Conversion of Physical Quantity and its Application

                            Takanori Ugai and Shohei Yamane

                                  Fujitsu Laboratories Limited
                                   ugai@jp.fujitsu.com



       Abstract. In this presentation, we show the design of a vocabulary set for the
       conversion of physical quantities and a prototype application using it. The vocab-
       ulary consists of facts and rules and is formalized with the W3C Web Ontology
       Language (OWL) under a resource description framework (RDF). Here, facts are
       physical quantities of things such as the weight of the Statue of Liberty, and rules
       are conversion relations such as “the energy of a cup of rice is 200 kilocalories.”
       The conversion between quantities is done by SPARQL query. An application
       was developed to educate users about global warming. The application converts
       different physical quantities under various circumstances such as the amount of
       gasoline a car burns, the weight of waste materials, and so on into CO2 emissions.


1 Introduction

Conversion to other quantities is often used as a method of expressing physical quantities
that are difficult to understand intuitively. For example, if you eat a cup of rice, you have
to run 5 km to consume the energy in it, because the energy of both is almost equal.
Likewise, health and welfare authorities can encourage people to exercise by giving
them information on converting the energy expended during movement into the number
of calories burned.
    Our research aims to automatically perform such conversions by resource description
framework (RDF). In our presentation, we show the design of an ontology for the
conversion of one physical quantity into equivalent physical quantities by using RDF
examples. The ontology consists of two parts. One is the conversion relations (rules),
e.g., for expressing that the amount of CO2 emitted during the combustion of 1 kl of
gasoline is 2.32 kg. The other is the physical quantities of the things converted (facts),
e.g., for expressing that the round trip distance from the Earth to the Moon at the average
distance between the two bodies is 770,000 km. Through the combination of rules
and facts, SPARQL query enables the physical quantity of the conversion to be found
automatically. The presentation also describes a prototype application for educating
users about global warming.


2 Ontology for Conversion

The ontology consists of conversion relations and the physical quantities of things. The
conversion relation is called a rule and expresses the relationships between two physical
quantities such as “the CO2 emitted during the combustion of 1 kl of gasoline is 2.32
kg.” The physical quantity of things is called a fact and expresses, e.g., that the round
trip distance from the Earth to the Moon at the average distance between the two bodies
is 770,000 km. An ontology of units of measurement (OM)[2] and related concepts[3]
are used as the basis of unit conversion. The OM is an RDF that expresses meanings
such as definitions and dimensions for various units such as kg, m, and t.
@prefix om: <http://www.wurvoc.org/vocabularies/om-1.8/> .
@prefix un: <http://lod4all.net/property/unit/> .

<http://lod4all.net/resource/unit/car_gas_to_distance>
     rdf:type <http://lod4all/ontology/unit/conversion> ;
     un:coefficient "20"^^xsd:decimal;
     un:numerator "Distance"@en ;
     un:denominator "Gasolin"@en ;
     un:numerator_unit om:kilometre ;
     un:denominator_unit om:litre ;
     un:event "Running␣of␣the␣car"@en .

<http://ex.com/unit/resource/burn_gas_to_co2>
     rdf:type <http://lod4all/ontology/unit/conversion> ;
     un:coefficient "2.32"^^xsd:decimal;
     un:numerator "CO2" ;
     un:denominator "Gasolin"@en ;
     un:numerator_unit om:tonne ;
     un:denominator_unit om:kilolitre ;
     un:event "combustion"@en .
                               List 1. Conversion factor(Rule)

    List 1 contains two rules. Car_gas_to_distance is the conversion coefficient (fuel
consumption) of gasoline in regards to the distance driven by a car, with a value
of 20. Burn_gas_to_co2 expresses the conversion coefficient between the amount of
CO2 emitted and the amount of gasoline combusted. The CO2 emitted due to the com-
bustion of 1kl of gasoline is 2.32 kg.
@prefix om: <http://www.wurvoc.org/vocabularies/om-1.8/> .
@prefix un: <http://lod4all.net/property/unit/> .

