OpenMath Content Dictionary: aggregate_cats

Canonical URL:

http://www.openmath.org/cd/aggregate_cats.ocd

CD File:

aggregate_cats.ocd

CD as XML Encoded OpenMath:

aggregate_cats.omcd

Defines:

aggregateType, continuousSetType, discreteSetType, finiteSetType, infiniteSetType, multisetType, non_continuousSetType, piecewiseContinuousSetType, setType

Date:

2002-08-25

Version:

0

Review Date:

2005-04-01

Status:

experimental

Uses CD:

logic1, meta_cats

A CD of basic aggregate category constructors. This CD holds constructors of individual instances of the categories, with defining properties of the categories.

aggregateType

Description:

This symbol represents a generic type for aggregates (or collections of objects.

Signatures:

sts

multisetType

Description:

This symbol represents the type of multisets.

Commented Mathematical property (CMP):

multisetType is an aggregate type

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="multisetType"/>
        <OMS cd="aggregate_cats" name="aggregateType"/>
      </OMA>
    </OMOBJ>

has (multisetType, aggregateType)

$$\mathrm{has}(\mathrm{multisetType},\mathrm{aggregateType})$$

Signatures:

sts

setType

Description:

This symbol represents the type of sets.

Commented Mathematical property (CMP):

setType is an aggregate type

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="setType"/>
        <OMS cd="aggregate_cats" name="aggregateType"/>
      </OMA>
    </OMOBJ>

has (setType, aggregateType)

$$\mathrm{has}(\mathrm{setType},\mathrm{aggregateType})$$

Signatures:

sts

finiteSetType

Description:

This symbol represents the type of finite sets.

Commented Mathematical property (CMP):

finite set type has set type

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="finiteSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

has (finiteSetType, setType)

$$\mathrm{has}(\mathrm{finiteSetType},\mathrm{setType})$$

Signatures:

sts

infiniteSetType

Description:

This symbol represents the type of infinite sets.

Commented Mathematical property (CMP):

infinite set type has set type

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="infiniteSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

has (infiniteSetType, setType)

$$\mathrm{has}(\mathrm{infiniteSetType},\mathrm{setType})$$

Commented Mathematical property (CMP):

infinite set type does not have finite set type

Signatures:

sts

continuousSetType

Description:

This symbol represents the type of continuous sets.

Commented Mathematical property (CMP):

continuous set type has set type

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="continuousSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

has (continuousSetType, setType)

$$\mathrm{has}(\mathrm{continuousSetType},\mathrm{setType})$$

Signatures:

sts

piecewiseContinuousSetType

Description:

This symbol represents the type of piecewise continuous sets.

Commented Mathematical property (CMP):

piecewise continuous set type has set type

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="piecewiseContinuousSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

has (piecewiseContinuousSetType, setType)

$$\mathrm{has}(\mathrm{piecewiseContinuousSetType},\mathrm{setType})$$

Signatures:

sts

non_continuousSetType

Description:

This symbol represents the type of non-continuous sets.

Commented Mathematical property (CMP):

non-continuous set type has set type

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="non_continuousSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

has (non_continuousSetType, setType)

$$\mathrm{has}(\mathrm{non\_continuousSetType},\mathrm{setType})$$

Commented Mathematical property (CMP):

non-continuous set type does not have continuous set type

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="logic1" name="not"/>
        <OMA>
          <OMS cd="meta_cats" name="has"/>
          <OMS cd="aggregate_cats" name="non_continuousSetType"/>
          <OMS cd="aggregate_cats" name="continuousSetType"/>
        </OMA>
      </OMA>
    </OMOBJ>

not (has (non_continuousSetType, continuousSetType) )

$$\neg \mathrm{has}(\mathrm{non\_continuousSetType},\mathrm{continuousSetType})$$

Signatures:

sts

discreteSetType

Description:

This symbol represents the type of discrete sets.

Commented Mathematical property (CMP):

discrete set type has set type

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="discreteSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

has (discreteSetType, setType)

$$\mathrm{has}(\mathrm{discreteSetType},\mathrm{setType})$$

Commented Mathematical property (CMP):

discrete set type does not have continuous set type or piecewise continuous set type

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="logic1" name="not"/>
        <OMA>
          <OMS cd="meta_cats" name="has"/>
          <OMS cd="aggregate_cats" name="discreteSetType"/>
          <OMS cd="aggregate_cats" name="continuousSetType"/>
        </OMA>
      </OMA>
    </OMOBJ>

not (has (discreteSetType, continuousSetType) )

$$\neg \mathrm{has}(\mathrm{discreteSetType},\mathrm{continuousSetType})$$

Signatures:

sts