Abstract. In the dominant view of knowledge bases (KB's), a KB is a set of facts (atomic sentences) and integrity constraints (IC's). 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 IC's 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 IC's, and a non-trivial example of a KB specification with static, dynamic and deontic constraints.

In this paper, we motivate and present a data model for conceptual design of structural and behavioural aspects of databases. We follow an object centered design paradigm in the spirit of semantic data models. The specification of structural aspects is divided into modelling of object structures and modelling of data types used for describing object properties. The specification of object structures is based on an Extended Entity--Relationship (EER) model. The specification of behavioural aspects is divided into the modelling of admissible database state evolutions by means of temporal integrity constraints and the formulation of database (trans)actions. The central link for integrating these design components is a descriptive logic-- based query language for the EER model. The logic part of this language is the basis for static constraints and descriptive action specifications by means of pre- and postconditions. A temporal extension of this logic is the specification language for tem...

In this paper, we argue that object-oriented models must be able to represent three kinds of taxonomic structures: static classes, dynamic classes, and role classes, that behave differently with respect to object migration. If CAR is a static subclass of V EHICLE, then a vehicle that is not a car can never migrate to the CAR subclass. On the other hand, if EMP loyee is a dynamic subclass of PERSON object class, 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. By contrast, if EMP is modeled as a role class of PERSON , then every employee differs from every person, but a PERSON instance can acquire one or more EMP instances as roles. The distinctions between the three kinds of classes are orthogonal, so that we can have, for example, dynamic subclasses of object or role classes, or role classes of dynamic or static classes. The paper is divided into two parts. In the first, infor...

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).

We give a semantics for lightweight UML class diagrams and ultra-lightweight statecharts in terms of labeled step transition systems that embody a minimal change, maximal step semantics, and in which changes generated in a step have effect in the following step. In order to define the semantics, we introduce dynamic step logic. 1 Introduction 1.1 Purpose In this paper we define a mixed formal specification language whose diagram syntax is a very simple subset of the UML syntax [27] and whose textual syntax is a version of ordersorted dynamic logic. We refer to this language as ultra-lightweight UML (ultra-LUML). The visual part of ultra-LUML consists of ultra-leightweight class diagrams (ultra-LCDs), which declare the decomposition of the system into objects, and of extended Mealy state diagrams (EMDs), which define object behavior. The textual part of utra-LUML is a version of dynamic logic and can be used to write a specification that is equivalent to a diagrammatic specificati...

The specification of a database system consists of the description of its static information structure as well as of its dynamic behaviour. Whereas in classic conceptual database design the main interest was on the static part, specification of database dynamics became an important topic in the last few years.

In [18,23], we presented a language for the specification of static, dynamic and deontic integrity constraints (IC's) for conceptual models (CM's). An important problem not dis-cussed in that paper is how IC's 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 IC's, where conditions are preconditions 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 (we)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.

: An extended entity-relationship model concentrating nearly all concepts of known "semantic" data models and especially allowing arbitrary user defined data types is introduced. The semantics of the model is described purely in algebraic terms mainly based on the notions of signature, algebra and extension. On this basis a calculus making intensive use of abstract data types is defined and employed for the formulation of typical integrity constaints like functional restrictions and key specifications. Keywords: Theory of data bases, data model, entity-relationship model, formal semantics, calculus, abstract data type, aggregate function, relational completeness, integrity constraint. 1. Introduction Among the different steps for the design of a database the conceptual design plays a mayor role [TF82, Ce83]. Here all requirements of later database users are collected and described in a formal way. Many authors (among them [Ch76]) agree that the Entity-Relationship model is the most ade...

In this paper we investigate preferential semantics for declarative specifications in a First Order Modal Action Logic. We address some well known problems: the frame problem, the qualification problem and the ramification problem. We incorporate the assumptions that are inherent to both the frame and qualification problem into the semantics of the modal Action Logic by defining orderings over Dynamic Logic models. These orderings allow us to identify for each declarative Dynamic Logic action specification a unique intended model.

Knowledge Base Systems should in principle be able to store and manipulate any sort of knowledge, including vague (indefinite) knowledge, knowledge about events and obligations and knowledge about temporal aspects. In this paper a language, CPL, is introduced in which all these different kinds of knowledge can be expressed. This language is based on the linguistic theory of Functional Grammar. The semantics of this language is based on a logical interpretation of the language structures, for which we use five different forms of logic: predicate, modal, deontic, dynamic and temporal logic. Inferences, based on these logics, that can be made within this language, are shown. Keywords: Knowledge Bases, Linguistics, Modal logic, Deontic logic, Dynamic Logic, Temporal Logic. 1. Introduction The word "knowledge base" has been introduced in computer science in the beginning of the eighties. There are mainly two fields in which the word occurs. The first is databases and the second i...