| slovo | definícia |
deduction
(mass) | deduction
- odpočet, zľava, dedukcia, poníženie |
deduction
(encz) | deduction,dedukce n: Zdeněk Brož |
deduction
(encz) | deduction,odečtení n: Zdeněk Brož |
deduction
(encz) | deduction,odpočet n: Zdeněk Brož |
deduction
(encz) | deduction,odvození n: Zdeněk Brož |
deduction
(encz) | deduction,sleva n: Zdeněk Brož |
deduction
(encz) | deduction,vývod n: Zdeněk Brož |
Deduction
(gcide) | Deduction \De*duc"tion\, n. [L. deductio: cf. F. d['e]duction.]
1. Act or process of deducing or inferring.
[1913 Webster]
The deduction of one language from another.
--Johnson.
[1913 Webster]
This process, by which from two statements we deduce
a third, is called deduction. --J. R. Seely.
[1913 Webster]
2. Act of deducting or taking away; subtraction; as, the
deduction of the subtrahend from the minuend.
[1913 Webster]
3. That which is deduced or drawn from premises by a process
of reasoning; an inference; a conclusion.
[1913 Webster]
Make fair deductions; see to what they mount.
--Pope.
[1913 Webster]
4. That which is or may be deducted; the part taken away;
abatement; as, a deduction from the yearly rent in
compensation for services; deductions from income in
calculating income taxes.
Syn: See Induction.
[1913 Webster] |
deduction
(wn) | deduction
n 1: a reduction in the gross amount on which a tax is
calculated; reduces taxes by the percentage fixed for the
taxpayer's income bracket [syn: tax write-off, {tax
deduction}, deduction]
2: an amount or percentage deducted [syn: deduction,
discount]
3: something that is inferred (deduced or entailed or implied);
"his resignation had political implications" [syn:
deduction, entailment, implication]
4: reasoning from the general to the particular (or from cause
to effect) [syn: deduction, deductive reasoning,
synthesis]
5: the act of subtracting (removing a part from the whole); "he
complained about the subtraction of money from their
paychecks" [syn: subtraction, deduction] [ant:
addition]
6: the act of reducing the selling price of merchandise [syn:
discount, price reduction, deduction] |
| | podobné slovo | definícia |
deductions
(encz) | deductions,dedukce pl. Zdeněk Brož |
entertainment deduction
(encz) | entertainment deduction, n: |
tax deduction
(encz) | tax deduction, n: |
tax deductions
(encz) | tax deductions,daňový odpočet [eko.] RNDr. Pavel Piskač |
Deduction
(gcide) | Deduction \De*duc"tion\, n. [L. deductio: cf. F. d['e]duction.]
1. Act or process of deducing or inferring.
[1913 Webster]
The deduction of one language from another.
--Johnson.
[1913 Webster]
This process, by which from two statements we deduce
a third, is called deduction. --J. R. Seely.
[1913 Webster]
2. Act of deducting or taking away; subtraction; as, the
deduction of the subtrahend from the minuend.
[1913 Webster]
3. That which is deduced or drawn from premises by a process
of reasoning; an inference; a conclusion.
[1913 Webster]
Make fair deductions; see to what they mount.
--Pope.
[1913 Webster]
4. That which is or may be deducted; the part taken away;
abatement; as, a deduction from the yearly rent in
compensation for services; deductions from income in
calculating income taxes.
Syn: See Induction.
[1913 Webster] |
business deduction
(wn) | business deduction
n 1: tax write-off for expenses of doing business |
entertainment deduction
(wn) | entertainment deduction
n 1: deduction allowed for some (limited) kinds of entertainment
for business purposes |
tax deduction
(wn) | tax deduction
n 1: a reduction in the gross amount on which a tax is
calculated; reduces taxes by the percentage fixed for the
taxpayer's income bracket [syn: tax write-off, {tax
deduction}, deduction] |
natural deduction
(foldoc) | natural deduction
ND
A set of rules expressing how valid proofs may be
constructed in predicate logic.
In the traditional notation, a horizontal line separates
premises (above) from conclusions (below). Vertical
ellipsis (dots) stand for a series of applications of the
rules. "T" is the constant "true" and "F" is the constant
"false" (sometimes written with a LaTeX \perp).
"^" is the AND (conjunction) operator, "v" is the inclusive
OR (disjunction) operator and "/" is NOT (negation or
complement, normally written with a LaTeX \neg).
P, Q, P1, P2, etc. stand for propositions such as "Socrates
was a man". P[x] is a proposition possibly containing
instances of the variable x, e.g. "x can fly".
A proof (a sequence of applications of the rules) may be
enclosed in a box. A boxed proof produces conclusions that
are only valid given the assumptions made inside the box,
however, the proof demonstrates certain relationships which
are valid outside the box. For example, the box below
labelled "Implication introduction" starts by assuming P,
which need not be a true proposition so long as it can be
used to derive Q.
Truth introduction:
-
T
(Truth is free).
Binary AND introduction:
-----------
| . | . |
| . | . |
| Q1 | Q2 |
-----------
Q1 ^ Q2
(If we can derive both Q1 and Q2 then Q1^Q2 is true).
N-ary AND introduction:
----------------
| . | .. | . |
| . | .. | . |
| Q1 | .. | Qn |
----------------
Q1^..^Qi^..^Qn
Other n-ary rules follow the binary versions similarly.
Quantified AND introduction:
---------
| x . |
| . |
| Q[x] |
---------
For all x . Q[x]
(If we can prove Q for arbitrary x then Q is true for all x).
Falsity elimination:
F
-
Q
(Falsity opens the floodgates).
OR elimination:
P1 v P2
-----------
| P1 | P2 |
| . | . |
| . | . |
| Q | Q |
-----------
Q
(Given P1 v P2, if Q follows from both then Q is true).
Exists elimination:
Exists x . P[x]
-----------
| x P[x] |
| . |
| . |
| Q |
-----------
Q
(If Q follows from P[x] for arbitrary x and such an x exists
then Q is true).
OR introduction 1:
P1
-------
P1 v P2
(If P1 is true then P1 OR anything is true).
OR introduction 2:
P2
-------
P1 v P2
(If P2 is true then anything OR P2 is true). Similar
symmetries apply to ^ rules.
Exists introduction:
P[a]
-------------
Exists x.P[x]
(If P is true for "a" then it is true for all x).
AND elimination 1:
P1 ^ P2
-------
P1
(If P1 and P2 are true then P1 is true).
For all elimination:
For all x . P[x]
----------------
P[a]
(If P is true for all x then it is true for "a").
For all implication introduction:
-----------
| x P[x] |
| . |
| . |
| Q[x] |
-----------
For all x . P[x] -> Q[x]
(If Q follows from P for arbitrary x then Q follows from P for
all x).
Implication introduction:
-----
| P |
| . |
| . |
| Q |
-----
P -> Q
(If Q follows from P then P implies Q).
NOT introduction:
-----
| P |
| . |
| . |
| F |
-----
/ P
(If falsity follows from P then P is false).
NOT-NOT:
//P
---
P
(If it is not the case that P is not true then P is true).
For all implies exists:
P[a] For all x . P[x] -> Q[x]
-------------------------------
Q[a]
(If P is true for given "a" and P implies Q for all x then Q
is true for a).
Implication elimination, modus ponens:
P P -> Q
----------
Q
(If P and P implies Q then Q).
NOT elimination, contradiction:
P /P
------
F
(If P is true and P is not true then false is true).
(1995-01-16)
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