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relational information structures. We bring these views to the point where data
and information are seen residing in the underlying signatures of logic, thus provid-
ing a strict basis for producing terms and sentences, in turn appearing in reasoning
empowered by a selected proof calculus.
Perhaps the most important point here is that there is not a single logic to model
all information and knowledge, and respective professional and ontology user can-
not be expected to adapt to one such universally chosen logic. This is not a question
about a professional not being able to adapt to such a chosen logic, but rather sup-
ports the view that context of decision-making is not related to semantics of data, but
to appropriate and necessary selections of underlying logics of reasoning. The realm
of general logic also and in particular in its generalized form makes explicit use
of mappings from one logic to another, so that the status of mutual understanding
between professional, possibly using different logics, resides in those morphisms
between respective logics.
The paper outline is as follows. We first recall some history of logic and devel-
opments of formal logic, and how we arrive at using our framework for generalized
general logic. In doing so, we then also provide the overall scope of that formal
logic framework. We then provide some related views on existing medical ontology
in order to show how these ontologies are logically very restricted and informal.
This is followed by a section on ageing, where we provide necessary background to
health and social care of older people, and also provide some detailed information
e.g. on assessment scales used in these
observe-assess-decide
processes in a care
of older people. The following section then goes into the strictly formal aspects of
generalized general logic, and we will see how assessment scale based information,
knowledge representation and reasoning can be managed in this purely categori-
cal framework. This also reveals where and how modelling of uncertainty can be
formally incorporated into this machinery.
26.2
Logic Defines Ontology
Programming in logic is manipulation of terms, and substitution with terms. Clas-
sical terms won't suffice. An ontology building upon classical terms, trying to en-
hance missing parts in the underlying structures by being clever about inference,
becomes logically sterile and basically useless in formal frameworks. We also need
to make a distinction between imprecise or vague information, and being formal
and accurate in reasoning with vague values. Furthermore, a value may be vague as
produced by a crisp operation, or a value is vague since the underlying operation is
vague.
From formal point of view this is all about underlying categories and monads,
and in this paper we will continue investigations [7] showing how the signatures
reside in term monads over chosen categories. Our approach is thus monadic, and
we consider monads over suitable categories.
