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Results for “Formal Reasoning”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Formalized Reasoning of Operational Volumes for Wildland Fire Fighting

This work is focused on the formalized reasoning of operational volumes as it relates to the current and future technologies developed by NASA to aid in wildland firefighting operations. One such technology is the Unmanned Aircraft System Pilot Kit (UASP-kit) developed by the Scalable Traffic Management for Emergency Response Operations (STEReO) project at NASA, which is used to increase situational awareness for a ground operator in the field. The UASP-kit utilizes operational volumes to represent mission areas and alerting volumes; these volumes, in combinations with ADS-B data, can then be used to alert the ground operator when another aircraft has entered one of these areas. This work presents a rigorous foundation for the concept of operational volumes for modeling and prototyping operations in such a tool as the UASP-kit. This includes establishing a class of algorithms to detect when an object is in an operational volume, and when one operational volume intersects or is contained in another. Additionally, this work provides rigorous proof that the algorithms work as intended. Scenarios are presented that model current UASP-kit operations and extend past the current capabilities of the technology to modeling more complex scenarios such as mission planning.

Operational Volumes↗
NASA NTRSDate not supplied

Formalized Reasoning of Operational Volumes for Wildland Fire Fighting

This work is focused on the formalized reasoning of operational volumes as it relates to the current and future technologies developed by NASA to aid in wildfire fighting operations. One such technology is the unmanned aircraft system pilot kit (UASP-kit) developed by the Scalable Traffic Management for Emergency Response Operations (STEReO) project at NASA, which is used to increase situation awareness for a ground operator in the field. The UASP-kit utilizes operational volumes which represent mission areas and alerting volumes, to alert when another aircraft is within one of these volumes from received ADS-B data. This work is focused on developing a rigorous foundation for the concept of operational volumes for modeling and prototyping operations in such a tool as the UASP-kit. This includes establishing a class of algorithms to detect when an object is in an operational volume, and when an operational volume is intersecting or contained within another. Additionally, this work is focused on providing rigorous proof in an interactive theorem prover that the algorithms work as intended. Scenarios are presented that model current UASP-kit operations and extend past the current capabilities of the technology to modeling more complex scenarios such as mission planning.

Operational Volumes↗
NASA NTRS1994

Open architectures for formal reasoning and deductive technologies for software development

The objective of this project is to develop an open architecture for formal reasoning systems. One goal is to provide a framework with a clear semantic basis for specification and instantiation of generic components; construction of complex systems by interconnecting components; and for making incremental improvements and tailoring to specific applications. Another goal is to develop methods for specifying component interfaces and interactions to facilitate use of existing and newly built systems as 'off the shelf' components, thus helping bridge the gap between producers and consumers of reasoning systems. In this report we summarize results in several areas: our data base of reasoning systems; a theory of binding structures; a theory of components of open systems; a framework for specifying components of open reasoning system; and an analysis of the integration of rewriting and linear arithmetic modules in Boyer-Moore using the above framework.

Mccarthy, John↗
NASA NTRS1996

Three-color resonance ionization spectroscopy of Zr in Si

As our society becomes technologically more complex, computers are being used in greater and greater numbers of high consequence systems. Giving a machine control over the lives of humans can be disturbing, especially if the software that is run on such a machine has bugs. Formal reasoning is one of the most powerful techniques available to demonstrate the correctness of a piece of software. When reasoning about software and its development, one frequently encounters expressions that contain partial functions. As might be expected, the presence of partial functions introduces an additional dimension of difficulty to the reasoning framework. This difficulty produces an especially strong impact in the case of high consequence systems. An ability to use formal methods for constructing software is essential if we want to obtain greater confidence in such systems through formal reasoning. This is only reasonable under automation of software development and verification. However, the ubiquitous presence of partial functions prevents a uniform application to software of any tools not specifically accounting for partial functions. In this paper we will describe a framework for reasoning about software, based on the nonstrict explicit domain approach, that is applicable to a large class of software/hardware systems. In this framework the Hoare triples containing partial functions can be reasoned about automatically in a well-defined and uniform manner.

Hansen, C. S.↗
NASA NTRS2012

Semantically-Rigorous Systems Engineering Modeling Using Sysml and OWL

The Systems Modeling Language (SysML) has found wide acceptance as a standard graphical notation for the domain of systems engineering. SysML subsets and extends the Unified Modeling Language (UML) to define conventions for expressing structural, behavioral, and analytical elements, and relationships among them. SysML-enabled modeling tools are available from multiple providers, and have been used for diverse projects in military aerospace, scientific exploration, and civil engineering. The Web Ontology Language (OWL) has found wide acceptance as a standard notation for knowledge representation. OWL-enabled modeling tools are available from multiple providers, as well as auxiliary assets such as reasoners and application programming interface libraries, etc. OWL has been applied to diverse projects in a wide array of fields. While the emphasis in SysML is on notation, SysML inherits (from UML) a semantic foundation that provides for limited reasoning and analysis. UML's partial formalization (FUML), however, does not cover the full semantics of SysML, which is a substantial impediment to developing high confidence in the soundness of any conclusions drawn therefrom. OWL, by contrast, was developed from the beginning on formal logical principles, and consequently provides strong support for verification of consistency and satisfiability, extraction of entailments, conjunctive query answering, etc. This emphasis on formal logic is counterbalanced by the absence of any graphical notation conventions in the OWL standards. Consequently, OWL has had only limited adoption in systems engineering. The complementary strengths and weaknesses of SysML and OWL motivate an interest in combining them in such a way that we can benefit from the attractive graphical notation of SysML and the formal reasoning of OWL. This paper describes an approach to achieving that combination.

