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glossary..I

I
In combinatory logic, the identity combinator, a function which, when applied to some value always returns that same value.
I = x. x
iff
if and only if
impredicative
not predicative
include
A includes B if everything in B is also in A
inclusion polymorphism
a kind of polymorphism found in the type systems of object oriented programming languages in which some types are included in others. A type of object consisting of multiple named components would typically include the types whose objects have the same set of named components together with some additional components.
induction
(mathematical)
a method of proving a general truth affirming that every one of a set of mathematical objects (e.g. the natural numbers) has a certain property (e.g. has exactly one prime factorisation). The method depends upon their being a systematic way of constructing all the elements of the set by starting with one of a finite set of basis elements and repeatedly applying a finite number of constructions (for the natural numbers the basis is the number 0, and the method of construction is addition of 1). An inductive proof then consists of a proof that the basis elements each have the required property and a proof that the construction, when applied to elements having the property, will yield an element also having the property. Mathematical induction is in fact a kind of deduction. It is also called structural induction.
(scientific)
scientific induction is the process of concluding empirical generalisations from particular instances, where this is not deductively sound because not all possible instances are premises
intersection
where two things lie across each other
(in set theory)
the intersection of two sets a and b is that set whose members are those things which are members both of a and of b
intuitionism
a position in the Philosophy of Mathematics mainly associated with L.E.J.Brouwer
intension
the meaning or internal content of a concept, as contrasted with its extension
the strenuous exertion of the mind or will
intensional
of a logic
not extensional
of an act
intended
intention
thing intended
intentional
intended
in error, or perhaps correctly in American English: intensional
intentional stance
the attempt to understand an artefact by second guessing the intentions of its designer [[Dennett95] ch.9 p.229]
intentional systems
Systems whose behaviour can be - at least sometimes - explained and predicted by relying on ascriptions to the system of beliefs and desires (and hopes, fears, intentions, hunches,...). [also from Dennett]


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