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M. Weber and E. A. Lee
Engineers of spatial IoT systems are tasked with finding the best location model for
their application. But IoT systems designed for interaction with other data sources
must additionally be created with an understanding of how a selected location model
is related to the location models of other sensors and IoT systems in the environment.
2 Location Modeling
The purpose of location modeling in this work is to support a logic for reasoning
about spatial ontologies across independently designed IoT systems. By moving
beyond just geometric position, this logic offers the possibility for a much richer set
of applications than just navigation, including for example security (e.g. restricting
access to some service to only devices in the same room); asset tracking (e.g. where
is the remote control for this device, or the device for this remote); spatial search
(e.g. find a temperature sensor in the same room as a mobile device); commissioning
(e.g. deploying sensors and actuators without manually specifying their location);
and context-aware services (e.g. lighting systems that automatically adjust to usage
patterns of a room). We believe semantic repositories are a good start for this, but
there is room for a larger suite of software components and services for creative
application designers to use when reasoning about location information.
Such services could handle mobility (e.g. notification when a device is no longer in
the same room) and superposition of disjoint maps constructed at different semantic
and geometric layers (e.g., relating geometric information to “in the same room”
semantic information).
2.1 Model Theory
Model theory is a domain of mathematical logic originally developed to analyze
logical formulas regarding mathematical structures such as groups, graphs, and fields.
The key observation behind model theory is that logical formulas can be written
to express properties in a manner independent of the mathematical structures with
respect to which they are evaluated. For example the formula ∃n 0 < n < 1 is true with
respect to R or Q, but not with respect to Z or N. A model (or structure) specifies
a domain, such as R, and gives interpretations to the symbols 0, 1, and < so that
their particular relationship may be determined. We summarize the fundamentals of
model theory relevant to CPS location modeling below. The main reference for the
following definitions is [21], which may be referred to for a more comprehensive
introduction to model theory.
2
A formula is a logical statement constructed in the usual way from:
2 A friendlier introduction can be found at https://plato.stanford.edu/entries/modeltheory-fo/
M. Weber and E. A. Lee
Engineers of spatial IoT systems are tasked with finding the best location model for
their application. But IoT systems designed for interaction with other data sources
must additionally be created with an understanding of how a selected location model
is related to the location models of other sensors and IoT systems in the environment.
2 Location Modeling
The purpose of location modeling in this work is to support a logic for reasoning
about spatial ontologies across independently designed IoT systems. By moving
beyond just geometric position, this logic offers the possibility for a much richer set
of applications than just navigation, including for example security (e.g. restricting
access to some service to only devices in the same room); asset tracking (e.g. where
is the remote control for this device, or the device for this remote); spatial search
(e.g. find a temperature sensor in the same room as a mobile device); commissioning
(e.g. deploying sensors and actuators without manually specifying their location);
and context-aware services (e.g. lighting systems that automatically adjust to usage
patterns of a room). We believe semantic repositories are a good start for this, but
there is room for a larger suite of software components and services for creative
application designers to use when reasoning about location information.
Such services could handle mobility (e.g. notification when a device is no longer in
the same room) and superposition of disjoint maps constructed at different semantic
and geometric layers (e.g., relating geometric information to “in the same room”
semantic information).
2.1 Model Theory
Model theory is a domain of mathematical logic originally developed to analyze
logical formulas regarding mathematical structures such as groups, graphs, and fields.
The key observation behind model theory is that logical formulas can be written
to express properties in a manner independent of the mathematical structures with
respect to which they are evaluated. For example the formula ∃n 0 < n < 1 is true with
respect to R or Q, but not with respect to Z or N. A model (or structure) specifies
a domain, such as R, and gives interpretations to the symbols 0, 1, and < so that
their particular relationship may be determined. We summarize the fundamentals of
model theory relevant to CPS location modeling below. The main reference for the
following definitions is [21], which may be referred to for a more comprehensive
introduction to model theory.
2
A formula is a logical statement constructed in the usual way from:
2 A friendlier introduction can be found at https://plato.stanford.edu/entries/modeltheory-fo/