Web Ontology Language (OWL)↗
NASA NTRS1992

Formal mechanization of device interactions with a process algebra

The principle emphasis is to develop a methodology to formally verify correct synchronization communication of devices in a composed hardware system. Previous system integration efforts have focused on vertical integration of one layer on top of another. This task examines 'horizontal' integration of peer devices. To formally reason about communication, we mechanize a process algebra in the Higher Order Logic (HOL) theorem proving system. Using this formalization we show how four types of device interactions can be represented and verified to behave as specified. The report also describes the specification of a system consisting of an AVM-1 microprocessor and a memory management unit which were verified in previous work. A proof of correct communication is presented, and the extensions to the system specification to add a direct memory device are discussed.

Schubert, E. Thomas↗
NASA NTRS2022

Towards an Implementation of Differential Dynamic Logic in PVS

This paper describes an ongoing effort to embed and verify differential dynamic logic (dL) in the Prototype Verification System (PVS). dL is a logic for specifying and formally reasoning about hybrid systems, which employ both continuous and discrete dynamics. There are several benefits of this effort. First, the embedding of dL in PVS offers an independent formal verification of the semantics and rules of dL. Second, the embedding is fully operational within PVS, giving PVS practitioners the ability to use dL in the formal specification and verification process. Third, the rich specification language, type system, and powerful interactive prover of PVS can be used on dL objects. In addition to the embedding and verification of dL, a custom extension for Visual Studio Code has been developed, so that a stylized dL syntax can be used to specify hybrid programs and their properties.

Differential Dynamic Logic↗
NASA NTRSDate not supplied

Towards Formalization of Advanced Linear Algebra with Applications to Dynamical Systems using PVS

Linear Algebra is essential for numerous aerospace problems of interest. Formal reasoning about hybrid systems that contain variables modeled by differential equations rely on concepts from Linear Algebra such as eigenvalues, matrix decompositions, and matrix valued functions. For example, the long-term dynamics of a system of differential equations depend on the stability/instability of its equilibrium points, which often reduces to an eigenvalue problem. This talk will embark on a quest to formalize theorems and results about eigenvalues and eigenvectors using PVS. We shall start our journey with 2 x 2 complex matrices, where we will apply our PVS code to a simple example of a dynamical system. Since it can be difficult or impossible to give simple expressions of eigenvalues for larger matrices (i.e. 5 x 5 or higher), we then move towards specifying the power method for verified computation of eigenvalue approximations in PVS. This effort requires development of multivariate complex arithmetic. At the end of the day, having such additions to the PVS NASA libraries will help move towards the use of formal methods to verify concepts of control theory and system level verification.

Linear Algebra↗
NASA NTRS1995

The scheme machine: A case study in progress in design derivation at system levels

The Scheme Machine is one of several design projects of the Digital Design Derivation group at Indiana University. It differs from the other projects in its focus on issues of system design and its connection to surrounding research in programming language semantics, compiler construction, and programming methodology underway at Indiana and elsewhere. The genesis of the project dates to the early 1980's, when digital design derivation research branched from the surrounding research effort in programming languages. Both branches have continued to develop in parallel, with this particular project serving as a bridge. However, by 1990 there remained little real interaction between the branches and recently we have undertaken to reintegrate them. On the software side, researchers have refined a mathematically rigorous (but not mechanized) treatment starting with the fully abstract semantic definition of Scheme and resulting in an efficient implementation consisting of a compiler and virtual machine model, the latter typically realized with a general purpose microprocessor. The derivation includes a number of sophisticated factorizations and representations and is also deep example of the underlying engineering methodology. The hardware research has created a mechanized algebra supporting the tedious and massive transformations often seen at lower levels of design. This work has progressed to the point that large scale devices, such as processors, can be derived from first-order finite state machine specifications. This is roughly where the language oriented research stops; thus, together, the two efforts establish a thread from the highest levels of abstract specification to detailed digital implementation. The Scheme Machine project challenges hardware derivation research in several ways, although the individual components of the system are of a similar scale to those we have worked with before. The machine has a custom dual-ported memory to support garbage collection. It consists of four tightly coupled processes--processor, collector, allocator, memory--with a very non-trivial synchronization relationship. Finally, there are deep issues of representation for the run-time objects of a symbolic processing language. The research centers on verification through integrated formal reasoning systems, but is also involved with modeling and prototyping environments. Since the derivation algebra is basd on an executable modeling language, there is opportunity to incorporate design animation in the design process. We are looking for ways to move smoothly and incrementally from executable specifications into hardware realization. For example, we can run the garbage collector specification, a Scheme program, directly against the physical memory prototype, and similarly, the instruction processor model against the heap implementation.

