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In-Depth Information
Γ
=
{
depression
,
stroke
,
hypertension
}
The theoremata
has a very
special form as it is a subset of
Sen(T
Σ
)
X
,where
X
is a variable 'set', usually
many-sorted. For
P
denoting the powerset functor, which is extendable to a monad,
we have
Γ
∈
PSen(T
Σ
)
X
. There is no reason why theoremata couldn't be given by
significantly more complicated monads
Φ
than just
P
.
Generalized general logic is
LOGIC
=(
Sign
,
Sen
,
Mod
,
Φ
,
,
where
Sign
is the category of signature,
Sen
is the sentence functor,
Mod
is the
functor capturing the generalized notion of corresponding algebras,
Φ
is the the-
oremata monad,
L
is a lattice of external truth values, not to be confused with a
possible lattice
K
appearing in the Goguen category
Set
(
L
,,|
=
,
ProofCalc
)
K
)
.Wemayhave
K
=
L
,
but it is not necessary. The entailment relation is
and the satisfaction relation is
|
=
.
ProofCalc
represents functors and natural transformations adding up to a gen-
eralized proof calculus. Details are and must be omitted in this paper, but part of
this framework was published by Eklund and Helgesson in 2010 [10], and further
detail are under preparation.
We may construct the category of generalized general logics with corresponding
morphisms, so that e.g.
:
LOGIC
Flo
→
LOGIC
Rence
captures some kind of
under-
standing
between
Flo
and
Rence
. The interesting thing here is that
LOGIC
Flo
is
obviously 'owned' by
Flo
and
LOGIC
Rence
by
Rence
, but who owns the morphism
Ξ
Ξ
? It may perhaps be seen as a convergent dialectics between
Flo
and
Rence
.
References
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orders, 4th edn. (DSM-IV-TR
), Text Revisions, American Psychiatric Association
(2000)
2. Beck, J.: Distributive laws. In: Seminars on Triples and Categorical Homology Theory,
1966/1967. Lecture Notes in Mathematics, vol. 80, pp. 119-140. Springer (1969)
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J.: The Neuropsychiatric Inventory: Comprehensive Assessment of Psychopathology in
Dementia. Neurology 44, 2308-2314 (1994)
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ics 52, 509-536, 789-834 (1930)
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In: 19th IAGG World Congress of Gerontology and Geriatrics, Paris (2009); Journal of
Nutrition, Health & Aging 13(suppl. 1), S558-S559
7. Eklund, P.: Signatures for Assessment, Diagnosis and Decision-Making in Ageing. In:
Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010, Part II. CCIS, vol. 81, pp.
271-279. Springer, Heidelberg (2010)
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