An algebraic–analytic framework for measurement theory

Domotor, Zoltan; Batitsky, Vadim

doi:10.1016/j.measurement.2010.05.006

Cited by 7 publications

(7 citation statements)

References 24 publications

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“…A close look at RTM's axioms for qualitative structures associated with measurable attributes reveals that these axioms invariably transcend simple qualitative observations and posit hypothetical infinite precisions that exceed the capacities of human measurement. (For some additional details and discussion of related issues, see [4] and [5]. )…”

Section: Conceptual Issues In the Representationalist Founda-mentioning

confidence: 99%

“…4 Along similar lines, the natural "less than" total order relation on positive real numbers automatically transfers to quantities by setting Q < Q ′ just in case Q Q ′′ < Q ′ Q ′′ for any reference quantity Q ′′ . The total order relation is called "natural" because it satisfies the solvability condition Q < Q ′ ⇐⇒ Q + Q ′′ = Q ′ for some quantity Q ′′ .…”

Section: Introduction and Overviewmentioning

confidence: 99%

“…4 The reader may be appalled that we are combining two unital length quantities involving different measurement units. This should not be a problem since, for example, in carpentry it is common to combine length values measured in yards with length values counted in inches and fractions thereof.…”

Section: Introduction and Overviewmentioning

confidence: 99%

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An Algebraic Approach to Unital Quantities and their Measurement

Domotor

Batitsky

2016

Measurement Science Review

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The goals of this paper fall into two closely related areas. First, we develop a formal framework for deterministic unital quantities in which measurement unitization is understood to be a built-in feature of quantities rather than a mere annotation of their numerical values with convenient units. We introduce this idea within the setting of certain ordered semigroups of physical-geometric states of classical physical systems. States are assumed to serve as truth makers of metrological statements about quantity values. A unital quantity is presented as an isomorphism from the target system's ordered semigroup of states to that of positive reals. This framework allows us to include various derived and variable quantities, encountered in engineering and the natural sciences. For illustration and ease of presentation, we use the classical notions of length, time, electric current and mean velocity as primordial examples. The most important application of the resulting unital quantity calculus is in dimensional analysis. Second, in evaluating measurement uncertainty due to the analog-to-digital conversion of the measured quantity's value into its measuring instrument's pointer quantity value, we employ an ordered semigroup framework of pointer states. Pointer states encode the measuring instrument's indiscernibility relation, manifested by not being able to distinguish the measured system's topologically proximal states. Once again, we focus mainly on the measurement of length and electric current quantities as our motivating examples. Our approach to quantities and their measurement is strictly state-based and algebraic in flavor, rather than that of a representationalist-style structure-preserving numerical assignment.

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Section: Conceptual Issues In the Representationalist Founda-mentioning

confidence: 99%

Section: Introduction and Overviewmentioning

confidence: 99%

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An Algebraic Approach to Unital Quantities and their Measurement

Domotor

Batitsky

2016

Measurement Science Review

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“…It is easy to see that the discrete homomorphism L ∞ (£ ε,ε ′ ) sends the earlier discussed half-open intervals [kε − 35 The dynamics of mercury-in-glass thermometers in terms of heat transfers from system to thermometer is treated in [4]. A second common derived temperature measurement is performed by resistance temperature devices.…”

Section: Indirect Temperature Measurementmentioning

confidence: 99%

“…As a by-product of classical systems and signal theories, STM is built around temporally (and spatially) varying smooth physical signals 3 and their transformations thereon by man-made physical systems, including but not limited to sensors, transducers, filters, amplifiers, analog-digital converters 4 , and signal reconstruction (inversion) modules. At the heart of STM rests the reductionist idea that measurement processes are merely special cases of other processes studied in mathematical systems and signal theories.…”

Section: Introduction and General Backgroundmentioning

confidence: 99%

Algebraic Frameworks for Measurement in the Natural Sciences

Domotor¹

2012

Measurement Science Review

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The goals of this paper fall into three related areas: (i) we present an overview of a universal algebraic paradigm in which measurement specialists can construct formal models of measurement in a unified manner and systematically reason about a large class classical measurement operations, (ii) we construct convenient von Neumann quantity algebras and quantity-channels between them to represent measurements, and introduce the dual framework of state spaces and state-channels between them to investigate the statistical structure of measurements, and (iii) we provide several detailed examples that illustrate the power and versatility of algebraic approaches to measurement procedures.

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Philosophy of Science, Mathematical Models in

Domotor¹

2014

Encyclopedia of Complexity and Systems Science

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An algebraic–analytic framework for measurement theory

Cited by 7 publications

References 24 publications

An Algebraic Approach to Unital Quantities and their Measurement

An Algebraic Approach to Unital Quantities and their Measurement

Algebraic Frameworks for Measurement in the Natural Sciences

Philosophy of Science, Mathematical Models in

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