Towards lightweight integration of SMT solvers

A large variety of SMT techniques and associated solvers have been developed by the formal modelling and verification communities. For a particular application domain, each technique has its own unique set of advantages and limitations. Within the context of a particular application domain (characterized by a particular set of possible logical formulas), the fitness of a technique can be characterized along multiple dimensions: expressiveness, soundness, completeness, response time, computational cost, and others. Furthermore, certain application domains may require that multiple techniques be used in concert in order to address the particular set of formulas that must be supported. We present a prototype lightweight integrated environment that incorporates four different cloud-hosted SMT solvers behind a single web-based interface: CVC3, Alt-Ergo, Yices, and Z3. Formulas submitted using a common logical syntax are translated into representations suitable for each of the underlying SMT solvers. We discuss the characteristics of each of the SMT solvers, in part by presenting the target syntaxes of the translations (including what outputs the solvers can produce and how this relates to their completeness with respect to the common syntax). We then discuss future directions, including the automated characterization of SMT solvers integrated into the infrastructure in terms of expressiveness, completeness, and response time

E-Generalization Using Grammars

We extend the notion of anti-unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of E-generalization sets. We present a framework to combine Inductive Logic Programming and E-generalization that includes an extension of Plotkin's lgg theorem to the equational case. We demonstrate the potential power of E-generalization by three example applications: computation of suggestions for auxiliary lemmas in equational inductive proofs, computation of construction laws for given term sequences, and learning of screen editor command sequences.Comment: 49 pages, 16 figures, author address given in header is meanwhile outdated, full version of an article in the "Artificial Intelligence Journal", appeared as technical report in 2003. An open-source C implementation and some examples are found at the Ancillary file

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

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Provably Correct Floating-Point Implementation of a Point-In-Polygon Algorithm

The problem of determining whether or not a point lies inside a given polygon occurs in many applications. In air traffic management concepts, a correct solution to the point-in-polygon problem is critical to geofencing systems for Unmanned Aerial Vehicles and in weather avoidance applications. Many mathematical methods can be used to solve the point-in-polygon problem. Unfortunately, a straightforward floating- point implementation of these methods can lead to incorrect results due to round-off errors. In particular, these errors may cause the control flow of the program to diverge with respect to the ideal real-number algorithm. This divergence potentially results in an incorrect point-in- polygon determination even when the point is far from the edges of the polygon. This paper presents a provably correct implementation of a point-in-polygon method that is based on the computation of the winding number. This implementation is mechanically generated from a source- to-source transformation of the ideal real-number specification of the algorithm. The correctness of this implementation is formally verified within the Frama-C analyzer, where the proof obligations are discharged using the Prototype Verification System (PVS)

Natural Communication

In Natural Communication, the author criticizes the current paradigm of specific goal orientation in the complexity sciences. His model of "natural communication" encapsulates modern theoretical concepts from mathematics and physics, in particular category theory and quantum theory. The author is convinced that only by looking to the past is it possible to establish continuity and coherence in the complexity science