D. Peleg. Concurrent dynamic logic. Journal of the ACM, 34(2):450-479, 1987.  Home/Search   Document Not in Database   Summary   ACM   TOC   Related Articles   Check

....that whether we can give EPDL a semantics of conditional logic. We believe that dynamic logic as an axiomatic logical system of action has a very promising future for applications in planning, cognitive robot and intelligent agent. It is hoped to extend EPDL further with the approach in [Peleg 1987] [Chen and Giacomo 1999] and etc. in order to express con current actions. However, a big challenge for reasoning about action with dynamic logic is whether first order dynamic logic can be also extended, without lost of completeness of its deductive system and embedability of first order ....

D. Peleg, Concurrent dynamic logic, J. ACM, 34(2):450-479, 1987.

....of sets of states U . The intuition is that starting in state u, the (concurrent) program can be run with its concurrent execution threads ending in the set of final states U . The basic concurrency operator will be denoted here by , although in the original work on concurrent Dynamic Logic ( Peleg, 1987b; Peleg, 1987c; Peleg, 1987a] the notation is used. The syntax of concurrent PDL is the same as PDL, with the addition of the clause: if ; 2 , then 2 . The program means intuitively, Execute and in parallel. The semantics of concurrent PDL is defined on Kripke ....

....assign to atomic programs sequential, non parallel, meaning; that is, for each a 2 0 , we require that if (u; U) 2 mK (a) then #U = 1. The true parallelism will stem from applying the concurrency operator to build larger sets U in the reachability pairs of compound programs. For details, see [Peleg, 1987b; Peleg, 1987c] The relevant results for this logic are the following: THEOREM 53. PDL concurrent PDL. THEOREM 54. The validity problem for concurrent PDL is decidable in deterministic exponential time. Axiom System 17, augmented with the following axiom, can be be shown to be complete for ....

[Article contains additional citation context not shown here]

D. Peleg. Concurrent dynamic logic. J. Assoc. Comput. Mach., 34(2):450--479, 1987.

....two sorts of nondeterminism as discussed at the beginning of section 3, or deal with the related notion of concurrency. We will briefly consider two such systems: one is the system of [Mey92] in which internal and external nondeterminism are considered for events, the other one is the system of [Pel87] that deals with concurrency. The system of [Mey92] is based on the following two equivalences: ffl do i (ff 1 Phi ff 2 ) do i (ff 1 ) do i (ff 2 ) ffl do i (ff 1 ff 2 ) do i (ff 1 ) do i (ff 2 ) It turns out that Meyer s starting point is exactly the opposite of ....

....The external observer has the implicit assumption that the agent shows a demonic behaviour, and that the external environment shows an angelic one. Thus the approach of Meyer is not in contradiction with ours: a shift in perspective causes these two approaches to behave differently. In [Pel87] Concurrent Dynamic Logic (CDL) is defined. In CDL the operator is used to combine two actions ff 1 and ff 2 into a new action, with intuitive meaning ff 1 and ff 2 in parallel . The operator is such that the following is a valid formula: ffl do i (ff 1 ff 2 ) do i (ff 1 ) do i ....

[Article contains additional citation context not shown here]

D. Peleg. Concurrent dynamic logic. Journal of the ACM, 34(2):450--479, 1987.

....6.6 essentially follows [97] except that we used a di#erent translation function which eliminates the need for an additional conjunct which forces the Kripke model to be of a particular shape. As a result, the proof of lemma 6.23 is simplified. Concurrent Propositional Dynamic Logic (CPDL, [108]) is a system closely related to Game Logic. Where Game Logic talks about games, CPDL talks about concurrent programs. Due to this di#erent interpretation, CPDL is not exactly a sublogic of Game Logic since the E # functions are not assumed to be monotonic. CPDL contains two disjunctions, ....

....survey articles and [60] for a recent textbook. A further reference which treats also other logics used in computer science is [54] RPDL (which is also known as #PDL) and a closely related system LPDL (PDL loop) are studied in [61] Concurrent Propositional Dynamic Logic was introduced in [108] and followed up by [107] For textbooks on Process Algebra, see [49, 8] Game semantics for Linear Logic is discussed in [21, 2] Game Over In this final chapter, we take another look at the relationship between Game Logic and Coalition Logic, showing that they embody two di#erent approaches to ....

