D. Harel. Towards a theory of recursive structures. volume 1450 of Lecture Notes in Computer Science, pages 36--53. Springer, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in [HLM93] a formal system, designed to deal with both the knowledge and abilities of agents, and the effects of the actions performed by the agent. Based on the concepts given in [Moo80] and [Moo84] the system of [HLM93] is firmly rooted in both epistemic logic (see [MH] and dynamic logic (see [Har79], Har84] KT90] and [Gol92] The actions that we considered in [HLM93] are deterministic: the event that consists of some agent performing some action has a unique outcome. In this paper we will consider a natural extension of the system of [HLM93] given by the introduction of ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer-Verlag, 1979.

....an iteration of plays in the guard of the loop producing true concatenated with complete plays in the body, followed by one single play in the guard, producing false. This is exactly the traced based interpretation used to interpret iteration as early as the 70s (see for example Section 2.3. 4 in [10]) Non termination diverge is interpreted as the empty set of complete plays. Our semantics identi es divergence with the run time error of numerical over ow, which comes about as a result of working with a nite set of integers. 11 Modeling the behaviour of arithmetical exceptions as diverge ....

D. Harel. First-order dynamic logic, volume 68 of Lecture Notes in Computer Science. Springer-Verlag Inc., New York, NY, USA,

....distinction is desired, then two sorts of predicates could be used, one for queries, 8 LOGICS FOR DATABASES AND INFORMATION SYSTEMS and one for updating transactions. This philosophy is quite di erent from the situation calculus [MH69] and from approaches based on dynamic and process logics [Har79; HKP82] where queries and updates are represented by di erent classes of syntactic objects (e.g. predicates vs. function terms vs. modal operators) The rest of this section illustrates our notation and the capabilities of T R through a number of simple examples. The examples illustrate how T ....

....languages de ned in [AV90] This lack of subroutines is re ected in the PSPACE data complexity of some of the languages, since subroutines would lead to alternating PSPACE, that is, EXPTIME [Bon] 1.7.2 Logics for Reasoning about Programs Dynamic Logic and Process Logic. Dynamic Logic [Har79] and Process Logic [HKP82] allow a user to express properties of procedural programs and to reason about them. 13 Dynamic Logic reasons about the initial and nal states of program execution. Thus, one can speak about the result of an execution; e:g: When the program terminates, the value of ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer-Verlag, 1979. REFERENCES 47

....and temporal logic. For each logic there are types of properties and systems for which it is highly suited, and others for which it is not. Epistemic logics are useful for stating knowledge or belief of agents (for example, HM92] Dynamic logics deal well with state changes of programs (see [Har79, Pel87] but are not appropriate for describing the progressive behaviour of programs. Finally, temporal logics are suitable for expressing liveness, fairness, and safety constraints of reactive systems [Pnu77] n agent logics are among the approaches that have been developed to reason about ....

D. Harel. First-order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1979.

....in all three, updates take place on base facts, not derived facts. Nevertheless, the three systems are very different. In EKS, the semantics is purely operational. The emphasis here has been on implementation, not on logical foundations. In Dynamic Prolog, the semantics is based on Dynamic Logic [37]. Unlike Hypothetical Datalog, in which all predicates and rules have equal status, Dynamic Prolog distinguishes many types of predicates and rules. Both EKS and Dynamic Prolog emphasize committed updates as well as hypothetical updates, while work on Hypothetical Datalog includes a logical ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer-Verlag, 1979.

....but the rewards are reduction in proof complexity (among others because of the principle of duality) and true generality (this will be shown in section 4. 5) For dynamic modelling techniques, domains like logic (exception: specialized logics, such as temporal logic [Gal87] and dynamic logic [Har79] and set theory are less suited. Category theory can still be used, but typically, domains like Petri nets and higher order variants thereof and algebraic approaches such as Process Algebra [BW90a] CCS [Mil89] and CSP [Hoa85] are particularly suitable. Petri netbased approaches provide formal ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer Verlag, Berlin, Germany, 1979.

