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 (IC's) for conceptual models (CM's). An important problem not discussed 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 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

Super Logic Programs

The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas. Our main results are two new and powerful characterizations of the static semant ics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions. Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs which we developed based on the model-theoretic characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200

Commonsense axiomatizations for logic programs

AbstractVarious semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second-order formulas. The semantics of Clark, Fitting, and Kunen are characterized in this framework, and a finite first-order presentation of Kunen's semantics is described. A new axiom to represent “commonsense” reasoning is proposed for logic programs. It is shown that the well-founded semantics and stable models are definable with this axiom. The roles of domain augmentation and domain closure are examined. A “domain foundation” axiom is proposed to replace the domain closure axiom

A general approach to temporal reasoning about action and change

Reasoning about actions and change based on common sense knowledge is one of the most important and difficult tasks in the artificial intelligence research area. A series of such tasks are identified which motivate the consideration and application of reasoning formalisms. There follows a discussion of the broad issues involved in modelling time and constructing a logical language. In general, worlds change over time. To model the dynamic world, the ability to predict what the state of the world will be after the execution of a particular sequence of actions, which take time and to explain how some given state change came about, i.e. the causality are basic requirements of any autonomous rational agent. The research work presented herein addresses some of the fundamental concepts and the relative issues in formal reasoning about actions and change. In this thesis, we employ a new time structure, which helps to deal with the so-called intermingling problem and the dividing instant problem. Also, the issue of how to treat the relationship between a time duration and its relative time entity is examined. In addition, some key terms for representing and reasoning about actions and change, such as states, situations, actions and events are formulated. Furthermore, a new formalism for reasoning about change over time is presented. It allows more flexible temporal causal relationships than do other formalisms for reasoning about causal change, such as the situation calculus and the event calculus. It includes effects that start during, immediately after, or some time after their causes, and which end before, simultaneously with, or after their causes. The presented formalism allows the expression of common-sense causal laws at high level. Also, it is shown how these laws can be used to deduce state change over time at low level. Finally, we show that the approach provided here is expressive