D. Peleg. Concurrent dynamic logic. Journal of the ACM, 34(2):450--479, 1987.

....chooses a pawn. He puts it on square one. 8x 2 player) 9y 2 pawn) chooses(x; y) puts on sqr one(x; y) The interested reader is referred to Fernando [7] where the step from f 2 Var M to non empty sets F Var M of such is linked to conjunctive branching, introduced into dynamic logic in Peleg [23] and widely found in so called and or graphs for 2 person games. 5 Discussion Having associated dynamic and proof conditional semantics (in the introduction) with the intriguing proposals (D) and (P) suggesting that truth be updated and proofs used in constructing well formed formulas, let us ....

David Peleg. Concurrent dynamic logic. J. Assoc. Computing Machinery, 34(2), 1987.

....First, the language of dynamic logic is expressive. It provides built in expression of compound actions (i.e. generated from primitive actions by the program connectives ; non deterministic e ects and quali cations of actions. It has also been extended to represent concurrent actions [24, 11], non execution of actions [9] indirect e ects of actions [12, 29] Second, dynamic logic features a sound and complete axiomatic deductive system and a well developed Kripkean semantics. Its proof and model theory have reached a high degree of sophistication through the development of ....

Peleg, D. 1987. Concurrent dynamic logic, J. ACM, 34(2):450-479.

....that whether we can give EPDL a semantics of conditional logic. We believe that dynamic logic as an axiomatic logical system of action has a very promising future for applications in planning, cognitive robot and intelligent agent. It is hoped to extend EPDL further with the approach in [Peleg 1987] [Chen and Giacomo 1999] and etc. in order to express concurrent actions. However, a big challenge for reasoning about action with dynamic logic is whether rst order dynamic logic can be also extended, without lost of completeness of its deductive system and embedability of rst order in nitary ....

D. Peleg, Concurrent dynamic logic, J. ACM, 34(2):450-479, 1987.

....of program veri cation [Hoare 1969] Programs with parallel composition operators have been considered by several authors (e. g [Apt et al. 1980] Dynamic logics, originally de ned over sequential programs [Harel 1984] have been extended with an operator for intersection to model synchronization [Peleg 1987]. However, a lot of work remains to be done on characterizing models for true concurrency using program indexed logics. 26 ....

Peleg D 1987 Concurrent dynamic logic, J. ACM 34,2:450-479.

....DL also non deterministic ones (due to program connectives [ and ) Consequently, means modal possibility (cf. 5] De nition 2. 4 By concurrent dynamic logic (CDL) we shall mean DL augmented with additional program connective , and the following rule concerning its semantics (cf. e.g. [12]) I; v j= CDL P Q A i I; v j= CDL P A and I; v j= CDL Q A: We shall say that I is a CDL model for a formula A 2 L(MCDL ) and denote this by I j= CDL A, i for any valuation v, I; v j= CDL A. 2 The last logic to be de ned in this section is temporal logic (TL) The version of TL we ....

Peleg D.: Concurrent Dynamic Logic, JACM, 34, 2, 1987, 450-479.

....for these logics do not exist. This explains why no axiomatizations for the logics on trace systems have existed so far. The lack of finitary axiomatizations is rather unusual for propositional logics. However, several examples of such logics are already known in the literature (see [Pe87, Pa91, LPRT92] In the present paper we give infinitary complete proof systems for several temporal logics interpreted on trace systems like the propositional version of the logic defined in [PKP91] an essential subset of CTL P [Pe93a] and of Interleaving Set Temporal Logic [PP94] The proof ....

: Peleg, D., Concurrent dynamic logic, Journal of ACM 34 (2), pp. 450--479, 1987.

....of concurrency, although recent work has explored logics for true concurrency [Thi94] Finally, other logics have also been developed for reasoning about concurrent systems, including various dynamic logics and logics of knowledge. The former permit the inclusion of programs inside formulas [Pel87] while the latter allow users to express the understanding that individual agents have of other agents states at a given point in time [HM90, HZ92] Behavioral Relations. Another popular approach to specifying concurrent systems involves the use of behavioral equivalences and preorders to ....

D. Peleg. Concurrent dynamic logic. Journal of the ACM, 34(2):450--479, April 1987.

....M (s) j= OE which implies that A is universal. 2.3.2 Application: PDL with concurrency In this section we give an application of our completeness technique for a variant of PDL. In this application we use the infinitary system AX1 and the variant is an addition of axioms to this system. Peleg [22] defined a variant of PDL by introducing the concurrency operator : Pi Theta Pi 7 Pi which has the following semantics for any Kripke model M: M; s j= hff fiiOE iff M; s j= hffiOE and M; s j= hfiiOE. An axiomatization for the resulting logic follows easily. Definition 2.12 The set AXC ....

