Hierarchical Distributed Reasoning System for Geometric Image Generation

The concept of hierarchical reasoning system was introduced in [5], where an intuitive method to build such systems based on their inputs is given. In this paper we formalize several concepts which open a possible research line concerning the use of these structures. A hierarchical reasoning system H is a directed graph organized on several levels such that each node of the level j is a hyper-schema of order j. As a mathematical structure, H is an abstract one and a special kind of formal computation is introduced. As a result of this computation we obtain a set F(H) of formulas. We explain what we understand by an interpretation of H and define its corresponding semantical computation. By means of an interpretation I(H) for H and applying the rules of the semantical computation, each element of w in F(H) becomes some object I(w) of a given space. We exemplify these concepts and we show that for two distinct interpretations I1(H) and I2(H) for the same system H, a given formula w in F(H) is transformed into a sentence I1(w) of a natural language whereas I2(w) is a geometric image. A short description of a Java implementation of a hierarchical system generating images is also given in a separate section. By examples we show that the mechanism introduced in this paper allows us to model the distributed knowledge. Finally several open problems are specified

Relationships among the metallurgical condition, hardness, and the electrical conductivity of aluminum alloys

Electrical conductivity measurements (eddy current determined) combined with indentation hardness measurements are now being used throughout the aerospace industry for nondestructive evaluation of the metallurgical condition of commercial precipitation hardenable aluminum alloys. The review of literature and experiments with two aluminum alloys, 7178 and a 5% Zn-Al binary, have shown that skilled interpretation of hardness-conductivity data depends not only upon a qualitative understanding of the modern wave mechanical theories of electron conduction, but also upon some knowledge of the precipitation reaction kinetics. In particular, the effects of quenched-in vacancies and retrogression upon the reaction kinetics must be considered. Studies of conductivity vs temperature in the range of 0 to 75⁰F show that the resulting conductivity changes do not result in increased interpretative information and the Matthiessen\u27s rule and Hansen\u27s equation both apply. Hansen\u27s equation relates conductivity (K) of a sample to its temperature coefficient of resistance (α) in the form of K = Bα + C where B and C are constants. The values of B and C depend only upon the alloy system being considered. A practical result is that the conductivity for an unknown sample can be evaluated at any known ambient temperature and then corrected to its room temperature value by calculating the sample\u27s coefficient of resistance using Hansen\u27s equation. The inverse calculation could also be made --Abstract, page ii

Refinement by interpretation in {\pi}-institutions

The paper discusses the role of interpretations, understood as multifunctions that preserve and reflect logical consequence, as refinement witnesses in the general setting of pi-institutions. This leads to a smooth generalization of the refinement-by-interpretation approach, recently introduced by the authors in more specific contexts. As a second, yet related contribution a basis is provided to build up a refinement calculus of structured specifications in and across arbitrary pi-institutions.Comment: In Proceedings Refine 2011, arXiv:1106.348

Predicate Abstraction with Indexed Predicates

Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model checking. We consider models containing first-order state variables, where the system state includes mutable functions and predicates. Such a model can describe systems containing arbitrarily large memories, buffers, and arrays of identical processes. We describe a form of predicate abstraction that constructs a formula over a set of universally quantified variables to describe invariant properties of the first-order state variables. We provide a formal justification of the soundness of our approach and describe how it has been used to verify several hardware and software designs, including a directory-based cache coherence protocol.Comment: 27 pages, 4 figures, 1 table, short version appeared in International Conference on Verification, Model Checking and Abstract Interpretation (VMCAI'04), LNCS 2937, pages = 267--28

Program development using abstract interpretation (and the ciao system preprocessor)

The technique of Abstract Interpretation has allowed the development of very sophisticated global program analyses which are at the same time provably correct and practical. We present in a tutorial fashion a novel program development framework which uses abstract interpretation as a fundamental tool. The framework uses modular, incremental abstract interpretation to obtain information about the program. This information is used to validate programs, to detect bugs with respect to partial specifications written using assertions (in the program itself and/or in system librarles), to genérate and simplify run-time tests, and to perform high-level program transformations such as múltiple abstract specialization, parallelization, and resource usage control, all in a provably correct way. In the case of validation and debugging, the assertions can refer to a variety of program points such as procedure entry, procedure exit, points within procedures, or global computations. The system can reason with much richer information than, for example, traditional types. This includes data structure shape (including pointer sharing), bounds on data structure sizes, and other operational variable instantiation properties, as well as procedure-level properties such as determinacy, termination, non-failure, and bounds on resource consumption (time or space cost). CiaoPP, the preprocessor of the Ciao multi-paradigm programming system, which implements the described functionality, will be used to illustrate the fundamental ideas

Incompleteness of States w.r.t. Traces in Model Checking

Cousot and Cousot introduced and studied a general past/future-time specification language, called mu*-calculus, featuring a natural time-symmetric trace-based semantics. The standard state-based semantics of the mu*-calculus is an abstract interpretation of its trace-based semantics, which turns out to be incomplete (i.e., trace-incomplete), even for finite systems. As a consequence, standard state-based model checking of the mu*-calculus is incomplete w.r.t. trace-based model checking. This paper shows that any refinement or abstraction of the domain of sets of states induces a corresponding semantics which is still trace-incomplete for any propositional fragment of the mu*-calculus. This derives from a number of results, one for each incomplete logical/temporal connective of the mu*-calculus, that characterize the structure of models, i.e. transition systems, whose corresponding state-based semantics of the mu*-calculus is trace-complete

Static Safety for an Actor Dedicated Process Calculus by Abstract Interpretation

The actor model eases the definition of concurrent programs with non uniform behaviors. Static analysis of such a model was previously done in a data-flow oriented way, with type systems. This approach was based on constraint set resolution and was not able to deal with precise properties for communications of behaviors. We present here a new approach, control-flow oriented, based on the abstract interpretation framework, able to deal with communication of behaviors. Within our new analyses, we are able to verify most of the previous properties we observed as well as new ones, principally based on occurrence counting