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At least 19 records

Logical inference derivation of the quantum theoretical description of Stern–Gerlach and Einstein–Podolsky–Rosen–Bohm experiments

Highlights: •Logical inference connects data and their description in terms of concepts. •It is used to derive the description of Stern–Gerlach experiments. •Logical inference yields the description of Einstein–Podolsky–Rosen–Bohm experiments. •These logical inference derivations do not rely on concepts of quantum theory. -- Abstract: It is shown that the quantum-theoretical descriptions of idealized Stern–Gerlach and Einstein–Podolsky–Rosen–Bohm experiments result from a logical inference treatment of robust experiments, without relying on concepts of quantum theory. For concreteness, the derivation is given for the case that the Stern–Gerlach magnet deflects the beam in three different directions, which in quantum theory corresponds to a description in terms of spin-1 particles. The logical inference description of the Einstein–Podolsky–Rosen–Bohm experiment is shown to contain the quantum theoretical description as a particular case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds. - Highlights: • Logical inference applied to relativistic, massive, charged, and spinless particle experiments leads to the Klein–Gordon equation. • The relativistic Hamilton–Jacobi is scrutinized by employing a field description for the four-velocity. • Logical inference allows analysis of experiments with uncertainty in detection events and experimental conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Single board system for fuzzy inference

The very large scale integration (VLSI) implementation of a fuzzy logic inference mechanism allows the use of rule-based control and decision making in demanding real-time applications. Researchers designed a full custom VLSI inference engine. The chip was fabricated using CMOS technology. The chip consists of 688,000 transistors of which 476,000 are used for RAM memory. The fuzzy logic inference engine board system incorporates the custom designed integrated circuit into a standard VMEbus environment. The Fuzzy Logic system uses Transistor-Transistor Logic (TTL) parts to provide the interface between the Fuzzy chip and a standard, double height VMEbus backplane, allowing the chip to perform application process control through the VMEbus host. High level C language functions hide details of the hardware system interface from the applications level programmer. The first version of the board was installed on a robot at Oak Ridge National Laboratory in January of 1990.

Symon, James R.↗

Rapid Inference of Logic Gate Neural Networks for Anomaly Detection in High Energy Physics

The increasing data rates and complexity of detectors at the Large Hadron Collider (LHC) necessitate fast and efficient machine learning models, particularly for rapid selection of what data to store, known as triggering. Building on recent work in differentiable logic gates, we present a public implementation of a Convolutional Differentiable Logic Gate Neural Network (CLGN). We apply this to detecting anomalies at the Level-1 Trigger at CMS using public data from the CICADA project. We demonstrate that the CLGN achieves physics performance on par with or superior to conventional quantized neural networks. We also synthesize an LGN for a Field-Programmable Gate Array (FPGA) and show highly promising FPGA characteristics, notably zero Digital Signal Processor (DSP) resource usage. This work highlights the potential of logic gate networks for high-speed, on-detector inference in High Energy Physics and beyond.

FOS: Physical sciences↗

Jaynesian Analysis of Environmental Chemistry: Systems Model Component Integration via the Arctic Aquatic Carbon Cycle

Focal Areas: All three are touched upon from the OBER call. We will consider formal logical inference and entropic information analysis for sparse but intensive chemical measurements, as optimal drivers for managing process complexity. As a centerpiece for the discussion we take soil-to-sea organic structural evolution within the Arctic hydro-geochemosphere, assessing detrital negentropy then algorithmic greed to generate ranked, reduced mechanisms for system integration.

54 ENVIRONMENTAL SCIENCES↗

Cooperation Among Theorem Provers

This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.

Waldinger, Richard J.↗

Certifying Auto-Generated Flight Code

Model-based design and automated code generation are being used increasingly at NASA. Many NASA projects now use MathWorks Simulink and Real-Time Workshop for at least some of their modeling and code development. However, there are substantial obstacles to more widespread adoption of code generators in safety-critical domains. Since code generators are typically not qualified, there is no guarantee that their output is correct, and consequently the generated code still needs to be fully tested and certified. Moreover, the regeneration of code can require complete recertification, which offsets many of the advantages of using a generator. Indeed, manual review of autocode can be more challenging than for hand-written code. Since the direct V&V of code generators is too laborious and complicated due to their complex (and often proprietary) nature, we have developed a generator plug-in to support the certification of the auto-generated code. Specifically, the AutoCert tool supports certification by formally verifying that the generated code is free of different safety violations, by constructing an independently verifiable certificate, and by explaining its analysis in a textual form suitable for code reviews. The generated documentation also contains substantial tracing information, allowing users to trace between model, code, documentation, and V&V artifacts. This enables missions to obtain assurance about the safety and reliability of the code without excessive manual V&V effort and, as a consequence, eases the acceptance of code generators in safety-critical contexts. The generation of explicit certificates and textual reports is particularly well-suited to supporting independent V&V. The primary contribution of this approach is the combination of human-friendly documentation with formal analysis. The key technical idea is to exploit the idiomatic nature of auto-generated code in order to automatically infer logical annotations. The annotation inference algorithm itself is generic, and parametrized with respect to a library of coding patterns that depend on the safety policies and the code generator. The patterns characterize the notions of definitions and uses that are specific to the given safety property. For example, for initialization safety, definitions correspond to variable initializations while uses are statements which read a variable, whereas for array bounds safety, definitions are the array declarations, while uses are statements which access an array variable. The inferred annotations are thus highly dependent on the actual program and the properties being proven. The annotations, themselves, need not be trusted, but are crucial to obtain the automatic formal verification of the safety properties without requiring access to the internals of the code generator. The approach has been applied to both in-house and commercial code generators, but is independent of the particular generator used. It is currently being adapted to flight code generated using MathWorks Real-Time Workshop, an automatic code generator that translates from Simulink/Stateflow models into embedded C code.

