programs. We extend this logic in two ways. First, we describe a first order variant of the logic. Second, we extend this logic to a possible worlds framework by introducing modal operators for beliefs, goals, and intentions. While ....

[Article contains additional citation context not shown here]

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer-Verlag, Berlin, 1989.

....been proposed [Miln80] Hoar85] Miln91] with slightly different characteristics and semantics. They are all derived from the semantic model developed for the Calculus of Communicating Systems (CCS) Miln80] and differ mainly in the set of operators they support. Temporal Logic [EmHe86] MaPu89] [EmSr89] [BCGr88] has been widely recognized as a suitable formalism for specifying temporal properties, supporting the notions of necessity, possibility, eventuality, etc. Model checking algorithms have been developed [BCDM86] and efficient tools exist [BCMD90] Process Algebras and Temporal Logic could ....

....as they offer complementary views of a system. Unluckily, the semantic models are not compatible. Process Algebras are interpreted on Labeled Transition Systems (LTSs) where transitions are labeled with the actions that cause the system to evolve from one state of the system to another. CTL [EmSr89], the most popular version of branching time temporal logic, is interpreted on Kripke structures where states are labeled to show how the truth of a formula is affected by a transition. To make the two worlds communicate, an action based version of CTL has been proposed [DNVa90a] ACTL ) whose ....

E.A. Emerson, J. Srinivasan: "Branching Time Temporal Logic," "Linear Time, Branching Time, and Partial Orders in Logics and Models for Concurrency," de Bakker editor, LNCS 354, Springer Verlag, Berlin (D), 1989, pp. 123-172

....model. Moreover, similar to the case of specification languages, there are several logics which are interpreted over the same class of models di#ering in expressiveness and complexity of the model checking problem. For transitions systems, the most important logics are LTL ( OA85] CTL and CTL ( ES88] and the calculus ( Koz83] Eme97] Linear Time temporal Logic (LTL) is interpreted over the linear behaviour model generated by the underlying transition system. Hence, a formula describes a property of a single run of the system. To determine a property of the system, one usually identifies ....

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proceedings of the School/Workshop on Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123-- 172. LNCS 354. Springer, June 1988.

....By pressing CNC (cancel) this pop up menu is closed, by selecting a value, the parameter is set, and by clicking on the arrows, the values presented are scrolled. 2. 3 The requirements A set of requirements that have to be fulfilled by the data link applications are expressed below in ACTL (Emerson 88) for those that imply temporal constraints, or using set theory for the other ones. Requirements can be classified in two categories : high level requirements related to the very semantics of air traffic control, and lower level ones, related to interaction techniques. A control order is only ....

Emerson E.A., Srinivasan J. Branching Time Temporal Logic, in LNCS 354 p.122-172, Springer-Verlag 1988.

....actions and inform their partners if something goes wrong. Our ontology allows explicit representation of successful and failed executions of plans. In order to capture interesting properties of executions, our temporal model must be very expressive. We use a formalism similar to the logic CTL [ Emerson and Srinivasan, 1989 ] in which the temporal structure is a tree with branching futures and a single past. The logic allows formulas which are evaluated at a specific point of time and also formulas which are evaluated with respect to paths in the tree. So we can reason about current and future possible states of the ....

....type is an abstract structure that, when executed by an agent, results in the occurrence of an action in the real world. Our temporal model of the realworld must be expressive enough to capture the different operations on plan types. We use a formalism similar to Computation Tree Logic, CTL [ Emerson and Srinivasan, 1989 ] to describe the temporal structures. The temporal structure in CTL is a tree with branching futures and a single past. A distinction is made between state formulas and path formulas: the former are evaluated at a specified time point in a time tree and the latter over a specified path in a ....

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer-Verlag, Berlin, 1989.

....of the tree. So, we may want to know: foliageMass(subtree from node n) Or we may want to know if there exists any canopy associate (CA) between nodes a and b: hasCA(branch[a; b] A guide to an appropriate logic comes from modal branching time logics such as the Computation Tree Logic CTL of (Emerson Srinivasan, 1989). In these logics the tree represents possible future histories of a system. The important point, however, is how various expressions related to the tree can be described. In CTL a distinction is made between state formulas and path formulas. State formulas are evaluated at a specified point ....

