Theory of Logic Programming
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Deductive databases need general formulas in rule bodies, not only conjuctions of literals. This is well known since the work of Lloyd and Topor about extended logic programming. Of course, formulas must be restricted in such a way that they can be effectively evaluated in finite time, and produce only a finite number of new tuples (in each iteration of the TP-operator: the fixpoint can still be infinite). It is also necessary to respect binding restrictions of built-in predicates: many of these predicates can be executed only when certain arguments are ground. Whereas for standard logic programming rules, questions of safety, allowedness, and range-restriction are relatively easy and well understood, the situation for general formulas is a bit more complicated. We give a syntactic analysis of formulas that guarantees the necessary properties.
Abstract interpretation-based model checking provides an approach to verifying properties of infinite-state systems. In practice, most previous work on abstract model checking is either restricted to verifying universal properties, or develops special techniques for temporal logics such as modal transition systems or other dual transition systems. By contrast we apply completely standard techniques for constructing abstract interpretations to the abstraction of a CTL semantic function, without restricting the kind of properties that can be verified. Furthermore we show that this leads directly to implementation of abstract model checking algorithms for abstract domains based on constraints, making use of an SMT solver.
The interest in extensions of the logic programming paradigm beyond the class of normal logic programs is motivated by the need of an adequate representation and processing of knowledge. One of the most difficult problems in this area is to find an adequate declarative semantics for logic programs. In the present paper a general preference criterion is proposed that selects the ‘intended’ partial models of generalized logic programs which is a conservative extension of the stationary semantics for normal logic programs of [Prz91]. The presented preference criterion defines a partial model of a generalized logic program as intended if it is generated by a stationary chain. It turns out that the stationary generated models coincide with the stationary models on the class of normal logic programs. The general wellfounded semantics of such a program is defined as the set-theoretical intersection of its stationary generated models. For normal logic programs the general wellfounded semantics equals the wellfounded semantics.
We propose a paraconsistent declarative semantics of possibly inconsistent generalized logic programs which allows for arbitrary formulas in the body and in the head of a rule (i.e. does not depend on the presence of any specific connective, such as negation(-as-failure), nor on any specific syntax of rules). For consistent generalized logic programs this semantics coincides with the stable generated models introduced in [HW97], and for normal logic programs it yields the stable models in the sense of [GL88].