Denney, Ewen↗

Using Ontologies to Formalize Services Specifications in Multi-Agent Systems

One key issue in multi-agent systems (MAS) is their ability to interact and exchange information autonomously across applications. To secure agent interoperability, designers must rely on a communication protocol that allows software agents to exchange meaningful information. In this paper we propose using ontologies as such communication protocol. Ontologies capture the semantics of the operations and services provided by agents, allowing interoperability and information exchange in a MAS. Ontologies are a formal, machine processable, representation that allows to capture the semantics of a domain and, to derive meaningful information by way of logical inference. In our proposal we use a formal knowledge representation language (OWL) that translates into Description Logics (a subset of first order logic), thus eliminating ambiguities and providing a solid base for machine based inference. The main contribution of this approach is to make the requirements explicit, centralize the specification in a single document (the ontology itself), at the same that it provides a formal, unambiguous representation that can be processed by automated inference machines.

Breitman, Karin Koogan↗

Cosmic logic: a computational model

We initiate a formal study of logical inferences in context of the measure problem in cosmology or what we call cosmic logic. We describe a simple computational model of cosmic logic suitable for analysis of, for example, discretized cosmological systems. The construction is based on a particular model of computation, developed by Alan Turing, with cosmic observers (CO), cosmic measures (CM) and cosmic symmetries (CS) described by Turing machines. CO machines always start with a blank tape and CM machines take CO's Turing number (also known as description number or Gödel number) as input and output the corresponding probability. Similarly, CS machines take CO's Turing number as input, but output either one if the CO machines are in the same equivalence class or zero otherwise. We argue that CS machines are more fundamental than CM machines and, thus, should be used as building blocks in constructing CM machines. We prove the non-computability of a CS machine which discriminates between two classes of CO machines: mortal that halts in finite time and immortal that runs forever. In context of eternal inflation this result implies that it is impossible to construct CM machines to compute probabilities on the set of all CO machines using cut-off prescriptions. The cut-off measures can still be used if the set is reduced to include only machines which halt after a finite and predetermined number of steps.

79 ASTRONOMY AND ASTROPHYSICS↗

The Ontology of Biological Attributes (OBA)—computational traits for the life sciences

Abstract Existing phenotype ontologies were originally developed to represent phenotypes that manifest as a character state in relation to a wild-type or other reference. However, these do not include the phenotypic trait or attribute categories required for the annotation of genome-wide association studies (GWAS), Quantitative Trait Loci (QTL) mappings or any population-focussed measurable trait data. The integration of trait and biological attribute information with an ever increasing body of chemical, environmental and biological data greatly facilitates computational analyses and it is also highly relevant to biomedical and clinical applications. The Ontology of Biological Attributes (OBA) is a formalised, species-independent collection of interoperable phenotypic trait categories that is intended to fulfil a data integration role. OBA is a standardised representational framework for observable attributes that are characteristics of biological entities, organisms, or parts of organisms. OBA has a modular design which provides several benefits for users and data integrators, including an automated and meaningful classification of trait terms computed on the basis of logical inferences drawn from domain-specific ontologies for cells, anatomical and other relevant entities. The logical axioms in OBA also provide a previously missing bridge that can computationally link Mendelian phenotypes with GWAS and quantitative traits. The term components in OBA provide semantic links and enable knowledge and data integration across specialised research community boundaries, thereby breaking silos.

59 BASIC BIOLOGICAL SCIENCES↗

Data-driven backward chaining

The C Language Integrated Production System (CLIPS) cannot effectively perform sound and complete logical inference in most real-world contexts. The problem facing CLIPS is its lack of goal generation. Without automatic goal generation and maintenance, forward chaining can only deduce all instances of a relationship. Backward chaining, which requires goal generation, allows deduction of only that subset of what is logically true which is also relevant to ongoing problem solving. Goal generation can be mimicked in simple cases using forward chaining. However, such mimicry requires manual coding of additional rules which can assert an inadequate goal representation for every condition in every rule that can have corresponding facts derived by backward chaining. In general, for N rules with an average of M conditions per rule the number of goal generation rules required is on the order of N*M. This is clearly intractable from a program maintenance perspective. We describe the support in Eclipse for backward chaining which it automatically asserts as it checks rule conditions. Important characteristics of this extension are that it does not assert goals which cannot match any rule conditions, that 2 equivalent goals are never asserted, and that goals persist as long as, but no longer than, they remain relevant.