....sense also for classes of infinite structures, provided that they admit a finite presentation. There have been a few studies of descriptive complexity theory on infinite structures concerning, for instance, metafinite structures and complexity theory over the reals [3, 4] recursive structures [8] and, as we do in the present paper, constraint databases (see e.g. 12, 6, 5] and the references there) Constraint databases are a modern database model admitting infinite relations that are finitely presented by quantifier free formulae (constraints) over some fixed background structure. For ....

D. Harel. Towards a theory of recursive structures. volume 1450 of Lecture Notes in Computer Science, pages 36--53. Springer, 1998.

....is advisable to establish a set of axioms and rules for deriving correctness judgements. Based on work of Floyd [8] Hoare [12] proposed a veri cation calculus (originally for partial correctness) now referred to as Hoare logic. The following presentation contains a re ned loop rule due to Harel [11] which leads to total correctness. 2 In classical systems i.e. in which the axiom of excluded middle holds, the distinction between the types bool and Prop is not required. Auxiliary Variables and Recursive Procedures 5 De nition 3.4. A veri cation calculus for Hoare logic is de ned as the ....

....q 1 ( q( 6) leads to a complete system while retaining soundness: Lemma 3.6 (Soundness) The consequence rule (6) preserves soundness. Proof. Straightforward. Theorem 3.7 (Completeness) The veri cation calculus de ned as the least relation satisfying (1) 6) is complete. Proof. See [11]. In the context of partial correctness, a completeness proof has recently been mechanised in Isabelle by Nipkow [18] 6 Thomas Schreiber 4 Imperative Programs with Recursive Procedures In this section, we extend Hoare logic for recursive procedures. Parameter passing is an orthogonal issue ....

D. Harel. First-order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer, 1979.

....can be broadly classified into two categories: those designed for database or logic programming and those designed for reasoning about programs and actions. Prolog [CM81] is an early (and the best known) example of the languages in the first category. The situation calculus [McC63] Dynamic Logic [Har79] and Temporal Logic [Pnu77] are, in our view, the forefathers of the modern approaches to reasoning about actions. As we shall see, both the situation calculus and Dynamic Logic influenced the design of several logic based languages for programming database transactions. Temporal Logic had a ....

....or assert(X) retract(Y ) Also, how does one logically account for the fact that the order of updates is important None of these questions is addressed by Prolog s operational semantics, or by the classical theory of logic programming. 2. 2 Dynamic Logic and Process Logic Dynamic Logic [Har79] and Process Logic [HKP82] allow a user to express properties of procedural programs and to reason about them. 3 Dynamic Logic reasons about the initial and the final states of program execution. For instance, one can speak about the result of an execution; e:g: Variable X assumes value 0 ....

[Article contains additional citation context not shown here]

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer-Verlag, 1979.

....rulebase. Thus, deletions from the database make no sense in intuitionistic logics. One alternative is to view our logic as a dynamic logic of database updates. In fact, our notation for hypothetical updates is reminiscent of dynamic logic, with additions and deletions being the primitive actions [14, 19]. This paper introduces a semantics for hypothetical updates which in some sense is midway between that of dynamic and intuitionistic logic. Semantics are introduced, however, mainly as a vehicle for establishing upper complexity bounds. We define a notion of rulebase interpretation and ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. SpringerVerlag, 1979.

....in [HLM93] a formal system, designed to deal with both the knowledge and abilities of agents, and the effects of the actions performed by the agent. Based on the concepts given in [Moo80] and [Moo84] the system of [HLM93] is firmly rooted in both epistemic logic (see [MH] and dynamic logic (see [Har79], Har84] KT90] and [Gol92] The actions that we considered in [HLM93] are deterministic: the event that consists of some agent performing some action has a unique outcome. In this paper we will consider a natural extension of the system of [HLM93] given by the introduction of ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer-Verlag, 1979.

....dis 8 LOGICS FOR DATABASES AND INFORMATION SYSTEMS tinction is desired, then two sorts of predicates could be used, one for queries, and one for updating transactions. This philosophy is quite different from the situation calculus [MH69] and from approaches based on dynamic and process logics [Har79; HKP82] where queries and updates are represented by different classes of syntactic objects (e.g. predicates vs. function terms vs. modal operators) The rest of this section illustrates our notation and the capabilities of T R through a number of simple examples. The examples illustrate how T ....