Emerson, E. A. & Srinivasan, J. (1989), Branching time temporal logic, in J. W. de Bakker, W.-P. de Roever & G. Rozenberg, eds, `Linear Time, Branching Time And Partial Order In Logics And Models For Concurrency', Springer-Verlag, pp. 123--172.

....of the specification into a process based notation such as CSP [Hji93, WM90] To detail completely these approaches is out of the scope of this paper but we just point out two interesting fields of interest that we intend to explore in future work: ffl Branching Semantics and B.D.D. verification [NV90, ES89] ffl Partial Order Semantics and associated verification [Sch94] Proceedings, 7th International Conference on: Putting into practice methods and tools for information system design , Nantes (France) October 95, IUT de Nantes, H. Habrias (Editor) 2 The Case Study: a periodic stream We want ....

E.A. EMERSON and J. SRINIVASAN. Branching Time Temporal Logic. 1989.

....between them. We have previously shown how this can be accomplished using a branching time possible worlds logic [ Rao and Georgeff, 1991b ] Briefly, the structure of our logic is as follows: Each world is a temporal structure with a branching time future and a single past called a time tree [ Emerson and Srinivasan, 1989 ] A particular time point in a particular world is called a situation. Event types transform one time point into another. For each situation we associate a set of belief accessible, goalaccessible, and intention accessible worlds; intuitively, those worlds that the agent believes to be possible, ....

....of the agent. It also de2 scribes how the agent s future beliefs and goals should change if he has to achieve his best plan of action [ Rao and Georgeff, 1991b ] 3 Possible Worlds Model In our earlier work [ Rao and Georgeff, 1991b ] we extended the propositional branching time logic CTL [ Emerson and Srinivasan, 1989 ] to a possible worlds framework and introduced modal operators for beliefs, goals, and intentions. In this section, we enhance this logic by introducing operators for probability (similar to that of Fagin and Halpern [ 1988 ] and payoffs. 3.1 Syntax and Semantics Similar to CTL , we have ....

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer-Verlag, Berlin, 1989.

.... We introduce the syntactic classes SS (simple sequence) and ICS (interval constrained sequence) of global predicates that define sets of global states related through the notion of causality preserving sequencing [12] Our formalism can be viewed as an application of branching time temporal logics [7, 4] to distributed computations. This relationship is further explored in Section 5. The syntax and semantics of class ICS is tailored for specifying and verifying properties that are of interest to distributed computing. The main contribution of our work lies in the development of procedures for ....

....graph) is given to produce the set of models. Interpreting our formulas over observations corresponds exactly to model checking in a linear time temporal logic. Interpreting our formulas over computations, on the other hand, corresponds [17] to model checking in branching time temporal logic [7]. There are strong parallels between our proposal and a particular branching time temporal logic known as computation tree logic (CTL) 4] Our computations are the analogs of the state transition graphs of CTL and the lattice structure representing consistent global states is the analog of the ....

[Article contains additional citation context not shown here]

E.A. Emerson and J. Srinivasan. Branching time temporal logic. In G. Rozenberg J.W. de Bakker, W.-P. de Roever, editor, Linear Time, Branching Time and Partial Order in Logics and Models of Concurrency, volume 354 of Lecture Notes on Computer Science, pages 123--172, Noordwijkerhout, The Netherlands, June 1988. Springer-Verlag.

....make decisions about plans and or deals that satisfy different subgoals or that satisfy their goals only partially. This ability to relax one s goal opens up new opportunities for agreement, and enlarge the space of cooperation. In order to model agents behaviour we use a branching tree structure [7] (as it is common in MAS literature [12, 20] where each branch depicts an alternative execution path, Each node in the structure represents a certain state of the world and each transition an action. Formally, i = s 0 ; s i Gamma1 ; a i ; s i ; s n ) The set of actions ....