Peleg, D., "Concurrent Dynamic Logic", J.ACM 34,2 (1987), 450--479.

.... of non deterministic behaviour by a set of (abstract) graphs [2, 21] on the other hand, the seperation of branching into non deterministic branching and concurrent branching by the conflict relation for event structures [27] or by introduction of and nodes leading to and or trees (e.g. [20]) The syntax and semantics of the process algebraic language derived from relational algebra are defined by the mathematical method of universal algebra (e.g. 9] syntax is given by a definition of the form X = X; r 1 ; r n ) is an S iff conditions hold , i.e. by the definition of a ....

.... use relational algebra aiming at concrete binary relations, we rather use the fact that relation algebras are boolean algebras with operators and they have associated atom structures [12, 14, 16] adding a concurrency operator to the framework of binary relations has been done in former years (see [20]) Thus, we do not use graphs as relations by their associated relation, we accept graphs as atomic elements of an abstract relation algebra. References 13 Finally, one of the decisive objectives of the paper has been the modelling of undo by the transposition operator, which arises from ....

Peleg, D., Concurrent Dynamic Logic, in: Journal of the ACM 34:2 (1987) 450--479

.... into object oriented DBMS (OODBMS) 19, 20] or enhance SQL with object oriented capabilities [16] The next step of this research will be to precisely define which are the relations between Linear Logic and other formalisms developed to assign a semantics to transactions and updates, e.g. [6, 41, 28]. See also the final section for a brief comparison between our approach and some of the above mentioned ones. In this work we have applied techniques already present in our previous studies on object orientation and concurrency [13, 14] These efforts allowed us to enrich our E hhf based ....

....this aspect into a database setting allows to fully characterize deductive object oriented databases. An aspect not yet provided by T L. As future development of this work, we plan to study from a more general point of view the relations between Linear Logic and the other approaches (e.g. [6, 41]) used to formalize the semantics of database systems, in order to capture other important notions like atomicity of a sequence of operations. Furthermore, we will implement a complete encoding of Chimera in the E hhf system, under development using Prolog, to experiment the connections between ....

D. Peleg. Concurrent Dynamic-Logic. Journal of ACM, 34(1):450--479, 1987.

....as much attention as it deserves. In fact, dynamic logic has many advantages in two aspects of representation and reasoning about actions and its e ects. First, dynamic logic can express compound actions 1 , indeterminate e ects of actions and can be extended to express concurrent actions ([15]) Second, it has an axiomatic deductive system that is sound and complete relative to a well developed semantics ( 8] Its complexity of computation (propositional dynamic logic is decidable and rst order one can be embedded in rst order in nitary logic L 1 ) is also well understood. ....

D. Peleg, Concurrent dynamic logic, J. ACM, 34(2), 1987, 450-479.

....results are expected in the application of these techniques to logical characterizations of objects and agents. Currently we are also investigating the relationships between linear logic and other formalisms developed to assign a semantics to transactions and updates in database systems, e.g. [6, 39, 27]. Forum also provides meta programming techniques inherited from higher order programming languages like Prolog [36] This aspect has interesting applications to the definition of high level supporting languages which can help the designing and the prototyping of deductive object oriented database ....

D. Peleg. Concurrent Dynamic-Logic. Journal of ACM, 34(1):450--479, 1987.

....9.1 Concurrent PDL Although we have postponed the modal analysis of k, the concurrency notion from process algebra, for future work, we do have something to say about concurrency. We will briefly look here at an extension of PDL with an operator for concurrency of programs. Concurrent PDL [35] has the following syntax. CPDL formulas : p j : j ( j h i j [ CPDL programs : a j j ; j [ j j The idea of the new operation 1 2 is: do 1 and 2 concurrently. Because CPDL allows programs to compute in parallel, several states may be reached in ....

....The full interpretation of program relations in a model M now runs as follows: ffl The accessibility relations for the atoms are given. ffl R 1 ; 2 = R 1 fi R 2 . ffl R 1[ 2 = R 1 [ R 2 . ffl R 1 2 = R 1 Omega R 2 . ffl R = R ( ffl R = fhs; fsgi j M; s j= g. Peleg [35] gives computational motivation, Goldblatt [25] has a completeness result. 9.2 CPDL Bisimulation Now, we introduce the appropriate generalization of our central notion of process equivalence. Definition 9.1 A relation C S(M) Theta S(N ) is a CPDL bisimulation (see Figure 17) if the following ....

