20 + recent turned up (20 or fewer displayed):
- Logic
Logic
(λόγος in Greek,
logos, "thought") is the most
fundamental of all the Sciences
and a major branch of Philosophy. ...
- Sole Sufficient Operator
A sole sufficient operator
or a sole sufficient
connective is an operator that is
sufficient by itself to generate all of the
operators in a specified class of operators. ...
- Propositional Calculus
In mathematical
logic, a propositional
calculus (sentential
calculus) is a formal system that represents the
materials and the principles of
propositional logic (sentential
logic). ...
- Peirce’s Law
Loi de
Peirce
Peirce
定律
Other Languages : (中文 : Peirce
定律)
Peirce's
law in logic is named after the philosopher and logician Charles
Sanders Peirce. It was taken as an axiom in his first
axiomatisation of propositional
calculus. ...
- Logical Graph
A logical graph is a
special type of graph-theoretic structure in any
one of several systems of graphical syntax that Charles
Sanders Peirce developed for logic.
In his papers on
qualitative
logic, entitative graphs, and existential
graphs, Peirce developed several
versions of a graphical formalism, or a graph-theoretic
formal language,
designed to be interpreted for logic.
In
the century since Peirce initiated this line
of development, a variety of formal systems
have branched out from what is abstractly the
same formal base of graph-theoretic
structures. ...
- Logic of Relatives
The logic of relatives,
short for the logic of relative
terms, is the study of relations
in their logical, philosophical, or semiotic aspects, as
distinguished from, though closely
coordinated with, their more properly formal,
mathematical, or objective aspects.
The
consideration of relative terms has its roots
in antiquity, but it entered a radically new
phase of development with the work of Charles
Sanders Peirce, beginning with his paper
"Description of a Notation for the
Logic of Relatives, Resulting from an
Amplification of the Conceptions of Boole's
Calculus of Logic" (1870).
References:
* Peirce,
C.S., "Description of a Notation for the
Logic of Relatives, Resulting from an
Amplification of the Conceptions of Boole's
Calculus of Logic", Memoirs of the
American Academy of Arts and Sciences 9,
317–378, 1870. ...
- Zeroth-Order Logic
零阶逻辑
O
ther Languages : (中文 :
零阶逻辑)
Zeroth order logic is a
term in popular use among practitioners for
the subject matter otherwise known as boolean
functions, monadic predicate logic, propositional
calculus, or sentential calculus. ...
- Truth Table
Waarheidstabel
Wahrheitstabelle
Tabla de valores de
verdad
Table de vérité
Tabella della veritŕ
טבלת
אמת
Waarheidstabel
真理値表
Sannhetstabell
Tabela verdade
Sanningstabell
真值表
Other
Languages : (中文 :
真值表)
A
truth table is a mathematical
table used in logic —
specifically in connection with boolean algebra,
boolean
functions, and propositional
calculus — to compute the functional
values of logical expressions on any of
their functional arguments, that is, with
respect to the various possible combinations
of values that their logical variables may
take. ...
- Tacit Extension
In logic and mathematics, a
tacit extension is in formal
respects the simplest or the logically least
committal of the several possible set
operations that are inverse to the
set-theoretic operation of projection.
See
also:
* Cartesian product
* Inverse
relation
* Projection
(set theory)
* Relation
(mathematics)
* Relation composition
* Relation
reduction
Some content
adapted from the Wikinfo
article "Tacit extension" under the GNU
Free Documentation License. ...
- Relational Reduction
In logic and mathematics,
relation reduction and
relational reducibility have
to do with the extent to which a given relation
is determined by an indexed family or a sequence of other
relations, called the relation
dataset. ...
- Relational Construction
In logic and mathematics,
relation construction and
relational constructibility
have to do with the ways that one relation
is determined by an indexed family or a sequence of other
relations, called the relation
dataset. ...
- Relational Composition
In logic and mathematics, the
composition of relations
is the generalization of
the composition of
functions.
Preliminaries:
The first order of business is to
define the operation on relations
that is variously known as the
composition of relations,
relational composition, or
relative multiplication. ...
- Rheme
A rhema or a
rheme (also "relative
term" and "topic comment"), is a logical
term that requires reference to any number of
other objects, called the correlates of the
term, in order to denote a definite
object, called the relate (pronounced
with the accent on the first syllable) of the
relative term in question. ...
- Prescisive Abstraction
Prescisive abstraction
or prescision, variously
spelled as precisive
abstraction or
prescission, is a formal
operation that marks, selects, or singles out
one feature of a concrete experience to the
disregard of others.
