Constructive problem solving : a model construction approach towards configuration

In this paper we give a formalisation of configuration as the task to construct for a given specification, which is understood as a finite set of logical formulas, a model that satisfies the specification. In this approach, a specification consists of two parts. One part describes the domain, the possible components, and their interdependencies. The other part specifies the particular object that is to be configured. The language that is used to represent knowledge about configuration problems integrates three sublanguages that allow one to express constraints, to build up taxonomies, and to define rules. We give a sound calculus by which one can compute solutions to configuration problems if they exist and that allows one to recognize that a specification is inconsistent. In particular, the calculus can be used in order to check whether a given configuration satisfies the specification

SCL with Theory Constraints

We lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory. In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution inferences by a partial model assumption instead of an a priori fixed order as done for instance in hierarchic superposition. The model representation consists of ground background theory literals and ground foreground first-order literals. One major advantage of the model guided approach is that clauses generated by SCL(T) enjoy a non-redundancy property that makes expensive testing for tautologies and forward subsumption completely obsolete. SCL(T) is a semi-decision procedure for pure clause sets that are clause sets without first-order function symbols ranging into the background theory sorts. Moreover, SCL(T) can be turned into a decision procedure if the considered combination of a first-order logic modulo a background theory enjoys an abstract finite model property.Comment: 22 page

{SCL} with Theory Constraints

We lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory. In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution inferences by a partial model assumption instead of an a priori fixed order as done for instance in hierarchic superposition. The model representation consists of ground background theory literals and ground foreground first-order literals. One major advantage of the model guided approach is that clauses generated by SCL(T) enjoy a non-redundancy property that makes expensive testing for tautologies and forward subsumption completely obsolete. SCL(T) is a semi-decision procedure for pure clause sets that are clause sets without first-order function symbols ranging into the background theory sorts. Moreover, SCL(T) can be turned into a decision procedure if the considered combination of a first-order logic modulo a background theory enjoys an abstract finite model property

Margrave: An Improved Analyzer for Access-Control and Configuration Policies

As our society grows more dependent on digital systems, policies that regulate access to electronic resources are becoming more common. However, such policies are notoriously difficult to configure properly, even for trained professionals. An incorrectly written access-control policy can result in inconvenience, financial damage, or even physical danger. The difficulty is more pronounced when multiple types of policy interact with each other, such as in routers on a network. This thesis presents a policy-analysis tool called Margrave. Given a query about a set of policies, Margrave returns a complete collection of scenarios that satisfy the query. Since the query language allows multiple policies to be compared, Margrave can be used to obtain an exhaustive list of the consequences of a seemingly innocent policy change. This feature gives policy authors the benefits of formal analysis without requiring that they state any formal properties about their policies. Our query language is equivalent to order-sorted first-order logic (OSL). Therefore our scenario-finding approach is, in general, only complete up to a user-provided bound on scenario size. To mitigate this limitation, we identify a class of OSL that we call Order-Sorted Effectively Propositional Logic (OS-EPL). We give a linear-time algorithm for testing membership in OS-EPL. Sentences in this class have the Finite Model Property, and thus Margrave\u27s results on such queries are complete without user intervention

Principles of Knowledge Representation and Reasoning in the FRAPPE System

The purpose of this paper is to elucidate the following four important architectural principles of knowledge representation and reasoning with the example of an implemented system: limited reasoning, truth maintenance, hybrid architecture, and many sorted logic.MIT Artificial Intelligence Laborator

A Rewriting Approach to the Combination of Data Structures with Bridging Theories

International audienceWe introduce a combination method à la Nelson-Oppen to solve the satisfiability problem modulo a non-disjoint union of theories connected with bridging functions. The combination method is particularly useful to handle verification conditions involving functions defined over inductive data structures. We investigate the problem of determining the data structure theories for which this combination method is sound and complete. Our completeness proof is based on a rewriting approach where the bridging function is defined as a term rewrite system, and the data structure theory is given by a basic congruence relation. Our contribution is to introduce a class of data structure theories that are combinable with a disjoint target theory via an inductively defined bridging function. This class includes the theory of equality, the theory of absolutely free data structures, and all the theories in between. Hence, our non-disjoint combination method applies to many classical data structure theories admitting a rewrite-based satisfiability procedure

Workshop on Database Programming Languages

These are the revised proceedings of the Workshop on Database Programming Languages held at Roscoff, Finistère, France in September of 1987. The last few years have seen an enormous activity in the development of new programming languages and new programming environments for databases. The purpose of the workshop was to bring together researchers from both databases and programming languages to discuss recent developments in the two areas in the hope of overcoming some of the obstacles that appear to prevent the construction of a uniform database programming environment. The workshop, which follows a previous workshop held in Appin, Scotland in 1985, was extremely successful. The organizers were delighted with both the quality and volume of the submissions for this meeting, and it was regrettable that more papers could not be accepted. Both the stimulating discussions and the excellent food and scenery of the Brittany coast made the meeting thoroughly enjoyable. There were three main foci for this workshop: the type systems suitable for databases (especially object-oriented and complex-object databases,) the representation and manipulation of persistent structures, and extensions to deductive databases that allow for more general and flexible programming. Many of the papers describe recent results, or work in progress, and are indicative of the latest research trends in database programming languages. The organizers are extremely grateful for the financial support given by CRAI (Italy), Altaïr (France) and AT&T (USA). We would also like to acknowledge the organizational help provided by Florence Deshors, Hélène Gans and Pauline Turcaud of Altaïr, and by Karen Carter of the University of Pennsylvania

Combining Decision Procedures for Sorted Theories

Abstract. The Nelson-Oppen combination method combines decision procedures for theories satisfying certain conditions into a decision pro-cedure for their union. While the method is known to be correct in the setting of unsorted first-order logic, some current implementations of it appear in tools that use a sorted input language. So far, however, there have been no theoretical results on the correctness of the method in a sorted setting, nor is it obvious that the method in fact lifts as is to logics with sorts. To bridge this gap between the existing theoretical results and the current implementations, we extend the Nelson-Oppen method to (order-)sorted logic and prove it correct under conditions sim-ilar to the original ones. From a theoretical point of view, the extension is relevant because it provides a rigorous foundation for the application of the method in a sorted setting. From a practical point of view, the extension has the considerable added benefits that in a sorted setting the method’s preconditions become easier to satisfy in practice, and the method’s nondeterminism is generally reduced.