D. Peleg. Concurrent dynamic logic. Journal of the ACM, 34:450--479, 1987.

....is to think of Result as a relation, rather 19 than as a function. For example, we can introduce RES(a; s 1 ; s 2 ) with the intuitive meaning that s 2 is one of the situations resulted from executing a, along with possibly some other actions, in s 1 . This is essentially the approach taken in [5, 21], and others. The drawback of this approach is that it does not explicitly list the additional actions that cause the transition from s 1 to s 2 . Thus Georgeff [5] had difficulty in formalizing the effect of a single action when performed exclusively. We have been only recently aware of a closely ....

D. Peleg. Concurrent dynamic logic. Journal of ACM, 34:450--479, 1987.

....algebra [BK84, Hoa85, HM85, BW90, vG90] On the other hand, the use of modal logics [Gol92] for characterizing properties of systems has evolved from the early works of Floyd [Flo67] and Hoare [Hoa69] on reasoning about programs. Among them we mention in particular dynamic logics [FL79, Har79, Pel87] temporal logics [Pnu77] and, more recently, logics of knowledge [HM90, HZ92, FHMV95] The distributed logics defined in this paper are based on temporal logic and an extension towards concurrency called n agent logic. Temporal logic has been succesfully applied to a number of reactive systems ....

D. Peleg. Concurrent dynamic logic. Journal of the ACM, 34(2):450--479, 1987.

....of locality or scope analyzed in Saraswat [14] should not be confused with what is called force below. No claim is (of course) made here that (i) and (ii) represent the proper notions of quantification and parallelism; only that there are works (e.g. Groenendijk and Stokhof [4] Peleg [13], and the references cited therein) where notions of quantification and parallelism different (in essential ways) from Saraswat [14] are studied (and that such notions are what concern the present paper) The clash in terminology is unfortunate, and surely ought to be resolved. The concluding ....

.... Kleene [9] can be adapted to ) or, more modestly, of (ii) extending the collection of states by a single application of the powerset construct, and then treating a state given by a set of states as a family of processes running conjunctively in parallel, as in Concurrent Dynamic Logic (Peleg [13]) The relationship between (i) and (ii) can be explained in the framework of labelled transition systems, on the basis of a transformation L that is essentially the familiar construction of a deterministic finite automaton from a non deterministic one (e.g. Hopcroft and Ullman [7] The ....

[Article contains additional citation context not shown here]

David Peleg. Concurrent dynamic logic. J. Assoc. Computing Machinery, 34(2), 1987.

....suggested in the present work. However, this deficiency has been recognized by some dynamic logicians, and has motivated the development of a number of frameworks for the representation of concurrency in dynamic logic. Dynamic logics have been proposed which model alternating computations [100] and which are built on the shuffle model of concurrency [96] Most closely related to our work in this dissertation, however, is the family of process logics proposed by Pratt [105] The semantics of process logic associates to an action a set of sequences representing the executions of the ....

D. Peleg. Concurrent dynamic logic. Journal of the ACM, 34(2):450--479, 1979.

....and 4.1 are towards the data oriented end of the spectrum, while Examples 2.4, 2.5 and 4.2 are towards the process oriented end, and Example 2.2 is in the middle. A comparison of Transaction Logic and the recently developed pi calculus [53, 54] can be found in [16] Concurrent Dynamic Logic: In [61, 60], Peleg develops Concurrent Dynamic Logic (CDL) There are two versions of CDL. The version developed in [61] is very different from TD. It is modeled on the kind of concurrency found in alternating Turing machines, which does not allow for communication between concurrent processes. A ....

....end, and Example 2.2 is in the middle. A comparison of Transaction Logic and the recently developed pi calculus [53, 54] can be found in [16] Concurrent Dynamic Logic: In [61, 60] Peleg develops Concurrent Dynamic Logic (CDL) There are two versions of CDL. The version developed in [61] is very different from TD. It is modeled on the kind of concurrency found in alternating Turing machines, which does not allow for communication between concurrent processes. A deductive database analogue of this version of CDL is Hypothetical Datalog [11] in which hypothetical databases ....

D. Peleg. Concurrent-dynamic logic. Journal of ACM, 34(2):450 -- 479, March 1987.

....one of the sets S i does not contain an accepting state. 3 PDL with Interleaving We review Abrahamsons s [1] definition of PDL with interleaving added as a program constructor. We call this logic interleaving PDL to avoid confusion with other definitions of concurrent PDL in the literature, e.g. [7, 15]. We begin with a set Phi 0 of atomic formulas that represent propositional variables and a set Psi 0 of atomic programs that represent indivisible program steps. Syntactically, if p and q are formulas and a and b are programs, then p q and :p are formulas, haip is a formula meaning it is ....