....languages defined in [AV90] This lack of subroutines is reflected in the PSPACE data complexity of some of the languages, since subroutines would lead to alternating PSPACE, that is, EXPTIME [Bon] 1.7.2 Logics for Reasoning about Programs Dynamic Logic and Process Logic. Dynamic Logic [Har79] and Process Logic [HKP82] allow a user to express properties of procedural programs and to reason about them. 13 Dynamic Logic reasons about the initial and final states of program execution. Thus, one can speak about the result of an execution; e:g: When the program terminates, the value ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer-Verlag, 1979.

....Most other logics are not capable of this uniform treatment, since they see queries as propositions, but updates (or actions) are seen as entities of a different, incompatible nature. For instance, in situation calculus [41, 42] actions are function terms, while in Dynamic and Process Logics [32, 33], actions are modal operators. Although T R is different from logics of action, it is comparable to declarative query languages, like Prolog and SQL. In Prolog, for instance, one does not reason about logic programs. Instead, one specifies and executes them. Thus, given a logic program and a ....

....problem syntactically. One interesting consequence of this is that, while in [58, 34] an elementary update is always deterministic, in [21, 20] updating a theory with a formula may lead to several alternative states. Several authors [16, 40, 49] base their approaches to updates on Dynamic Logic [32]. Casanova [16] applies an adaptation of Dynamic Logic to reasoning about concurrent execution of procedural programs that are built out of relational algebra operators plus an explicit relational assignment operator. Updates are done in the hypothetical mode and no complete proof theory is given. ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. SpringerVerlag, 1979.

....does. Most other logics are not capable of this uniform treatment, since they see queries as propositions, but updates (or actions) are seen as entities of a different, incompatible nature. For instance, in situation calculus [12] actions are function terms, while in Dynamic and Process Logics [7, 8], actions are modal operators. Although T R is different from logics of action, it is comparable to declarative query languages, like Prolog and SQL. In Prolog, for instance, one does not reason about logic programs. Instead, one specifies and executes them. Thus, given a logic program and a ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer Verlag, 1979.

....typical AI problems as plan generation [BK95] Recently, it has also been applied to workflow analysis [DKRR98] Although many other formalisms have been developed for reasoning about action and change, they all represent significant deviations from the logicprogramming paradigm. Dynamic Logic [Har79], Temporal Logic [Pnu77] and the situation calculus [McC63] are three examples. These formalisms were not intended for logic programming, and they are a world apart from Prolog with assert and retract. It may be possible to model Prolog updates using these formalisms (perhaps through a complex ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer-Verlag, 1979.

....logics are not capable of this uniform treatment, since for them, queries are propositions, but updates (or actions) are entities of a different and incompatible nature. 1 INTRODUCTION 4 For instance, in situation calculus [67] actions are function terms, while in Dynamic and Process Logics [46, 47], actions are modal operators. It is worth noting that relational databases already attempt to treat queries and updates uniformly. Typically, the two are lumped together under the rubric Data Manipulation Language, or DML. Indeed, SQL updates are often referred to as queries. However, queries ....

....problem syntactically. One interesting consequence of this is that, while in [93, 51] an elementary update is always deterministic, in [32, 31] updating a theory with a formula may lead to several alternative states. Several authors [24, 65, 74] base their approaches to updates on Dynamic Logic [46]. Casanova [24] applies an adaptation of Dynamic Logic to reasoning about concurrent execution of procedural programs that are built out of relational algebra operators plus an explicit relational assignment operator. Updates are done in the hypothetical mode and no complete proof theory is given. ....

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. SpringerVerlag, 1979.

No context found.

D. Harel. Towards a theory of recursive structures. volume 1450 of Lecture Notes in Computer Science, pages 36--53. Springer, 1998.

No context found.

D. Harel. First-Order Dynamic Logic, volume 68 of Lecture Notes in Computer Science. Springer Verlag, Berlin, Germany, 1979.

No context found.

D. Harel. First order dynamic logic. Volume 68 of Lecture Notes in Computer Science, Springer Verlag, 1979.

No context found.

First International Workshop on Conditional Term Rewriting Systems #Orsay, France#,volume 308 of Lecture Notes in Computer Science, pages 45#55, Berlin, July 1987. Springer-Verlag.

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