E.A. Emerson and J. Srinivasan. Branching time temporal logic. In J.W. de Bakker, de Roever W.P., and G. Rozenberg, editors, Linear Time, Branching Time, and Partial Models in Logics and Models for Concurrency, pages 123--172, Berlin, Germany, 1989. Springer-Verlag.

....so that errors can be detected early in the design process. Also, modification, redesigns, maintenance, and re usability are facilitated when using formal techniques. Among other formalisms adopted for specification and design of distributed software systems Petri nets, 15] and temporal logics [9, 14] are the among the most applied ones. Petri nets as well as temporal logics have been applied for the modeling of many systems that can be characterized as distributed, concurrent and asynchronous. The problem to manage large systems is mainly a question of modularity. Therefore, it would be ....

E.A. Emerson and J. Srinivasan. Branching time temporal logic. In J.W. Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, volume 354 of Lecture Notes in COmputer Science. Springer-Verlag, 1988.

....for achieving these goals fail. If intentions are defined in terms of goals, such means end reasoning is not transparent and can only be captured by resorting to various book keeping mechanisms. 5 Branching Time Intention Logic The language we use for branching time intention logic is a CTL [ Emerson and Srinivasan, 1989 ] branching time logic within a possible worlds framework (see [ Rao and Georgeff, 1991 ] for more details) In addition to the operators of linear time intention logic, the branchingtime logic has two additional operators: inevitable(OE) meaning that in all future paths OE is true; and ....

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer-Verlag, Berlin, 1989.

No context found.

Emerson E. A., and J. Srinivasan (1989) Branching time temporal logic, Linear Time, Branching Time and Partial Order, Proceedings of Logics and Models for Concurrency, Springer-Verlag, pp. 123--172.

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Emerson, E. A., and Srinivasan, J. 1989. Branching time temporal logic. In Bakker, J. W.; Roever, W. P.; and Rozenberg, G., eds., Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency. Berlin: Springer. 123--172.

No context found.

Emerson E. A., and J. Srinivasan (1989) Branching time temporal logic, Linear Time, Branching Time and Partial Order, Proceedings of Logics and Models for Concurrency, Springer-Verlag, pp. 123--172.

No context found.

Emerson, E. A. & Srinivasan, J. (1989), Branching time temporal logic, in J. W. de Bakker, W.-P. de Roever & G. Rozenberg, eds, `Linear Time, Branching Time And Partial Order In Logics And Models For Concurrency', Springer-Verlag, pp. 123--172.

No context found.

E. A. Emerson, J. Srinivasan (1988): Branching Time Temporal Logic, LNCS 354.

No context found.

E.A. Emmerson and J. Srinivasan (1989). Branching Time Temporal Logic. In Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency (J.W.de Bakker, W.P. de Roever and G.Rozenberg eds), pp.123-172.

No context found.

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, volume 354 of Lect. Notes in Comp. Sci., pages 123-172. Springer, 1989.

No context found.

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In J. W. Bakker, W. P. Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Springer, Berlin, 1989.

No context found.

E.A. Emerson and J. Srinivasan. Branching Time Temporal Logic. In J.W. de Bakker, W.P. de Roever, and G. Rozenberg, editors, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172. Lecture Notes in Computer Science, 354, Springer Verlag, 1988.

No context found.

Emerson, E. A., and Srinivasan. Branching time temporal logic. In Proc. of the REX School/Workshop 1988.

No context found.

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proceedings of the School/Workshop on Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, pages 123--172, number 354 in Lecture Notes in Computer Science, Springer, New York, 1988.

No context found.

E. A. Emerson and J. Srinivasan. Branching time temporal logic. In REX workshop, volume 354 of LNCS, pages 123#172. Springer-Verlag, 1989.

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: Emerson, E.A., Srinivasan, J., Branching Time Temporal Logic, LNCS 354, pp. 123-172, 1988.

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E. A. Emerson, J. Srinivasan (1988): Branching Time Temporal Logic, LNCS 354.

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