Haley, Paul↗

Extension of the Kohn-Sham formulation of density functional theory to finite temperature

Based on Mermin's extension of the Hohenberg and Kohn theorems to non-zero temperature, the Kohn-Sham formulation of density functional theory (KS-DFT) is generalized to finite temperature. Here, we show that present formulations are inconsistent with Mermin's functional containing expressions, in particular describing the Coulomb energy, that defy derivation and are even in violation of rules of logical inference. More; current methodology is in violation of fundamental laws of both quantum and classical mechanics. Based on this feature, we demonstrate the impossibility of extending the KS formalism to finite temperature through the self-consistent solutions of the single-particle Schrödinger equation of T>0. Guided by the form of Mermin's functional that depends on the eigenstates of a Hamiltonian, determined at T>0 we base our extension of KS-DFT on the determination of the excited states of a non-interacting system at the zero of temperature. The resulting formulation is consistent with that of Mermin constructing the free energy at T>0 in terms of the excited states of a non-interacting Hamiltonian (system) that, within the KS formalism, are described by Slater determinants. To determine the excited states at T=0 use is made of the extension of the Hohenberg and Kohn theorems to excited states presented in previous work applied here to a non-interacting collection of replicas of a non-interacting N-particle system, whose ground state density is taken to match that of K non-interacting replicas of an interacting N-particle system at T>0. The formalism allows for an ever denser population of the excitation spectrum of a Hamiltonian, within the KS approximation. The form of the auxiliary potential, (Kohn-Sham potential), is formally identical to that in the ground state formalism with the contribution of the Coulomb energy provided by the derivative of the Coulomb energy in all excited states taken into account. Once the excited states are determined, the minimum of the free energy within the KS formalism follows immediately in the form of Mermin's functional, but with the exact excited states in that functional represented by Slater determinants obtained through self-consistency conditions at the zero of temperature. Lastly, it is emphasized that, in departure from all existing formulations, no self-consistency conditions are implemented at finite T; as we show, in fact, such formulations are rigorously blocked.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Smart Barrier Design and Evaluation (ReKonTM: An Integrated Detection and Assessment Perimeter System)

Many government and military sites continue to demand high performance security technologies such as those afforded by a traditional perimeter intrusion detection and assessment system (PIDAS), but require additional standoff beyond the existing perimeter. To meet such varied needs, a perimeter security system needs to be configurable to meet the demands unique to each site, adaptable to the latest sensor technology and security requirements, and scalable to provide for installation at short temporary perimeters just as well as large multi-mile perimeters. ReKonTM is an integrated perimeter security system solution, one that couples access delay with detection and assessment. A prototype system was designed and built that integrated fiber optic break sensors, active infrared sensors, fence disturbance sensors, video motion detection, ground sensors, and vehicle/human delay barriers. ReKonTM uses a machine learning fusion technique to determine whether an alarm event has occurred as opposed to the conventional system which simply triggers an alarm event when any one sensor is activated. This novel perimeter solution was designed to be configurable for use at facilities ranging from high-security military sites to commercial power plants, to petro/chemical facilities of various kinds. ReKonTM was evaluated against a conventional system and logical inference fusion system with a fixed dataset that was collected over five months from the perimeter. ReKon outperformed both systems with respect to nuisance alarm rate and had only one less alarm detection than the conventional system out of a total of 133 total true alarm events. The sensors on the ReKonTM perimeter generated approximately 8.86 nuisance alarms per day using the conventional system. Using the machine learning fusion these were greatly reduced to approximately 0.02 alarms per day. ReKonTM may enable the use of high performance perimeter security for reduced cost in environments previously incapable of achieving such performance due to budget or installation constraints.

47 OTHER INSTRUMENTATION↗

What Are Ontologies and When Should They Be Used?

Data without description is at best unusable, and at worst, misused. If we do not understand the assumptions and meaning of our data, we are unable to confidently use it. Data today is largely described within a database’s schema, detailing structure and primitive datatypes as part of a relational model, but if we require assurance some data value can be correctly evaluated alongside others beyond the immediate systems in which they are defined, a more portable, richer semantics is needed. Ontologies define knowledge unambiguously across systems and establish the means to reason upon said knowledge using logical inference. They model neutral domains of information rather than data definitions from software or databases that would only serve to enrich a single system’s idiosyncrasies. In this paper, we take a casual stance to explore what ontologies are, how they are built, why they are useful, and when they should be used.

97 MATHEMATICS AND COMPUTING↗

Research and applications: Artificial intelligence

A program of research in the field of artificial intelligence is presented. The research areas discussed include automatic theorem proving, representations of real-world environments, problem-solving methods, the design of a programming system for problem-solving research, techniques for general scene analysis based upon television data, and the problems of assembling an integrated robot system. Major accomplishments include the development of a new problem-solving system that uses both formal logical inference and informal heuristic methods, the development of a method of automatic learning by generalization, and the design of the overall structure of a new complete robot system. Eight appendices to the report contain extensive technical details of the work described.

Raphael, B.↗