| slovo | definícia |
axiomatic
(mass) | axiomatic
- axiomatický |
axiomatic
(encz) | axiomatic,samozřejmý adj: |
Axiomatic
(gcide) | Axiomatic \Ax`i*o*mat"ic\, Axiomatical \Ax`i*o*mat"ic*al\, a.
[Gr. ?.]
Of or pertaining to an axiom; having the nature of an axiom;
self-evident; characterized by axioms. "Axiomatical truth."
--Johnson.
[1913 Webster]
The stores of axiomatic wisdom. --I. Taylor.
[1913 Webster] |
axiomatic
(wn) | axiomatic
adj 1: evident without proof or argument; "an axiomatic truth";
"we hold these truths to be self-evident" [syn:
axiomatic, self-evident, taken for granted(p)]
2: containing aphorisms or maxims; "axiomatic wisdom" [syn:
axiomatic, aphoristic]
3: of or relating to or derived from axioms; "axiomatic
physics"; "the postulational method was applied to geometry"-
S.S.Stevens [syn: axiomatic, axiomatical,
postulational] |
| | podobné slovo | definícia |
axiomatic
(mass) | axiomatic
- axiomatický |
axiomatický
(msas) | axiomatický
- axiomatic |
axiomaticky
(msasasci) | axiomaticky
- axiomatic |
axiomatic
(encz) | axiomatic,samozřejmý adj: |
axiomatically
(encz) | axiomatically,samozřejmě adj: |
Axiomatical
(gcide) | Axiomatic \Ax`i*o*mat"ic\, Axiomatical \Ax`i*o*mat"ic*al\, a.
[Gr. ?.]
Of or pertaining to an axiom; having the nature of an axiom;
self-evident; characterized by axioms. "Axiomatical truth."
--Johnson.
[1913 Webster]
The stores of axiomatic wisdom. --I. Taylor.
[1913 Webster] |
Axiomatically
(gcide) | Axiomatically \Ax`i*o*mat"ic*al*ly\, adv.
By the use of axioms; in the form of an axiom.
[1913 Webster] |
axiomatic
(wn) | axiomatic
adj 1: evident without proof or argument; "an axiomatic truth";
"we hold these truths to be self-evident" [syn:
axiomatic, self-evident, taken for granted(p)]
2: containing aphorisms or maxims; "axiomatic wisdom" [syn:
axiomatic, aphoristic]
3: of or relating to or derived from axioms; "axiomatic
physics"; "the postulational method was applied to geometry"-
S.S.Stevens [syn: axiomatic, axiomatical,
postulational] |
axiomatical
(wn) | axiomatical
adj 1: of or relating to or derived from axioms; "axiomatic
physics"; "the postulational method was applied to
geometry"- S.S.Stevens [syn: axiomatic, axiomatical,
postulational] |
axiomatically
(wn) | axiomatically
adv 1: on the basis of axioms; "this is axiomatically given" |
axiomatic architecture description language
(foldoc) | Axiomatic Architecture Description Language
AADL
(AADL) A language allowing
concise modular specification of multiprocessor
architectures from the compiler/operating-system interface
level down to chip level. AADL is rich enough to specify
target architectures while providing a concise model for
clocked microarchitectures.
["AADL: A Net-Based Specification Method for Computer
Architecture Design", W. Damm et al in Languages for Parallel
Architectures, J.W. deBakker ed, Wiley, 1989].
(2003-06-30)
|
axiomatic semantics
(foldoc) | axiomatic semantics
A set of assertions about properties of a system and
how they are effected by program execution. The axiomatic
semantics of a program could include pre- and post-conditions
for operations. In particular if you view the program as a
state transformer (or collection of state transformers), the
axiomatic semantics is a set of invariants on the state which
the state transformer satisfies.
E.g. for a function with the type:
sort_list :: [T] -> [T]
we might give the precondition that the argument of the
function is a list, and a postcondition that the return value
is a list that is sorted.
One interesting use of axiomatic semantics is to have a
language that has a finitely computable sublanguage that is
used for specifying pre and post conditions, and then have the
compiler prove that the program will satisfy those conditions.
See also operational semantics, denotational semantics.
(1995-11-09)
|
axiomatic set theory
(foldoc) | axiomatic set theory
One of several approaches to set theory, consisting
of a formal language for talking about sets and a collection
of axioms describing how they behave.
There are many different axiomatisations for set theory.
Each takes a slightly different approach to the problem of
finding a theory that captures as much as possible of the
intuitive idea of what a set is, while avoiding the
paradoxes that result from accepting all of it, the most
famous being Russell's paradox.
The main source of trouble in naive set theory is the idea
that you can specify a set by saying whether each object in
the universe is in the "set" or not. Accordingly, the most
important differences between different axiomatisations of set
theory concern the restrictions they place on this idea (known
as "comprehension").
Zermelo Fränkel set theory, the most commonly used
axiomatisation, gets round it by (in effect) saying that you can
only use this principle to define subsets of existing sets.
NBG (von Neumann-Bernays-Goedel) set theory sort of allows
comprehension for all formulae without restriction, but
distinguishes between two kinds of set, so that the sets
produced by applying comprehension are only second-class sets.
NBG is exactly as powerful as ZF, in the sense that any
statement that can be formalised in both theories is a theorem
of ZF if and only if it is a theorem of ZFC.
MK (Morse-Kelley) set theory is a strengthened version of NBG,
with a simpler axiom system. It is strictly stronger than
NBG, and it is possible that NBG might be consistent but MK
inconsistent.
NF (http://math.boisestate.edu/~holmes/holmes/nf.html) ("New
Foundations"), a theory developed by Willard Van Orman Quine,
places a very different restriction on comprehension: it only
works when the formula describing the membership condition for
your putative set is "stratified", which means that it could
be made to make sense if you worked in a system where every
set had a level attached to it, so that a level-n set could
only be a member of sets of level n+1. (This doesn't mean
that there are actually levels attached to sets in NF). NF is
very different from ZF; for instance, in NF the universe is a
set (which it isn't in ZF, because the whole point of ZF is
that it forbids sets that are "too large"), and it can be
proved that the Axiom of Choice is false in NF!
ML ("Modern Logic") is to NF as NBG is to ZF. (Its name
derives from the title of the book in which Quine introduced
an early, defective, form of it). It is stronger than ZF (it
can prove things that ZF can't), but if NF is consistent then
ML is too.
(2003-09-21)
|
|