Would those then be tensors?

Matrices are Tensors but with the matrix product operator instead of the tensor product operator.

Pandas supports MultiIndex DataFrames but the pandas docs recommend xarray for 3D and N-Dimensional data.

xarray supports N-Dimensional data as for example NetCDF but not tensor arithmetic.

xarray_jax: https://github.com/google-deepmind/xarray_jax :

> This library solves that problem. It registers xarray data structures as custom JAX PyTrees. This allows JAX to seamlessly flatten xarray objects into their raw arrays for accelerated computation and then unflatten the results back into fully labeled xarray objects, preserving critical metadata like dimension names and coordinates.

flatten and unflatten with datatypes is necessary for unrolling loops for performance.

Which is the correct logic for probabilistic logic, for expressions with frequentist or symbolic distributions as values? Are quantum logic and quantum statistical mechanics the appropriate or useful tools for all probabilistic logic?

dist_a1 <operator> dist_a2

uncertainties does mean±dev in Python with numpy types.

From https://news.ycombinator.com/item?id=41411280 :

> W3C CSVW supports per-column schema. ( with URIs for datatypes )

> Serialize a dict containing a value with uncertainties and/or Pint (or astropy.units) and complex values to JSON, then read it from JSON back to the same types. Handle datetimes, complex values, and categoricals

IEEE-754 specifies NaN (null), ±0, three infinities (positive, negative, and unsigned), but IEEE-754 does not specify a representation for categoricals, datetimes (like ISO8601), or complex numbers.

XSD (XML Schema Datatypes), which RDFS vocabularies often use to specify the rdfs:range of an rdfs:Property, does not specify how to specify abstract complex numbers; but OpenMath RDF, and QUDT (Quantities, Units, Dimensions, and Types) and OM Ontology all have a way to save complex numbers to disk, too.