Allen L. Brown

A program development tool

In this paper we describe how we have combined a number of tools (most of which are tailored to a particular programming language) into a single system to aid in the reading, writing, and running of programs. We discuss the efficacy and the structure of two such systems, one of which has been used to build several large application programs. We report some of the experience we have gained in evolving these systems. We first describe the system components which users have found most important; some of the facilities described here are new in the literature. Second, we attempt to show how these tools form a synergistic union, and we illustrate this point with a number of examples. Third, we illustrate the use of various system commands in the development of a simple program. Fourth, we discuss the implementation of the system components and indicate how some of them have been generalized.

New results on semantical non-monotonic reasoning

In earlier reports we presented a semantical account of nonmonotonic reasoning based on the partial ordering of interpretations of standard logics. In this article we generalize and extend the earlier work. We elucidate the structural relation between the new work and the old. Finally, we apply the new results to give a logical semantical account of justification-based truth maintenance.

A Logical Reconstruction of Constraint Relaxation Hierarchies in Logic Programming

We propose an extension to Definite Horn Clauses by placing partial orders on the bodies of clauses. Such clauses are called relaxable clauses. These partial orders are interpreted as a specification of relaxation criteria in the proof of the consequent of a relaxable clause, i.e., the order in which to relax the conditions of truthhood of the consequent if all the goals in the body cannot be satisfied. We present a modal logic of preference that enables us to characterize these preference orders, both syntactically and semantically. The richer structure of the modal preference models reflects these preference orders; something that is absent in the essentially flat structure of traditional Herbrand models. A variant of SLD-resolution that generates solutions in the preferred order is presented. The notion of control as preference is introduced as a first step towards specifying control information in a logically coherent fashion. Relaxable Horn clauses can be used to succinctly specify constraint problems in formal design. It is worth noting that the development of preference logic was driven by the desire to characterize declaratively, problems in document layout. In [4] we give a completely declarative account of the stable models of a general logic program. The reader is referred to [3],[5]and [14] for a detailed account of nonmonotonicity as preferential reasoning,the soundness and completeness proofs for the logics and applicationsto Artificial Intelligence, such as deontic reasoning.

Default reasoning in natural language processing

In natural language, as in other computational task domains it is important to operate by default assumptions. First, many constraints required for constraint propagation are initially unspecified. Second, in highly ambiguous tasks such as text analysis, ambiguity can be reduced by considering more plausible scenarios first. Default reasoning is problematic for first-order logic when allowing non-monotonic inferences. Whereas in monotonic logic facts can only be asserted, in non-monotonic logic a system must be maintained consistent even as previously assumed defaults are being retracted.Non-monotonicty is pervasive in natural language due to the serial nature of utterances. When reading text left-to-right, it happens that default assumptions made early in the sentence must be withdrawn as reading proceeds. Truth maintenance, which accounts for non-monotonic inferences, can resolve this issue and address important linguistic phenomena. In this paper we describe how in NMG (Non-Monotonic Grammar), by monitoring a logic parser, a truth maintenance system can significantly, enhance the parsers capabilities.

Preference logics and nonmonotonicity in logic programming

It is claimed that the notion of preference is a fundamental modality in computing and is a generalization of the notion of minimality. A logic of feasible preference is presented. The non-monotonic behavior of negation in logic programming is modeled as a symbolic optimization problem. As a case study, for the class of logic programs with one or more stable models, we give a preferential transformation of logic programs that identifies their stable models as the optimal worlds in the intended model of the corresponding preferential theory. Minimization and minimization orderings are given explicit syntactic representations and their due status in the model theory. Preference logics gives a very elegant model theory for defaults, without any mention of fixpoints. Further, nonmonotonic reasoning is carried out in a monotonic logic, since members of the optimal worlds are not identified with theorems of a preferential theory. Preference logics have great potential to bring the areas of Symbolic Computation, Knowledge Representation and Classical Optimization closer.