R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53-91, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of view, this update query should delete only one tuple from emp non deterministically. From deductive databases point of view, this query should delete all tuples from emp. In the past decade, various approaches for the inclusion of update capabilities in rule based languages have been proposed [1, 2, 4, 7, 9, 10, 13, 21, 23, 24, 25, 27, 30]. However, most of them are logic programming based that support nondeterministic tuple at a time updates and fail to provide a natural account for setoriented (or bulk) updates in deductive databases syntactically and semantically. Some database oriented approaches either lack intuitive ....

R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53-91, 1995.

....constraints as static integrity constraints, 3) Transform history de pendent preconditions for updates into local preconditions. Keywords: Situation Calculus, Knowledge Representation, Specifications of Database Updates, Automated Reasoning, Integrity Con straints. I Introduction In [9], as an application of his solution to the frame problem [8] Raymond Reiter proposed to specify the transaction based updates of database by means of a particular kind of axioms written in the situation calculus (SC) 7] In [1] the implementation and the functionalities of a computational system ....

....a given condition C , or Has there been a state of the database where a certain condition C has been satisfied , or Has the salary of some employee decreased along the database evolution . Reiter raised this problem in the context of his specifications of transaction based database updates [9]. Although there is no explicit time in our situation calculus, for their similarity with dynamic integrity constraints [9] also called temporal con straints [3] we call these queries temporal queries 2. Furthermore, we call this queries hypothetical because we have an initial, physical ....

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R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53-91, 1995.

....where a certain property has been satisfied , or Has the salary of some employee decreased along the database evolution . This problem was originally proposed by Raymond Reiter in the context of his specifications in the Situation Calculus (SC) 13] of transaction based database updates [16], and addressed, in the same context, in [19, 18, 20] The main ingredient of Reiter s specifications are the successor state axioms for tables , that fully specify when a tuple belongs to a table after executing an arbitrary transaction, in terms of the contents of the database at the execution ....

....explained in [21] We consider static queries, that is, about one single database state, as a particular case of dynamic queries. In the same spirit, static integrity constraints, that refer to (all) individual database states, are considered a particular case of dynamic integrity constraints [16, 15]. For example, a typical dynamic integrity constraint is The salary of an individual cannot decrease along the database evolution , whereas There is a functional dependency between table T1 and table T 2 is a static integrity constraint. In [6] Chomicki considers the problem of checking ....

[Article contains additional citation context not shown here]

R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53--91, 1995.

....integrity constraints as static integrity constraints, 3) Transform history dependent preconditions for updates into local preconditions. Keywords: Situation Calculus, Knowledge Representation, Specifications of Database Updates, Automated Reasoning, Integrity Constraints. 1 Introduction In [9], as an application of his solution to the frame problem [8] Raymond Reiter proposed to specify the transaction based updates of database by means of a particular kind of axioms written in the situation calculus (SC) 7] In [1] the implementation and the functionalities of a computational system ....

....a given condition C , or Has there been a state of the database where a certain condition C has been satisfied , or Has the salary of some employee decreased along the database evolution . Reiter raised this problem in the context of his specifications of transaction based database updates [9]. Although there is no explicit time in our situation calculus, for their similarity with dynamic integrity constraints [9] also called temporal constraints [3] we call these queries temporal queries . Furthermore, we call this queries hypothetical because we have an initial, physical ....

[Article contains additional citation context not shown here]

R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53--91, 1995.

....the semantics of a database using mathematical logic [Min97,CS98] In particular, we deal with a logical framework in which transactions are treated as objects within the logical language, allowing one to reason about the dynamics of change in a database as transactions are executed. As shown in [Rei95], it is possible to specify the dynamics of a relational database with a special formalism written in the situation calculus (SC) MH69] a language of many sorted predicate logic for representing knowledge and reasoning about actions and change. Apart from providing a natural and well studied ....

....rami cation constraints are introduced. These are constraints that force the database to make indirect changes in tables due to changes in other tables. There are several options to deal with this problem: 1. One can assume that the ICs are somehow embedded in the SSAs. This is the approach in [Rei95]. They should be logical consequences of the DB speci cation. 2. Some ICs can be considered as quali cation constraints, that is, they are considered as constraints on the executability of the database actions. In [LR94] a methodology for translating these constraints into axioms on the ....

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R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53-91, 1995.

....can be integrated by adding a temporal theory describing the state of the database at any particular time point. One way of doing so is by using situation calculus . In this approach a database is described by initial information and a history of events performed during the database lifetime (see [25]) Here we use a di erent approach, which is based on event calculus . The idea is to make a distinction between two kinds of events: add db and del db that describe the database modi cations, and the composerdriven events insert and retract that are used for constructing database repairs. In ....

R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1), 53-91, 1995.

....the database. Our research is based on two logical languages that have been developed in parallel: The Situation Calculus, a logical language developed to represent knowledge about action and change [8] The Situation Calculus has been used as a medium for the specification of database updates [14], and our work is a further development of this approach. The Metric Time Temporal Logic, a first order modal temporal logic, has been used . Subject Category: Knowledge Representation in Databases. 1 Introduction 2 Theories of Action in the Situation Calculus 2.1 Foundations of the ....

