Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Applications of modules on unital quantales P . Eklund, U. Höhle, J. Kortelainen LINZ 2017, Austria February 7–10, 2017
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Simple applications require no more than simple formalism to explain them. Complicated calls for complicated . Simple for complicated simplifies and disrespects the complicated. Complicated for simple is "overmathematization", if there is a difficulty to provide reasonable interpretations of the model. Theory acceptance in relation to and as based on dealing mostly with simple examples, runs the risk of not sufficiently well driving theory development out from shallow waters. As an example, description logic for health ontology is, as a logic, not rich enough to captures all subtleties connected with terminologies and their dependencies.
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Mathematical structures in SUP have real world applications! Objects of SUP are complete lattices. We have the task to explain the role of the elements of complete lattices and the role of the underlying partial order. We understand the elements of lattices as states, because these are phenomena changing after an action has been applied. We understand the underlying partial order as the hierarchy between levels of, on the one hand, disorder, and, on the other hand, grades of evidence in clinical guidelines as undestood within Evidence-Based Medicine (EBM).
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Does many-valuedness start from two-valuedness or three-valuedness? In the two-valued case, Boole attaches "all beings" to 1 and "no beings" to 0, as related to geometric logic. In the three-valued case { 0 , a , 1 } , how should we understand a ? The fuzzy community argues that a is a degree of truth, more like an attitude than as a semantics. Boˇ cvar calls a "senseless", and Kleene calls it "undefined". Łukasiewicz was interpreting a as the probability of truth, where he was changing the meaning of truth values coming from Boole and Frege.
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion If truth is seen as an ontological notion, the interpretation given by the fuzzy community is meaningless in the sense of not leaning on some ontology. Scott’s geometric logic views a as a domain of truth distinct from the total (1) and empty (0) domain of truth in the sense of Boole. Truth is context dependent and the size of the domain of truth is changing in a sheaf-theoretic view, sometimes being larger, sometimes smaller, and this suggests to put a in between 1 and 0. This gives the three chain C 3 = { 0 , a , 1 } which is the unique complete lattice structure on a set of three elements.
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Health care involves information related to disease, functioning and condition, and related interventions Disease and disorder is sometimes understood as the same concepts, but the medical domain provides no strict definitions. Functioning is a counterpart to disease, a bit similar as social care is the counterpart and complement for health care. Condition is less clear, as it combines the two, and involves also aspect than just disease and functioning. Whereas disease and functioning are classified, conditions are harder to classify, but embrace both disease and functioning. In ageing, these mixtures become very visible.
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Intervention can involve drugs, surgery, physiotherapy, i.e., interventions with shorter duration and being more instant, but also with longer duration and being more like processes and care pathway. Common to all interventions is the necessity to have a expected outcome of the intervention. Ongoing treatment can be seen as annotated with condition, aiming at favourably affecting the condition. Prevention is yet another concept, and complicates the overall picture of classifications in health, and the view of integrated care pathways. Information and Process must be connected!
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Examples of terminologies in health care WHO’s ICD (diseases) and ICF (functioning) as Reference Classifications ATC/DDD (drugs) as a Derived Classification IHTSDO’s SNOMED as a structure of concepts equipped with description logic as its underlying logic for ontology (But note: ’Ontology’ in health ontology and web ontology is not the same thing! Web ontology does not come with rigorous terminologies.) How to use terminology as part of providing documentation about treatment of various health conditions? Intuitively, classifications involve typing and underlying signatures.
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Who, Where, What, Why, How Who: Respective professionals recognized by their a) competence (education), b) job title, c) work content. Where: Point-of-Care, e.g., in ageing ranging from home care to ward. What: Information in form of terminology based data as expressions, and expressions in turn appearing within rules in treatment guidelines. Why: Objectives. How: Intervention as a Process , and intervention also as sequences and compositions of interventions crossing over professionals (Who) and points of care (Where).
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion In applications, for example in health care, many-valuedness modelled using quantales plays an important role. ICF’s generic scale has five (5) values, and an explicit sixth value for ’not specified’. ICD is two-valued in the sense that either the diagnose is or isn’t. There is implicitly a third value for ’not (yet) known’ or ’suspected’. In the case of condition, and as viewed being closer to a disease related condition, we may see it more like a three-valued than a six-valued issue. Numerics cannot compute with ’unspecified’ or ’missing’. In logic and algebra we can. We present variations of the three chain modules C 3 over unitalization of the three chain quantale C 3 is the smallest possible quantale to model many-valuedness), thus, variations of right actions are given.
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Health care communities and professionals comply with a range classifications and terminologies, also including scales to qualify strength or hierarchies of evidence (in the sense of evidence-based medicine ) or interaction, or as related to levels of functioning. Such hierarchies adopted in health care are ad hoc as compared to the potentially algebraic and logic structures of terminology infused reasoning. We show how these hierarchies canonically derive as actions where transitions appear as levels in hierarchies of evidence. We will also see how three-valuedness related to health conditions, rather than two-valuedness, is the generator of many-valuedness related to strength of evidence.
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Bivalence is fundamental in health and related statistical computation. Sampling often involves hesitation about a patient being suitable in a population related to a randomized clinical trial (RCT). In cohorts, inclusion is based on some criteria, and debate often appears about criteria perhaps not being sharply and unambiguously defined. Mean values cannot be computed until we ’believe sharply’ in the numbers it involves. By the time mean values are computed, many-valuedness as related to subject inclusion in the process of sampling is hidden and thereafter ignored as statistics continue to apply its machinery and produce ’evidence’ as appearing in Evidence-Based Medicine (EBM).
Motivation Three-valuedness as a starting point for many-valuedness Actions Health classifications Conclusion Uncertainty obviously re-enters, but in a different form and in connection with variances attached to mean values. Trials and studies are about explaining outcomes of action in form of intervention or prevention, where interventions can involve drug treatment, surgery, or other types of actions expected to intervene with disease and its possible progression. Bivalence appears then in the way outcomes are classified as successful or unsuccessful. This bivalent classification then divides a population into two parts, one side said to fulfill a given hypothesis, the other side not fulfilling. Strength of evidence is then connected with the values quantifying the acceptance or rejection of such a hypothesis. Acceptance and rejection are not logically antithetic, so ’evidence’ in the sense of EBM is not to be confused with ’truth’ in the sense of logic.
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