<http://ex.com/unit/resource/W016>
     rdf:type <http://lod4all.net/ontology/unit/object> ;
     un:value "770000"^^xsd:float;
     un:unit om:kilometre ;
     un:name "Round-trip␣distance␣to␣the␣moon"@en ;
     un:kazoe "distance"@en .
                               List 2. Physical quantity(Fact)

    List 2 is representing a fact. The fact is that the round trip distance from the Earth to
the Moon at the average distance between the two bodies is 770,000 km.
    Fig.1 shows a combination of the coefficient of emissions due to the combustion of
gasoline and the fuel consumption of a car. In this example, gasoline in the denominator
                   Fig. 1. Examples of combination of conversion factors


in the “CO2 -Gasoline” coefficient and gasoline in the denominator in the “Distance-
Gasoline” coefficient match, and the unit can be converted between kl and l, thus
showing that combinations are possible. In this way, the calculation of convertible
quantities and conversion relations can be automated by giving the quantities and units
(“CO2 emissions” and “tons”) as input. Using the combined rules and facts which
correspond to various amounts, it is possible to generate expressions such as “X times
the earth’s circumference.”
    Using the combination in Fig. 1, a Japanese city’s CO2 emissions of 330.4 kt are
calculated as the same amount a car emits when using 155,000,000 liters of gasoline,
which would enable the car to make 1,699 round trips to the Moon.


3 CO2 emissions conversion application

On the basis of the ontology, we developed a prototype application that relates different
physical quantities under various circumstances to CO2 emissions, as shown in Fig. 2.
This application has two functions. First, it simulates reductions in physical quantities
on the basis of a conversion relation. Second, it calculates reductions in CO2 emissions
in relation to the reduced physical quantities.
    Pressure, energy, temperature, angular velocity, acceleration, time, power factor,
magnetic field, mass, frequency, volume, force, voltage, electric resistivity, current,
length, speed, and specific heat capacity are expressed in tabular form in Wikipedia.
By analyzing the structure of this table, those physical quantities are systematically
extracted. As conversion relations, CO2 emissions from the combustion of gasoline, the
fuel consumption of cars, CO2 emissions due to the combustion of garbage, the specific
gravity of waste, CO2 emissions for the generation of electric power, and the power
consumption of air conditioners are used. The rules are described by their authors.
    The application converts CO2 emissions from the given circumstances and cate-
gorizes them into three kinds of quantities: amount of garbage combusted, amount
of power consumed by air conditioners, and distance in terms of Earth circumfer-
ences driven in a car. As for amount of garbage combusted, the application converts
CO2 emissions into masses and volumes by using burned waste and the specific gravity
of the waste as conversion relations. Conversions to physical quantities could be for
example “CO2 emitted when burning garbage of a weight corresponding to X times the
                Fig. 2. An application system of green gas emission conversion


Eiffel Tower” or “CO2 emitted when burning garbage of a weight equivalent to Y times
Wembley Stadium.” As for the power consumed by air conditioners, CO2 emissions
from power stations and air conditioner power consumption are used as conversion rela-
tions, and the emissions are converted into air conditioner usage time. As for car travel
distance, CO2 emissions from gasoline-burning and the fuel effciency of cars are used
as conversion relations, and the emissions are converted into quantities representing the
Earth’s circumference or the average distance between the Earth and the Moon.


4 Summary
This article described the design of a vocabulary set for the conversion of physical
quantities and a prototype application using it. The vocabulary is formalized with OWL,
and RDF is used for representing facts and rules. Facts are physical quantities of things
such as the weight of the Statue of Liberty, and rules are conversion relations such as “the
energy of a cup of rice is 200 kilocalories.” The conversion between quantities is done
by a simple SPARQL query. An application was developed to educate users about global
warming. The application converts different physical quantities such as the amount of
gasoline a car burns, the weight of waste materials, and so on into CO2 emissions.
Currently, 300 facts and 40 rules are available as a dataset from LOD4ALL1. The graph
name is <http://lod4all.net/graph/unit>. Rules and facts are extracted with a
tool based on [1]. We are continuing to extract more facts and rules from the Internet.


References
1. Pasupat, P., Liang, P.: Compositional semantic parsing on semi-structured tables (2015)
2. Rijgersberg, H., van Assem, M., Top., J.: wurvoc.org Ontology of units of Measure (OM),
   http://www.wurvoc.org/vocabularies/om-1.8/
3. Rijgersberg, H., van Assem, M., Top., J.: Ontology of units of measure and related concepts
   (2012)

 1 http://lod4all.net/