....the RHS, but we can get rid of it applying Reiter s regression operator R, that takes a formula, instantiated at a successor state of the form do(A; s) to a formula instantiated at the previous state, s. For doing this, it uses the SSAs of the tables appearing in the formula holds( x) do(a; s) [11, 14]. We obtain: 8(a; s)P oss(a; s) oe 8x[R Phi mtl (x; do(a; s) j R[holds( x) do(a; s) R Phi mtl (x; s) holds( x) s) 15) Notice that the application of the regression operator leaves the RHS of the equivalence above as a simple formula in s. Also notice that when Phi mtl is a MTL ....

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REITER, R. On Specifying Database Updates. Journal of Logic Programming 25, 1 (1995), 53--91.

....and similarly when the expression combines and . A simple formula is a first order formula which does not mention the predicate symbols P oss or , that mentions a unique situation variable (e.g. s) and no other situation terms, and which does not quantify over variables of sort situation (S) [12]. ffl A set T una of uniqueness of names axioms for actions. For distinct action names a and a a(x 1 ; x n ; t) 6= a (y 1 ; y m ; t ) Identical actions have identical arguments. Thus, for each function symbol of sort A in the language, we write: a(x 1 ; x n ; ....

REITER, R. On Specifying Database Updates. Tech. Rep. KRR-TR-92-3, University of Toronto, July 1992.

....is used in the sense of Reiter s. That is, a simple formula is a first order formula which does not mention the predicate symbols P oss, OE or (nor or ) that mentions a unique situation variable (e.g. s) and no other situation terms, and which does not quantify over variables of sort state (S) [48]. Furthermore, we require that s not appear outside the scope of a holds predicate (as its second argument) In this work, we assume that all the necessary conditions for the execution of an action are known. This completeness assumption allows us to write for each action A, an axiom of the ....

....for the defined fluents as well as for the primitive fluents. To do so, we take the set T ss (T T def (T ef ) from (3.9) which are successor state axioms for the primitive fluents. We obtain a set T def of successor state axioms for the defined fluents by applying regression, as defined in [48], to the primitive fluents in each definition. Thus, if f 0 is a defined fluent, and its definition is of the form: where fluents f 1 ; f n are primitive, then: holds(f 0 (x) do(a; s) j Phi 0 (f 1 ; f n ; x; do(a; s) 3.10) Now, we may use Reiter s regression operator R ....

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Reiter, R. On specifying database updates. Tech. Rep. KRR-TR-92-3, University of Toronto, July 1992.

....refer to all past states, and not only the to the previous one. They provide the formal semantics of the corresponding ATMs. They are an extension of the classical relational theories of [19] to the database transaction setting. 2. We extend the notion of legal database logs introduced in [20] to accomodate transactional actions such as Begin, Commit, etc. These logs are first class citizen of the logic and properties of the ATM are expressed as formulas of the situation calculus that logically follow from the basic relational theory representing that ATM. 3. Our approach goes far ....

R. Reiter. On specifying database updates. J. of Logic Programming, 25:25--91, 1995.

....deferred updates semantically and operationally, but on the other hand requires hypothetical reasoning. Of course, it would also be possible to model enough knowledge about the effects of further actions in addition to insert and delete to enable hypothetical reasoning in other contexts. Reiter [Rei95] for instance, provides a viable axiomatization technique in terms of the situation calculus. Axioms that describe the effects of some external actions, e.g. the movements of a robot, could be integrated into an ULTRA evaluation engine. Unfortunately, the semantics of external actions is ....

....that describe the effects of some external actions, e.g. the movements of a robot, could be integrated into an ULTRA evaluation engine. Unfortunately, the semantics of external actions is typically more difficult than the semantics of database operations like insert and delete. The frame problem [Rei95] causes further intractabilities for bigger sets of basic operations and observable predicates. Consequently, there exist many questions and problems w.r.t. an operational semantics, and its design is not a simple, straight forward task. The semantics we presented in this section, however, is ....

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R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53--91, 1995.

....In this work, we view workflows as a collection of cooperative agents and use recent results on reasoning about actions [4, 6, 29, 36] to formalize the process of their specification and test their correctness. Our approach, in a philosophical sense, resembles formalization of database updates [43] and transactions [15, 16] Our main contributions are as follows. We present a very simple, high level language AW and, based on it, a prototype tool, which facilitates the process specification (i.e. the domain where the workflow activities will execute) The tool enables dual (textual and ....

R. Reiter. On specifying database updates. Journal of Logic Programming, 19,20:1--39, 1994.

....and goes back to step one of the loop. Of course this architecture is only valid if computation performed during the execution of the body of the loop is fast 1 To the best of our knowledge the idea that observations should be added together with possible explanations was first published in (Reiter, 1995). 276 LOGIC BASED ARTIFICIAL INTELLIGENCE enough to not allow the possibility of occurrence of exogenous actions, that may change the relevant characteristics of the domain, before a 1 is performed. In many situations the process can be made considerably faster by pre computing solutions of ....

Reiter, R. (1995). On specifying database updates. Journal of Logic Programming, 25:25--91.

....adding :C to the theory results in inconsistency. Reasonable ways to incorporate the request could result in fA; A B C; Cg, fB; A B C; Cg, fA; B; Cg, or the disjunction of the three. The update problem is not unique to database theory. One also encounters it in Artificial Intelligence [McC68, Rei92] and in belief revision theory [Mak85, Gar88] The common fundamental question is: What should be the result of changing a theory T with a sentence OE The departure point of belief revision theory is the rationality postulates proposed by Alchourr on, Gardenfors and Makinson [AGM85] and ....

R. Reiter. On specifying database updates. In: Proceedings of the Third International Conference on Extending Database Technology, to appear in 1992.

....unlike the original situation calculus, which was entirely rst order [McC63; MH69] Reiter s development includes an induction axiom speci ed in second order logic, for reasoning about sequences of transactions. Applying this approach, Reiter has developed a logical theory of database evolution [Rei95] This theory is perfectly compatible with T R. Through its oracle mechanism, T R can use the theory to specify the semantics of database states and elementary actions. 40 LOGICS FOR DATABASES AND INFORMATION SYSTEMS Horn T R can then combine these actions into complex programs, and full T R can ....

....preserved forever, and the history of database transactions is recorded in a kind of log. Thus, the current database state is not materialized, but is virtual. In this framework, queries to the current state are answered by querying the log and reasoning backwards through it to the initial state [Rei95] Unfortunately, this means that simple operations, like retrieving a single tuple from the database, become long and complicated reasoning processes. Since database logs are typically large (perhaps millions of transaction records long) reasoning backwards through them is unacceptably ....

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R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53-91, October 1995.

....of view, this update query should delete only one tuple from emp non deterministically. From deductive databases point of view, this query should delete all tuples from emp. In the past decade, various approaches for the inclusion of update capabilities in rule based languages have been proposed [1, 2, 4, 7, 9, 10, 13, 19, 22, 23, 25, 27, 21]. However, most of them are logic programming based that support nondeterministic tuple at a time updates and fail to provide a natural account for set oriented (or bulk) updates in deductive databases syntactically and semantically. Some database oriented approaches either lack intuitive ....

R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53-91, 1995.

....the semantics of a database using mathematical logic [22, 9] In particular, we deal with a logical framework in which transactions are treated as objects within the logical language, allowing one to reason about the dynamics of change in a database as transactions are executed. As shown in [32], it is possible to specify the dynamics of a relational database with a special formalism written in the situation calculus (SC) 18] a language of many sorted predicate logic for representing knowledge and reasoning about actions and change. Apart from providing a natural and well studied ....

....ramification constraints, that is, constraints that force the database to make indirect changes in tables due to changes in other tables of the database. There are several options to deal with this problem: 1. One can assume that the ICs are somehow embedded in the SSAs. This is the approach in [32]. They should be logical consequences of the DB specification. In [5] a mechanism for the automated proof of these ICs is provided. 2. Some ICs can be considered as qualification constraints, that is, they are considered as constraints on the executability of the database actions. In [14] a ....

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R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53-- 91, 1995.

....Acknowledgments We would like to thank V. Lifschitz, E. Erdem, M. Nogueira, J. Minker and the referees for their useful comments. Notes 1. To the best of our knowledge the idea that observations should be added together with possible explanations was rst published in (Reiter, 1995). 2. More details on the combination of reactive and deliberative reasoning in the context of action based languages can be found in (Baral and Son, 1998) It also contains more detailed comparison to the reactive aspects of ConGolog (De Giacomo et al. 1997) ....

Reiter, R. (1995). On specifying database updates. Journal of Logic Programming, 25:25-91.

....as a framework for a great variety of update languages. This is exempli ed by an alternative instantiation which is well suited for the (mostly sequential) programming of external operations as illustrated by a variation of the famous robot world example that can be found e.g. in [LRL 97, Rei95] Despite major di erences between the world of a robot arm and a database system, both update languages behave as instances of our ULTRA framework, see Figure 1. Transitions Basic Operations States Transitions Basic Operations States ULTRA Framework Instantiation for Logic Databases ....

....be semantically and operationally based on deferred updates, but on the other hand requires hypothetical reasoning. Of course, it would also be possible to model enough knowledge about the e ects of further actions than insert and delete to enable hypothetical reasoning in other contexts. Reiter [Rei95] for instance, provides a viable axiomatization technique in terms of the situation calculus. Axioms that describe the e ects of some external actions, e.g. the movements of the robot arm, could be integrated into an ULTRA evaluation engine. Unfortunately, the semantics of external actions is ....

[Article contains additional citation context not shown here]

R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53-91, 1995.

.... Poss(a; s) G f (x; a; s) oe f (x; do(a; s) 2 A simple formula is a first order formula which does not mention the predicate symbols Poss or , that mentions a unique situation variable (e.g. s) and no other situation terms, and which does not quantify over variables of sort situation (S) (Reiter 1992). 3 We write x to denote a tuple of domain variables (i.e. variables of sort D) 10 Whereas negative effect axioms are of the form: Poss(a; s) G Gamma f (x; a; s) oe : f (x; do(a; s) Now, all the positive (negative) effect axioms for a fluent predicate can be put together in a single ....

Reiter, R. (1992, July). On Specifying Database Updates. Technical Report KRR-TR-92-3, University of Toronto.

....allowed. Furthermore, the reasoning process may dynamically become more expensive with every subsequent state, since it always starts at the (physical) initial state. Axiomatization of effects of actions and (hypothetical) reasoning about these actions was investigated in more detail by Reiter [Rei95] situation calculus) and Kowalski [Kow92] event calculus) A second practical problem results from performing a transaction in two strictly separated phases (evaluation and materialization) Such a system does not show a continuous behaviour and thus is not suitable to be extended by ....

R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53--91, 1995.

....proposal to integrate the specification of active rules with the specification of the dynamics of transaction based change in relational databases. Our approach extends previous work in which the situation calculus, a language of many sorted predicate logic, is used to specify updates in databases [14]. To achieve this, we first specify database transactions in the situation calculus, and then active rules using the notion of occurrence as proposed in [13] 1.1 Introduction This chapter provides a predicate logic based semantics for active rules in active databases [18, 9] Our work is based ....

....that was originally proposed to represent knowledge about dynamic domains [12] An important characteristic of Sitcalc is its treatment of actions, primitive transactions in a database setting 2 , at the object level. Furthermore, the language has sorts for domain individuals and situations. In [14], Reiter proposed a logical framework based on the Sitcalc to specify transaction based database updates. The only transactions involved in the original proposal are primitive in the sense that they are not decomposable. Logical specifications, in Reiter s style, include axioms to specify ....

R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53--91, 1995.

....having the persistence axiom in our theory of action entail: 8a; s: Q(P; s) j persistent(P; a; s) Example 6 Let hir stand for high injury risk , pmc for Sue practices mountain climbing , and pt for Sue is a professional tennist. Let be the natural temporal partial order of situations (see [Reiter, 1992] for a precise second order definition) We have a constraint: 8s: holds(pmc; s) holds(pt; s) oe holds(hir; s) hir should be persistent iff it was caused by professional practice of tennis and no treatment was performed to eliminate this risk, i.e. the persistence axiom should entail: 8a; ....

Reiter, Raymond 1992. On specifying database updates. Technical Report KRRTR -92-5, Computer Science Department, University of Toronto.

....8 RELATION TO OTHER WORK 19 8 Relation to Other Work Our approach to updates has its foundation in Transaction Logic. Bonner and Kifer s papers on Transaction Logic [6, 7] contain substantial reviews of related literature, including work on updating databases [2, 1, 25] the situation calculus [30], the event calculus [23, 22] and temporal logic [3] The paper by Reiter [30] contains some further remarks comparing Transaction Logic to the situation calculus. We invite the reader to consult these papers for comparison with related work. Instead of repeating Bonner and Kifer s work we shall ....

....has its foundation in Transaction Logic. Bonner and Kifer s papers on Transaction Logic [6, 7] contain substantial reviews of related literature, including work on updating databases [2, 1, 25] the situation calculus [30] the event calculus [23, 22] and temporal logic [3] The paper by Reiter [30] contains some further remarks comparing Transaction Logic to the situation calculus. We invite the reader to consult these papers for comparison with related work. Instead of repeating Bonner and Kifer s work we shall turn to two areas not addressed directly in their reviews: meta programming and ....

Raymond Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53--91, October 1995.

....answering historical queries in databases. Other uses of the semantical concepts of relevance and extensions are discussed. 1 Introduction In this paper we present semantical notion of relevance in specifications of database updates written in the situation calculus [12] as proposed by Reiter in [15, 17]. We also recall a computational counterpart presented in [18] and we compare the two approaches. In this work we were motivated by the problem of answering historical queries in relational databases [18] Given a initial (physical) relational database D 0 and a list of legal atomic transactions ....

.... way when a fluent does not change when an action is performed [12] The formulas on the right hand side of the SSAs are simple in s [14] that is, s appears free in them and no other state term is mentioned (but a tacit universal quantification on a and s is assumed in (1) According to [15, 17], a database is specified by a theory of the form Sigma = Sigma bd [ Sigma ap [ Sigma una [ Sigma ssa [ Sigma S 0 , where: 1. Sigma bd contains (a) state independent axioms for the domain of discourse and (b) the foundational axioms [10, 13] of situation calculus, which describe the ....

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R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53--91, 1995.

....Depto. de Ciencia de Computacion Casilla 306, Santiago 22, Chile Email: fbsiu,bertossig ing.puc.cl Abstract In this paper we present a syntactical class of historical queries in databases, and an algorithm for answering them automatically and efficiently. We adopt Ray Reiter s formalism [17, 19] based on the situation calculus [13] for specifying database updates. For this purpose, we introduce a procedural notion of relevant transactions and tuples, and also a semantical notion of relevance against which the computational notion is compared and established as complete. In this way we ....

....in SCDBR [3, 1] a computational system that is able to reason from and about database specifications written in Reiter s formalism. We discuss some implementation issues. Keywords: Specification of Database Updates, Historical Queries, Knowledge Representation, Situation Calculus, Relevance In [17, 19], Reiter presented a formalism for specifying database updates, using the situation calculus [13] as logical language. In this paper we address the problem of posing and answering historical queries on databases, when their dynamics are expressed in that formalism: Given a initial, physical, ....

R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53--91, 1995.

....queries about the evolution of the database along a sequence of transactions. To make the algorithm efficient, we introduce procedural notions of relevant transactions and tuples, that allow us to know which transactions to execute and which tuples to update. We start from Ray Reiter s formalism [14, 16] based on the situation calculus [11] for specifying database updates. This paper extends previous work by Aris Zakinthinos on historical queries [19] which is also based on Reiter s work. Our algorithms have been implemented in SCDBR [3, 2, 1] a computational system that is able to reason from ....

....Updates, Historical Queries, Knowledge Representation, Situation Calculus, Relevance 1 Introduction In this paper we present a syntactical class of historical queries on databases for which the process of answering them can be done automatically and efficiently. We follow Ray Reiter s proposal [14, 16] to specify the database evolution in the situation calculus, a first order language for representing knowledge about dynamical worlds [11] The database updates are specified in Reiter s formalism for solving the frame problem in the situation calculus [13] This paper considerably extends ....

[Article contains additional citation context not shown here]

R. Reiter. "On Specifying Database Updates". Journal of Logic Programming, 25(1):53-- 91, 1995.

....queries about the evolution of the database along a sequence of transactions. To make the algorithm efficient, we introduce procedural notions of relevant transactions and tuples, that allow us to know which transactions to execute and which tuples to update. We start from Ray Reiter s formalism [14, 16] based on the situation calculus [11] for specifying database updates. This paper extends previous work by Aris Zakinthinos on historical queries [19] which is also based on Reiter s work. Our algorithms have been implemented in SCDBR [3, 2, 1] a computational system that is able to reason from ....

....Updates, Historical Queries, Knowledge Representation, Situation Calculus, Relevance 1 Introduction In this paper we present a syntactical class of historical queries on databases for which the process of answering them can be done automatically and efficiently. We follow Ray Reiter s proposal [14, 16] to specify the database evolution in the situation calculus, a first order language for representing knowledge about dynamical worlds [11] The database updates are specified in Reiter s formalism for solving the frame problem in the situation calculus [13] This paper considerably extends ....

[Article contains additional citation context not shown here]

R. Reiter. "On Specifying Database Updates". Technical Report KRR-TR-92-3, University of Toronto, Department of Computer Science, Toronto, Canada, 1992.

....world and therefore an update must affect them minimally. keywords: Disjunctive Deductive Databases (DDDBs) Database Updates, Minimal Model Semantics, Minimal Model Generation. 1 Introduction As a routine task in database maintenance, the update problem was extensively covered in the literature [4, 2, 5, 6, 13, 8, 9, 10, 14]. Different semantics were suggested and several methods for accomplishing updates were advanced. Since more than one way may be available to accomplish an update, minimality under certain criteria can be used to decide in favor of a particular choice. Minimal models play an important role in ....

....it returns all and only minimal models of its input. The algorithm depends heavily in utilizing denial rules to guide the model search process. The detailed discussion, an implementation and comments on efficiency results can also be found in [3] Our approach differs from those discussed in [13, 4] in that we consider a more general class of theories and updates. In [7] DDDBs are considered and the approach can be extended to the case of range restricted theories. However, they treat only positive clause updates and our approach tends to expand much less of the model structure through ....

R. Reiter. On specifying database updates. J. Logic Programming, 25(6):53--91, June 1995.

....world and therefore an update must affect them minimally. Keywords: Disjunctive Deductive Databases (DDDBs) Database Updates, Minimal Model Semantics, Minimal Model Generation. 1 Introduction As a routine task in database maintenance, the update problem was extensively covered in the literature [1, 7, 4, 25, 27, 14, 15, 13, 26, 28]. Different semantics were suggested and several methods for accomplishing updates were advanced. Since more than one way may be available to accomplish an update, minimality under certain criteria can be used to decide in favor of a particular choice. Minimal models play an important role in ....

....of direct model updates [17] discussed in [19, 29] In this sense our approach is closer to program update [19] or rule update [24] or formula update [28] than it is to direct model (interpretation) update [17] and is applied to the case of DDDBs. Our approach differs from those discussed in [2, 25, 7] in that we consider a more general class of theories and updates. We treat DDDBs and consider adding deleting general clauses to such theories. In [12, 9] DDDBs are considered and the approach can be extended to the case of range restricted theories. However, they treat only positive clause ....

R. Reiter. On specifying database updates. J. Logic Programming, 25(6):53--91, June 1995.

....varies from one situation to another. All actions in the situation calculus are assumed to be primitive and determinate. The situation calculus has been traditionally used for hypothetical reasoning in Artificial Intelligence. Reiter proposed its use in the specification of database updates [Rei95] and the specification of state constraints [LR92] LR94] One of the main drawbacks of the situation calculus is its inability to constrain the occurrences of events. Unlike linear temporal logics, 1 FOTL formulae are interpreted over a history of domain states. it can be viewed as defining ....

....temporal logics, such as FOTL, Allen s intervalbased temporal logic [All83] and the Event Calculus [KS86] can be realized in the extended situation calculus. Of particular interest to the present work is the formulation of database transactions in the situation calculus as this appears in [Rei95] Transactions are formulated as actions are in planning domains. Reiter also provides a solution to the frame problem as it arises in the context of database transactions. This solution is employed for proving the satisfaction of static and dynamic constraints using a form of mathematical ....

R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53--91, 1995.

....where a certain property has been satisfied , or Has the salary of some employee decreased along the database evolution . This problem was originally proposed by Raymond Reiter in the context of his specifications in the Situation Calculus (SC) 13] of transaction based database updates [16], and addressed, in the same context, in [19, 18, 20] The main ingredient of Reiter s specifications are the successor state axioms for tables , that fully specify when a tuple belongs to a table after executing an arbitrary transaction, in terms of the contents of the database at the execution ....

....explained in [21] We consider static queries, that is, about one single database state, as a particular case of dynamic queries. In the same spirit, static integrity constraints, that refer to (all) individual database states, are considered a particular case of dynamic integrity constraints [16, 15]. For example, a typical dynamic integrity constraint is The salary of an individual cannot decrease along the database evolution , whereas There is a functional dependency between table T1 and table T 2 is a static integrity constraint. In [6] Chomicki considers the problem of checking ....

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R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53--91, 1995.

....to reason across states to infer what remains true after a transaction, and what does not [Hayes, 1973] Reasoning is inherently harder because this representation is closer to the full first order predicate calculus as some use of terms is permitted. 16 In [Pinto and Reiter, 1993] and [Reiter, 1995], the authors argue for the situation calculus as a representation for temporal databases, and show how the frame problem can be alleviated. As demonstrated, there are a number of approaches to representing time and change formally in databases. Such a formalism offers us a way to extend integrity ....

Reiter, R. (1995). On specifying database updates. Journal of Logic Programming, 25(1):53--91.

....criticisms. 2 Y.Zhang and N.Y. Foo Deriving Invariants and Constraints from Action Theories be derived from a collection of frame axioms within their action formalization [3] while Reiter presented some observations that state constraints may be implied in action axioms in some situations [8, 9]. Furthermore, by introducing induction axioms in the situation calculus [5] Reiter provided a formal method to prove properties of states from action axioms [10] Other researchers also made similar observations [6, 11] The work of extracting state constraints from action specifications is ....

Reiter, R.: "On specifying database updates". KRR-TR-92-3, University of Toronto, July, 1992.

.... Schubert observed that frame axioms may be extracted from action axioms or explanation closure axioms of actions under some assumptions [Pednault, 1989, Schubert, 1990] Reiter also presented some observations that state constraints may be implied in action axioms in some situations [Reiter, 1991, Reiter, 1992] In this chapter, we address the problem of generating action invariants and generalizing action invariants into state constraints. Generally, an action invariant ex 1 In our formalization, we do not need specify frame axioms explicitly, while in some other action theories, they must be ....

....that there are interesting connections between them. del Val and Shoham proposed a method to derive Katsuno and Mendelzon s update properties from Lin and Shoham s action theory [del Val and Shoham, 1992, del Val and Shoham, 1993] Reiter also studied the update within the situation cal113 culus [Reiter, 1992] where Reiter defined a database transaction exactly the same as an action. From our point of view, on the other hand, an update can also be achieved by a sequence of actions. For example, suppose a knowledge base presenting that block A is on block B, B is on block C and C is on the table. If we ....

R. Reiter. On specifying database updates. KRR-TR-92-3, University of Toronto, July, 1992.

....are allowed. Since those languages are designed to represent knowledge and reason about actions and dynamic properties subject to discrete change due to action executions, it is natural to think of applying them to specify the dynamics of a relational database. This was done by Reiter in [Re2] on the basis of his formalism for solving the frame problem [Re1] that is the problem of obtaining a succinct specification of the properties that do not change when actions are executed. In [Be1] the main features of an automated system able to reason with and from those database specifications ....

....they can be materialized as physical tables for certain purposes, e.g. in data warehousing [CD1] They are an important component of the database. In this paper we show how to derive action effect based SSAs for views from the SSAs for the base tables. This problem was originally formulated in [Re2]. We also prove consistency properties for those axioms. This is done in section 5, after having made our problem precise in section 4. In section 6, we establish the relationship between the derived SSA and the view definition as a static integrity constraint of the database. Having appropriate ....

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Reiter, R.: On specifying database updates. Journal of Logic Programming 25 (1995) 53--91.

....transactions and procedures [LML96] The extended language includes a form of sequential composition modeled on the connective of serial conjunction in Transaction Logic. Finally, it is instructive to compare Datalog with State to Golog [LRL 97] and to Reiter s theory of database evolution [Rei95] described in Section 4.4. One important difference is that Datalog with State relies on a small, fixed set of elementary updates, so only a small, fixed set of frame axioms is needed. Another difference is that Datalog with State uses a form of closed world semantics (XY stratification [Zan93] ....

....includes an induction 10 Here we use the syntax of T R, which can be translated into the original syntax of [MvdM92] axiom specified in second order logic, for reasoning about sequences of transactions. Applying this approach, Reiter has developed a logical theory of database evolution [Rei95] From the perspective of database theory [AHV95,Ull88] Reiter s approach is quite unusual. For instance, a database state is usually modeled as set of relations or logical formulas; but in Reiter s theory, a state is identified with a sequence of actions. Thus, different transactions always ....

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R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53--91, October 1995.

....plus a specification of the dynamics of the database that describes M. Arenas, L. Bertossi 04 1 how the tables in it evolve as primitive transactions are executed. The formalism we considered for specifying the transaction based updates of the relational database is the one shown by Reiter [Rei95], who proposed a particular kind of axioms written in the situation calculus (SC) McC69] In [Ber94, Ber98] the implementation and functionalities of a computational system for doing automated reasoning from and about these specifications are reported. Here we present a solution to the problem of ....

....applying Reiter s regression operator R, that takes a formula, instantiated at a successor state of the form do(A; s) into a formula instantiated at the previous state, s. For doing this, R uses the SSAs of the tables appearing in h ( x; do(a; s) This operator preserves logical equivalence [Rei95]. In consequence, we obtain: 8(a; s)P oss(a; s) oe 8 x(R ff ( x; do(a; s) j R[ h ( x; do(a; s) R ff ( x; s) h ( x; s) As before, we also define 8 x :R ff ( x; S 0 ) It is possible to prove that D 0 ; Dn ; Sn j= is equivalent to Sigma H j= h (do(T; S 0 ) where ....

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R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53--91, 1995.

....the Catholic University of Chile (DIPUC) for their financial support. We are grateful to Javier Pinto for his generous support. y Corresponding and Current Address: TU Berlin, FB Informatik, CIS Sekr. EN7, Einsteinufer 17, D 10587 Berlin, Germany. bertossi cs.tu berlin.de 1 Introduction In [15], as an application of his solution to the frame problem [14] Ray Reiter proposed to specify the transaction based evolution of relational database by means of a particular kind of axioms written in the situation calculus (SC) 13] In [3] the implementation and the functionalities of a ....

....a given condition C , or Has there been a state of the database where a certain condition C has been satisfied , or Has the salary of some employee decreased along the database evolution . Reiter raised this problem in the context of his specifications of transaction based database updates [15]. The problem was treated in detail in [17] and a solution was implemented as reported in [3] Nevertheless that solution is based on a kind of minimal progression of the database that depended on a detailed syntactical processing of the axioms of the specification, and on the particular ....

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R. Reiter. On Specifying Database Updates. Journal of Logic Programming, 25(1):53--91, 1995.

....is useful. Some other approaches dealing with updates in deductive databases should be mentioned: Naish, Thom, and Ramamohanarao [NTR87] show the problems that arise from non declarative update constructs in logic programming and propose a clean concept based on deferred updates. Reiter [Rei95] describes possible actions and its effects in the situation calculus and addresses the frame problem. In the language GOLOG [LRL 96] procedural structures and complex operations are introduced, their semantics is described by macro expansion and second order constructs. Like in our ....

R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53--91, 1995.

....; s 2 ; a) do(a; s 1 ) 10) s 1 s 2 do(b; s) oe repl(do(b; s) s 1 ; s 2 ; a) do(b; repl(s; s 1 ; s 2 ; a) 11) In the following, we shall denote by Dmin the set of axioms (6) 11) 4. 4 Basic action theories A basic action theory D is one that has the following form: cf. Reiter [13] and Lin and Reiter [8] D = Sigma [ D ss [ D ap [ D una [ DS0 ; where ffl Sigma is the set of the foundational axioms (1) 5) ffl D ss is a set of successor state axioms, one for each fluent F , of the form: P oss(a; s) oe H(F ( x) do(a; s) j H ( Phi F ( x; a) s) 12) where Phi ....

R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53--91, 1995.

.... investigations of various technical problems that arise in theorizing about actions and their effects (e.g. 19] 8] 13] But only recently has it been taken seriously as a foundation for practical work in planning, control, simulation, database updates, agent programming and robotics (e.g. [18, 9, 17, 34, 33, 2, 14, 16]) In parallel with these developments of its applications, there have emerged axiomatizations for the situation calculus, and explorations of some of their metamathematical and computational properties (e.g. 32, 21] This paper continues these explorations, focusing on a rich axiomatization for ....

....we focus on the domain of situations. The primary intuition about situations that we wish to capture axiomatically is that they are finite sequences of actions. We want also to be able to say that a certain sequence of actions is a subsequence of another. By modifying earlier proposals of Reiter [33], Lin and Reiter [20] and Pinto [29] we adopt the following four foundational axioms for the situation calculus. do(a 1 ; s 1 ) do(a 2 ; s 2 ) oe a 1 = a 2 s 1 = s 2 ; 1) 8P ) P (S 0 ) 8a; s) P (s) oe P (do(a; s) oe (8s)P (s) 2) Axiom (1) is a unique names axiom for situations; two ....

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R. Reiter. On specifying database updates. Journal of Logic Programming, 25:25--91, 1995.

....c) Notice that for these axioms to have their intended effects, we need unique names axioms for actions. See [13] for a discussion. Reiter ( 13] shows how such axioms may be obtained from the effect, or causal axioms of the domain, and how it is that they solve the frame problem. In [14] Reiter shows how successor state axioms can be used to specify transactions in database update applications. To summarize, our solution to the successor state persistence assumption consists of a set of successor state axioms, one for each fluent, together with a set of unique names axioms for ....

Reiter, R. On specifying database updates. Tech. Rep. KRR-TR-92-3, University of Toronto, July 1992.

....at one time a. Occur(a) and another one that the actions are distinct iff their names and arguments are distinct (the so called unique name axioms) for i j, x,y[ p i (x) p j (y) p i (x) p i (y) x=y) Details of the axiomatization and a discussion of its limitations can be found in [Reiter95]. In particular, as described here, change axioms do not always have their intended effects, for instance in cases involving non deterministic procedures. For an approach to change axioms in the presence of non determinism, see [Reiter95] 4.2 Frame Problem Variations Revisited To show how this ....

....and a discussion of its limitations can be found in [Reiter95] In particular, as described here, change axioms do not always have their intended effects, for instance in cases involving non deterministic procedures. For an approach to change axioms in the presence of non determinism, see [Reiter95]. 4.2 Frame Problem Variations Revisited To show how this approach handles the problems raised earlier, consider again the examples of sections 2.3 2.5. With the frame axioms out of the way, the specification of the more complex enrolment s postcondition in Section 2.3 would be as at the ....

R. Reiter, "On Specifying Database Updates", Journal of Logic Programming (to appear).

....and (5) as a consequence, we obtained that Reiter s solution is correct and complete for a broad class of problems. 7 Future Work There are still several issues that need to be addressed. We have only considered Reiter s original solution, not its extension to some kinds of ramifications [7] In [15, 10], Reiter formalizes the evolution of a database according to his solution to the frame problem [14] In [1] this formalization was positively assessed with Sandewall s methodology. In that paper, there was a restriction to ground databases, i.e. without null values. It seems interesting to ....

Reiter, R.: On specifying database updates. Tech. Rept. University of Toronto, Dept. of Computer Science, Toronto, Canada, KRR-TR-92-3 (1992)

.... and supporting metatheory presented in this paper have provided foundations for a wide range of practical work in modeling dynamical systems, including planning (Green [6] Levesque [14] control (Levesque et al. [15] De Giacomo et al. [4] simulation (Kelley [10] database updates (Reiter [27], Bertossi et al. [2] diagnosis of dynamical systems (McIlraith [20] and agent programming and robotics (Jenkin et al. [9] Lesp erance et al. [13] Burgard et al. [3] Shapiro et al. [31] Reiter [29] 2 The Language of the Situation Calculus The following description is taken from Pirri and ....

....s 0 . The situation calculus induction axiom (2) is simply the induction principle for lists: If the empty list has property P and if, whenever list s has property P so does cons(a;s) then all lists have property P . 3 These foundational axioms are simpler than those presented by Reiter [27] and others. These earlier axiomatizations for the situation calculus are all derivable from the four axioms given here. 4 4 Domain Axioms and Basic Theories of Actions Our concern here is with axiomatizations for actions and their effects that have a particular syntactic form. These are called ....

R. Reiter. On specifying database updates. Journal of Logic Programming, 25:25--91, 1995.

....think about database updates (Abiteboul [1] In fact, the STRIPS action and the database update paradigms are essentially the same. Accordingly, this paper is as much about database updates as it is about STRIPS actions and their generalizations. For more on the database perspective, see Reiter [23]. sisting of all the actions it has performed since the initial situation, has become extremely long, and regressing over such a sequence becomes computationally expensive. 2. Similarly, after a long while, the initial world state often becomes so rearranged that significantly many final steps ....

....0 , oe 0 , j 0 , 8x) 9x) 8a) 9a) 8p) and (9p) where x and a are variables of sort object and action, respectively, and p is a predicate variable of arity object n , n 0. 3 BASIC ACTION THEORIES We assume that our action theory D has the following form (cf. Reiter [23] and Lin and Reiter [13] D = Sigma [ D ss [ D ap [ D una [ D S 0 ; where ffl Sigma, given below, is the set of the foundational axioms for situations. ffl D ss is a set of successor state axioms of the form: 2 P oss(a; s) oe [F ( x; do(a; s) j Phi F ( x; a; s) 1) where F is a ....

[Article contains additional citation context not shown here]

R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53-- 91, 1995.

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R. Reiter. On specifying database updates. Journal of Logic Programming, to appear.

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R. Reiter. On specifying database updates. Journal of Logic Programming, 25(1):53--91, 1995.

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Raymond Reiter. On specifying database updates. Technical Report KRR-TR-92-3, University of Toronto, Toronto, July 1992.

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