Johnson, Steven D.↗
NASA NTRS2010

A Prototype Embedding of Bluespec System Verilog in the PVS Theorem Prover

Bluespec SystemVerilog (BSV) is a Hardware Description Language based on the guarded action model of concurrency. It has an elegant semantics, which makes it well suited for formal reasoning. To date, a number of BSV designs have been verified with hand proofs, but little work has been conducted on the application of automated reasoning. We present a prototype shallow embedding of BSV in the PVS theorem prover. Our embedding is compatible with the PVS model checker, which can automatically prove an important class of theorems, and can also be used in conjunction with the powerful proof strategies of PVS to verify a broader class of properties than can be achieved with model checking alone.

Richards, Dominic↗
NASA NTRS2017

R2U2: Tool Overview

R2U2 (Realizable, Responsive, Unobtrusive Unit) is an extensible framework for runtime System HealthManagement (SHM) of cyber-physical systems. R2U2 can be run in hardware (e.g., FPGAs), or software; can monitorhardware, software, or a combination of the two; and can analyze a range of different types of system requirementsduring runtime. An R2U2 requirement is specified utilizing a hierarchical combination of building blocks: temporal formula runtime observers (in LTL or MTL), Bayesian networks, sensor filters, and Boolean testers. Importantly, the framework is extensible; it is designed to enable definitions of new building blocks in combination with the core structure. Originally deployed on Unmanned Aerial Systems (UAS), R2U2 is designed to run on a wide range of embedded platforms, from autonomous systems like rovers, satellites, and robots, to human-assistive ground systems and cockpits. R2U2 is named after the requirements it satisfies; while the exact requirements vary by platform and mission, the ability to formally reason about realizability, responsiveness, and unobtrusiveness is necessary for flight certifiability, safety-critical system assurance, and achievement of technology readiness levels for target systems. Realizability ensures that R2U2 is suficiently expressive to encapsulate meaningful runtime requirements while maintaining adaptability to run on different platforms, transition between different mission stages, and update quickly between missions. Responsiveness entails continuously monitoring the system under test, real-time reasoning, reporting intermediate status, and as-early-as-possible requirements evaluations. Unobtrusiveness ensures compliance with the crucial properties of the target architecture: functionality, certifiability, timing, tolerances, cost, or other constraints.

Rozier, Kristin Y.↗
NASA NTRS1985

A formalization of commonsense reasoning based on fuzzy logic

The basic idea underlying the approach outlined in this paper is that commonsense knowledge may be regarded as a collection of dispositions, that is, propositions which are preponderantly, but not necessarily always, true. Technically, a disposition may be interpreted as a proposition with implicit fuzzy quantifiers, e.g., most, almost all, usually, often, etc. For example, a disposition such as Swedes are blond may be interpreted as most Swedes are blond. For purposes of inference from commonsense knowledge, the conversion of a disposition into a proposition with explicit fuzzy quantifiers sets the stage for an application of syllogistic reasoning in which the premises are allowed to be of the form Q A's are B's, where A and B are fuzzy predicates and Q is a fuzzy quantifier. In general, the conclusion yielded by such reasoning is a proposition which may be converted into a disposition through the suppression of fuzzy quantifiers.

Zadeh, L. A.↗
NASA NTRS2013

On a Formal Tool for Reasoning About Flight Software Cost Analysis

A report focuses on the development of flight software (FSW) cost estimates for 16 Discovery-class missions at JPL. The techniques and procedures developed enabled streamlining of the FSW analysis process, and provided instantaneous confirmation that the data and processes used for these estimates were consistent across all missions. The research provides direction as to how to build a prototype rule-based system for FSW cost estimation that would provide (1) FSW cost estimates, (2) explanation of how the estimates were arrived at, (3) mapping of costs, (4) mathematical trend charts with explanations of why the trends are what they are, (5) tables with ancillary FSW data of interest to analysts, (6) a facility for expert modification/enhancement of the rules, and (7) a basis for conceptually convenient expansion into more complex, useful, and general rule-based systems.

Spagnuolo, John N., Jr.↗
NASA NTRS1988

Approximate spatial reasoning

Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.

Dutta, Soumitra↗
DOE OSTI2022

Analytic Gaussian covariance matrices for galaxy N-point correlation functions

Here, we derive analytic covariance matrices for the N-point correlation functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary N and projected onto the isotropic basis functions given by spherical harmonics and Wigner 3j symbols. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a nonuniform window function. Our result is recently shown to facilitate NPCF analysis on a realistic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Testing T2K’s Bayesian constraints with priors in alternate parameterisations

Bayesian analysis results require a choice of prior distribution. In long-baseline neutrino oscillation physics, the usual parameterisation of the mixing matrix induces a prior that privileges certain neutrino mass and flavour state symmetries. Here we study the effect of privileging alternate symmetries on the results of the T2K experiment. We find that constraints on the level of CP violation (as given by the Jarlskog invariant) are robust under the choices of prior considered in the analysis. On the other hand, the degree of octant preference for the atmospheric angle depends on which symmetry has been privileged.

Bayesian Inference↗