D. Peleg, Concurrent dynamic logic, J. Assoc. Comput. Mach. 34 (1987) 450-- 479.

....working in process algebra [BK84; Hoa85; HM85; BW90; vG90] On the other hand, the use of modal logics [Gol92] for characterizing properties of systems has evolved from the early works of Floyd [Flo67] and Hoare [Hoa69] on reasoning about programs. Among them we stress dynamic logics [FL79; Har79; Pel87] temporal logics [Pnu77] and, more recently, logics of knowledge [HM90; HZ92] The distributed logics defined in this paper are based on temporal logic and an extension towards concurrency called n agent logic. Temporal logic has been succesfully applied to a number of reactive systems ....

D. Peleg. Concurrent dynamic logic. Journal of the ACM, 34(2):450--479, 1987.

....two sorts of nondeterminism as discussed at the beginning of section 3, or deal with the related notion of concurrency. We will briefly consider two such systems: one is the system of [Mey92] in which internal and external nondeterminism are considered for events, the other one is the system of [Pel87] that deals with concurrency. The system of [Mey92] is based on the following two equivalences: ffl do i (ff 1 Phi ff 2 ) do i (ff 1 ) do i (ff 2 ) ffl do i (ff 1 ff 2 ) do i (ff 1 ) do i (ff 2 ) It turns out that Meyer s starting point is exactly the opposite of ....

....The external observer has the implicit assumption that the agent shows a demonic behaviour, and that the external environment shows an angelic one. Thus the approach of Meyer is not in contradiction with ours: a shift in perspective causes these two approaches to behave differently. In [Pel87] Concurrent Dynamic Logic (CDL) is defined. In CDL the operator is used to combine two actions ff 1 and ff 2 into a new action, with intuitive meaning ff 1 and ff 2 in parallel . The operator is such that the following is a valid formula: ffl do i (ff 1 ff 2 ) do i (ff 1 ) do i ....

[Article contains additional citation context not shown here]

D. Peleg. Concurrent dynamic logic. Journal of the ACM, 34(2):450--479, 1987.

....promoted by these languages is related to rewriting logic and linear objects in the sense that once the flow of control commits to a certain action, this action never backtracks; this style is quite unlike the one promoted by CT R. Finally, a comparison of CT R with Concurrent Dynamic Logic (CDL) [29, 28] is in order. There are two versions of CDL. The version developed in [29] is very different from CT R. It is modeled on the kind of concurrency found in alternating Turing machines, which does not allow for communication between concurrent processes. A deductive database analogue of this version ....

....the sense that once the flow of control commits to a certain action, this action never backtracks; this style is quite unlike the one promoted by CT R. Finally, a comparison of CT R with Concurrent Dynamic Logic (CDL) 29, 28] is in order. There are two versions of CDL. The version developed in [29] is very different from CT R. It is modeled on the kind of concurrency found in alternating Turing machines, which does not allow for communication between concurrent processes. A deductive database analogue of this version of CDL is Hypothetical Datalog [5] in which hypothetical databases ....

D. Peleg. Concurrent-dynamic logic. Journal of ACM, 34(2):450 -- 479, March 1987.

No context found.

D. Peleg. Concurrent dynamic logic. Journal of the ACM, 34(2):450-479, 1987.

No context found.

: Peleg, D., Concurrent dynamic logic, Journal of ACM 34 (2), pp. 450--479, 1987.

No context found.

D. Peleg. Concurrent dynamic logic. In Proceedings of the seventeenth annual ACM symposium on Theory of computing, pages 232--239. ACM Press, New York, 1985.

No context found.

Peleg, D. (1987). Concurrent Dynamic Logic, J.Comp.Syst.Sci., vol.35, pp.450-479

No context found.

Peleg, D. (1987). Concurrent Dynamic Logic, J.Comp.Syst.Sci., vol.35, pp.450-479

No context found.

Peleg, D.: Concurrent Dynamic Logic, Journal of the ACM, 34(2), 1987, 450--479.

No context found.

Peleg, David (1987), `Concurrent dynamic logic', Journal of the Association for Computing Machinery 2: 450-479.

No context found.

Peleg, D. Concurrent dynamic logic, J. ACM, 34(2):450-479,1987.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC