Roel Wieringa

Specifying dynamic and deonitc integrity constraints

In the dominant view of knowledge bases (KBs), a KB is a set of facts (atomic sentences) and integrity constraints (ICs). An IC is then a sentence which must at least be consistent with the other sentences in the KB, This view obliterates the distinction between, for example, the constraint that age is a natural number (which is true of the universe of discourse (UoD) but may be false in a particular implementation of a KB), and the constraint that a class must have precisely one teacher (which is false of the UoD if a class actually has two teachers). The second constraint is called deontic and constrains the UoD; the first constraint is a necessary truth of the UoD and does not constrain the UoD. Instead, it constrains the implementation of the KB. We argue that the distinction between necessary and deontic ICs is relevant for KB modeling and that it imposes a more complicated modeling discipline on the KB designer than hitherto realized. We show that both types of constraints can be specified in the single framework provided by a deontic variant of dynamic logic, which has the added advantage of being able to specify dynamic constraints as well. We give a simple example to illustrate the difference between dynamic and static specification of deontic ICs, and a non-trivial example of a KB specification with static, dynamic and deontic constraints.

Roles and Dynamic Subclasses: A Modal Logic Approach

In this paper, we argue that object-oriented models must be able to represent three kinds of taxonomic structures: static subclasses, dynamic subclasses and role classes. If CAR is a static subclass of VEHICLE, then a vehicle that is not a car can never migrate to the CAR subclass. If EMPloyee is a dynamic subclass of PERSON, then a PERSON that is not an employee may migrate to EMP. In both cases, an instance of the subclass is identical to an instance of the superclass. Finally, if EMP is modeled as a role class of PERSON every employee differs from every person, but a PERSON instance can acquire one or more EMP instances as roles. We outline an approach to formalizing these taxonomic structures in order-sorted dynamic logic with equality.

A formalization of objects using equational dynamic logic

Order-sorted equational logic is extended with dynamic logic to a specification language for dynamic objects. Special attention is paid to different concepts of encapsulation that play a role in object-orientation. It is argued that the resulting language, CMSL, meets those requirements of the object-oriented database system manifesto [6] that are applicable to object-oriented conceptual models (as opposed to OO databases).

The inheritance of dynamic and deontic integrity constraints or: Does the boss have more rights?

In [18,23], we presented a language for the specification of static, dynamic and deontic integrity constraints (ICs) for conceptual models (CMs). An important problem not discussed in that paper is how ICs are inherited in a taxonomic network of types. For example, if students are permitted to perform certain actions under certain preconditions, must we repeat these preconditions when specializing this action for the subtype of graduate students, or are they inherited, and if so, how? For static constraints, this problem is relatively trivial, but for dynamic and deontic constraints, it will turn out that it contains numerous pitfalls, caused by the fact that common sense supplies presuppositions about the structure of IC inheritance that are not warranted by logic. In this paper, we unravel some of these presuppositions and show how to avoid the pitfalls. We first formulate a number of general theorems about the inheritance of necessary and/or sufficient conditions and show that for upward inheritance, a closure assumption is needed. We apply this to dynamic and deontic ICs, where conditions arepreconditions of actions, and show that our common sense is sometimes mistaken about the logical implications of what we have specified. We also show the connection of necessary and sufficient preconditions of actions with the specification of weakest preconditions in programming logic. Finally, we argue that information analysts usually assume “constraint completion” in the specification of (pre)conditions analogous to predicate completion in Prolog and circumscription in non-monotonic logic. The results are illustrated with numerous examples and compared with other approaches in the literature.

Combining Troll with the Object Modeling Technique

The focus of this paper is the development of a formally based object-oriented modeling formalism called oMmOLL by using features from mostly informal object-oriented modeling approaches (mainly OMT) and from a formal object-oriented specification approach (Troll). The goals of our approach are to improve popular informal modeling techniques by giving formal semantics to modeling constructs and to improve the applicability of formally-based specification approaches. Based on a brief analysis of OMT against Troll we will present OMTROLL using examples.

Aziomatization, Declarative Semantics and Operational Semantics of Passive and Active Updates in Logic Databases

The use of logic in database theory is commonly restricted to the specification of database states. Reasoning about state changes (the database updates) must then be done outside the logic. In this report, we consider a logic that also takes the updates into account. Taking propostional dynamic logic as a starting point, we define PDDL: prepositional dynamic database logic. The main features of PDDL are: n n•There are two kinds of atomic updates in PDDL, passive and active updates. Passive updates just change the truth value of an atom to true/false and active updates set one atom to true/false and then compute derived updates using a logic program. Just like the atomic actions of dynamic logic, the atomic updates can be combined into update programs with the operators sequential composition, choice and iteration. We have one more update action (also present in dynamic logic): the test of a formula. n n•The declarative semantics for formulas and updates, is based on Kripke structures. Because of the specific language of updates, we have many properties of the semantics that are not present in propositional dynamic logic (PDL). One of these properties is that we can identify worlds with the same valuation in a structure, the resulting structure is called normalized, and it is equivalent to the original structure. n n•We have a proof system for PDDL which is soundand complete for the class of ‘full’ structures. For non-full structures, the main problem is the axiomatization of successor worlds. For the most interesting class of (non-full) structures given some set of constraints, we give a reduction of the non-full case to the full case. n n•We have a Plotkin-style operational semantics for update programs. The operational semantics allows us to compute the result of executing an update in some database state. A database state is a set of (propositional) formulas and specifies some subset of the worlds in a structure (the worlds in whichs the database state is true). The operational and declarative semantics are shown to be equivalent.

A Specification Language for Static, Dynamic and Deontic Integrity Constraints

In the proof-theoretic view of knowledge bases (KBs), a KB is a set of facts (atomic sentences) and integrity constraints (ICs). An IC is then a sentence which must at least be consistent with the other sentences in the KB. This view obliterates the distinction between, for example, the constraint that age is a non-negative integer (which is true of the universe of discourse (UoD) but may be false in a particular implementation of a KB), and the constraint that a class must have precisely one teacher (which is false of the UoD if a class actually has two teachers). The second constraint is called deontic and constrains the UoD; the first constraint is a necessary truth of the UoD and does not constraint the UoD. Instead, it constrains the implementation of the KB. We show that both types of constraints can be specified in the single framework provided by a deontic variant of dynamic logic, which has the added advantage of being able to specify dynamic constraints as well. We give a non-trivial example of a KB specification with static, dynamic and deontic constraints.

Integrating Semi-formal and Formal Requirements

In this paper, we report on the integration of informal, semiformal and formal requirements specification techniques. We present a framework for requirements specification called TRADE, within which several well-known semiformal specification techniques are placed. TRADE is based on an analysis of structured and object-oriented requirements specification methods. In this paper, we combine TRADE with the logic-based specification language Albert II and show that this leads to a coherent formal and semiformal requirements specification. We illustrate our approach with examples taken from a large distributed telecommunication application case study performed in the context of the Esprit project 2RARE.

Dynamic Database Logic: the First-order Case

We present Dynamic Database Logic (DDL), a language designed to reaxadson about database updates. DDL is based on dynamic logic. We give a declarative semantics and a sound proof system for DDL (for a restricted case, we also have a completeness result). We show with a detailed example, how the proof system of DDL can be used to prove correctness of an update program given some specification for the update program. The update language part of DDL is shown to be update complete and specification complete (in the sense of Abiteboul & Vianu).

Formal analysis of the Shlaer-Mellor method: Towards a toolkit of formal and informal requirements specification techniques

In this paper, we define a number of tools that we think belong to the core of any toolkit for requirements engineers. The tools are conceptual and hence, they need precise definitions that lay down as exactly as possible what their meaning and possible use is. We argue that this definition can best be achieved by a formal specification of the tool. This means that for each semi-formal requirements engineering tool we should provide a formal specification that precisely specifies its meaning. We argue that this mutually enhances the formal and semi-formal technique: it makes formal techniques more usable and, as we will argue, at the same time simplifies the diagram-based notations.At the same time, we believe that the tools of the requirements engineer should, where possible, resemble the familiar semi-formal specification techniques used in practice today. In order to achieve this, we should search existing requirements specification techniques to look for a common kernel of familiar semi-formal techniques and try to provide a formalisation for these.In this paper we illustrate this approach by a formal analysis of the Shlaer-Mellor method for object-oriented requirements specification. The formal specification language used in this analysis is LCM, a language based on dynamic logic, but similar results would have been achieved by means of another language. We analyse the techniques used in the information model, state model, process model and communication model of the Shlaer-Mellor method, identify ambiguities and redundancies, indicate how these can be eliminated and propose a formalisation of the result. We conclude with a listing of the tools extracted from the Shlaer-Mellor method that we can add to a toolkit that in addition contains LCM as formal specification technique.