The above definition
is adapted from the one given by Charles
Sanders Peirce (CP 4.235, "The Simplest
Mathematics" (1902), in Collected
Papers, CP 4.227–393).
References:
* Peirce,
C.S., Collected Papers of Charles
Sanders Peirce, vols. 1–6, Charles
Hartshorne and Paul
Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard
University Press, Cambridge, MA, 1931–1935,
1958.
See also:
* Hypostatic
abstraction
* Hypostatic object
Some content adapted from the Wikinfo article "Prescisive abstraction" under
the GNU
Free Documentation License. ...
- Logical Implication
In mathematics and mathematical
logic, the concept of logical
implication encompasses, depending
on the context of use, a specific logical function,
a specific logical relation,
and the various symbols that are used to
denote this function or this relation. ...
- Logical NAND
Logical NAND, for
Not And, sometimes denoted
by a symbol "|" or "↑" called the
Sheffer stroke, is a logical operation that is
equivalent to the negation of the conjunction
operation, expressed in ordinary language as
"not both". ...
- Logical NNOR
\{\{disclaim\}\}
{{dablink|This
article is about NOR in the logical sense.
For the electronic NOR gates see NOR gate, for other uses of similar
terms, see NOR
(disambiguation).}}
The
logical NNOR, for
Neither Nor, also called
NOR, for Not
Or, or joint
denial, is a boolean logic operator that
produces a result that is the inverse of logical or.
That is, (not or), p NNOR
q is only true when both p
and q are false. ...
- Exclusive Disjunction
: For the corresponding concept in combinational
logic, see XOR
gate.
Exclusive
disjunction, also known as
exclusive or and symbolized
by XOR or
EOR, is a logical operation on two
operands that results in a logical value of true if
and only if one of the operands, but not
both, has a value of true.
Definition:
In many natural languages, English included, the
interpretation of the word "or" requires a
certain amount of care. ...
- Logical Conjunction
In logic and mathematics,
logical conjunction (usual
symbol and) is a two-place
logical
operation that results in a value of
true if both of its operands are
true, otherwise a value of
false.
Definition:
Logical conjunction is an operation on
two logical values,
typically the values of two propositions, that
produces a value of true if and only
if both of its operands are true.
The truth table of p AND
q (also written as p ∧
q, p & q, or
p · q) is as follows:
{|
align="center" border="1" cellpadding="8"
cellspacing="0" style="background:lightcyan;
font-weight:bold; text-align:center;
width:45%"
|+ Logical Conjunction
|-
style="background:paleturquoise"
!
style="width:15%" | p
! style="width:15%" |
q
! style="width:15%" | p ∧ q
|-
| F
|| F || F
|-
| F || T || F
|-
| T || F ||
F
|-
| T || T || T
|}
The
analogue of conjunction for a (possibly infinite) family of
statements is universal
quantification, which is part of predicate
logic.
Introduction and elimination
rules:
As a rule of inference.
conjunction introduction is a classically valid, simple argument form. The
argument form has two premises, A
and B. Intuitively, it permits the
inference of their
conjunction.
:A,
:B.
:Therefore, A and
B.
or in logical operator
notation:
: A,
: B
: vdash A and B
Here is an example of an
argument that fits the form conjunction
introduction:
:Everyone should
vote.
:Democracy is the best system of
government.
:Therefore, everyone should vote
and Democracy is the best system of
government.
Conjunction elimination is
another classically valid,
simple argument form.
Intuitively, it permits the inference from
any conjunction of ...
- Disjunction
{{Spoken Wikipedia|Logical
disjunction.ogg|2006-07-21}}
In logic and mathematics,
logical disjunction (written
or) is a logical operator
that results in true just whenever
some of its operands are
true.
Definition:
Logical disjunction is an operation on
two logical values,
typically the values of two propositions, that
produces a value of false if and
only if both of its operands are
false.
The truth table of p OR
q (also written as p ∨
q) is as follows:
{|
align="center" border="1" cellpadding="8"
cellspacing="0" style="background:lightcyan;
font-weight:bold; text-align:center;
width:45%"
|+ Logical
Disjunction
|-
style="background:paleturquoise"
!
style="width:15%" | p
! style="width:15%" |
q
! style="width:15%" | p ∨ q
|-
| F
|| F || F
|-
| F || T || T
|-
| T || F ||
T
|-
| T || T || T
|}
More
generally a disjunction is a logical formula
that can have one or more literals
separated only by ORs. A single literal is
often considered to be a degenerate
disjunction.
Symbol:
The
mathematical symbol for logical disjunction
varies in the literature. ...
|
