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Logical operator in propositional calculus
Logical equality is a logical operator that compares two truth values, or more generally, two formulas, such that it gives the value True if both arguments
Logical_equality
Mathematical table used in logic
functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In
Truth_table
If and only if relation
needed][vague][clarification needed] Logical equality (also known as biconditional) is an operation on two logical values, typically the values of two
Logical_biconditional
Mathematical symbol of equality
U+2263 ≣ STRICTLY EQUIVALENT TO 2 + 2 = 5 Double hyphen Equality (mathematics) Logical equality Plus and minus signs Weisstein, Eric W. "Equal". mathworld
Equals_sign
Basic notion of sameness in mathematics
mathematical symbols § Equality, equivalence and similarity Identity type Identity (object-oriented programming) Inequality Logical equality Logical equivalence
Equality_(mathematics)
Concept in logic
Psychology portal Entailment Equisatisfiability If and only if Logical biconditional Logical equality ≡ the iff symbol (U+2261 IDENTICAL TO) ∷ the a is to b as
Logical_equivalence
Topics referred to by the same term
Logical equivalent may refer to: Logical equivalence, in logic and mathematics Logical equality, the logical operator in propositional calculus XNOR gate
Logical_equivalent
Symbols requiring interpretation
syntax. The equality symbol is sometimes treated as a non-logical symbol and sometimes treated as a symbol of logic. If it is treated as a logical symbol,
Non-logical_symbol
Digital logic gate
known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the
XNOR_gate
Hardware description language
== Logical equality (bit-value 1'bX is removed from comparison) != Logical inequality (bit-value 1'bX is removed from comparison) === 4-state logical equality
Verilog
Topics referred to by the same term
EQV may refer to: Logical biconditional, a type of logical connective Logical equality, a logical operator Mercedes-Benz Concept EQV, a concept van in
EQV
Type of logical system
considers the equality relation to be a non-logical symbol. This convention is known as first-order logic without equality. If an equality relation is included
First-order_logic
Symbol with a fixed meaning in logic
types of logical constants are logical connectives and quantifiers. The equality predicate (usually written '=') is also treated as a logical constant
Logical_constant
Topics referred to by the same term
legislation Equality (mathematics), the relationship between expressions that represent the same value or mathematical object Equals sign, = Logical equality Equality
Equality
Inverse functions of sin, cos, tan, etc.
k . {\displaystyle k.} " The symbol ⟺ {\displaystyle \,\iff \,} is logical equality and indicates that if the left hand side is true then so is the right
Inverse trigonometric functions
Inverse_trigonometric_functions
Mathematical theory of data types
Gregory Bateson introduced a theory of logical types into the social sciences; his notions of double bind and logical levels are based on Russell's theory
Type_theory
Assignment of meaning to the symbols of a formal language
equality (see the section "Interpreting equality" below). Finally, the formulas of the language are assembled from atomic formulas using the logical connectives
Interpretation_(logic)
Symbol connecting formulas in logic
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is an operator that combines or modifies
Logical_connective
Classical logic of two values, either true or false
Extensionality False dilemma Fuzzy logic Liar paradox Logical disjunction Logical equality Logical value Multi-valued logic Perspectivism Propositional
Principle_of_bivalence
Programming language construct
condition. Relational operators can be seen as special cases of logical predicates. Equality is used in many programming language constructs and data types
Relational_operator
completeness Logical biconditional Logical conjunction Logical disjunction Logical equality Logical implication Logical negation Logical NOR Majority
List of Boolean algebra topics
List_of_Boolean_algebra_topics
Symbol representing a property or relation in logic
In logic, a predicate is a non-logical symbol that represents a property or a relation, though, formally, does not need to represent anything at all.
Predicate_(logic)
Whether a decision problem has an effective method to derive the answer
first-order logical validities in the signature with only equality, established by Leopold Löwenheim in 1915. The set of first-order logical validities
Decidability_(logic)
Logical connective
Equivalence relation Logical biconditional Logical equality Logical equivalence If and only if in logic programs Polysyllogism "Logical Connectives". sites
If_and_only_if
Statement that is taken to be true
predicate calculus, but additional logical axioms are needed to include a quantifier in the calculus. Axiom of equality. Let L {\displaystyle {\mathfrak
Axiom
are said to be convergent if they are confluent and terminating. Logical equality Logical equivalence Rule of replacement Franz Baader; Tobias Nipkow (1998)
Convergence_(logic)
defined. C and C++ have the same logical operators and all can be overloaded in C++. Note that overloading logical AND and OR is discouraged, because
Operators_in_C_and_C++
explosion in fuzzy logic rules. The Combs method takes advantage of the logical equality ( ( p ∧ q ) ⇒ r ) ⟺ ( ( p ⇒ r ) ∨ ( q ⇒ r ) ) {\displaystyle ((p\land
Combs_method
Mathematical model for deduction or proof systems
with the deductive nature of the system. The logical consequence (or entailment) of the system by its logical foundation is what distinguishes a formal system
Formal_system
Value indicating the relation of a proposition to truth
semantics of logical connectives are truth functions, whose values are expressed in the form of truth tables. Logical biconditional becomes the equality binary
Truth_value
Function returning one of only two values
inputs are true ("not both") NOR or logical nor - true when none of the inputs are true ("neither") XNOR or logical equality - true when both inputs are the
Boolean_function
Extraction of information from a running system to verify certain properties
needed. In the following examples Java syntax is assumed, thus "==" is logical equality, while "=" is assignment. Some methods (e.g., update() in the UnsafeEnumExample)
Runtime_verification
Standards and rules used to judge the accuracy of statements and claims
about vagueness List of cognitive biases Logical equality – Logical operator in propositional calculus Logical value – Value indicating the relation of
Criteria_of_truth
Mathematical analysis
properties for the reals, i.e. for this class of sets, expressed using the logical equality. Constructive reals in the presence of appropriate choice axioms will
Constructive_analysis
1943 paper proposing artificial neural networks
"A Logical Calculus of the Ideas Immanent in Nervous Activity" is a 1943 paper written by Warren Sturgis McCulloch and Walter Pitts, published in the
A Logical Calculus of the Ideas Immanent in Nervous Activity
A_Logical_Calculus_of_the_Ideas_Immanent_in_Nervous_Activity
1960 mathematics textbook by Paul Halmos
have the same elements. This guarantees that the membership and (logical) equality relations interact appropriately. 2. Axiom of Specification (Section
Naive_Set_Theory_(book)
3-volume treatise on mathematics, 1910–1913
"identical with", i.e., contemporary mathematical "equality" (cf. discussion in section ✱13). Logical equivalence is represented by "≡" (contemporary "if
Principia_Mathematica
Jain doctrine of many-sidedness
Indian logic Jain epistemology Jaina seven-valued logic Logical disjunction Logical equality Logical value Multiplicities Multi-valued logic Perspectivism
Anekantavada
Algebraic manipulation of "true" and "false"
mod 2 is 1 + 1 = 0. Logical equivalence The third operation, the complement of exclusive or, is equivalence or Boolean equality: x ≡ y, or Exy, is true
Boolean_algebra
Matrix of binary truth values
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a
Logical_matrix
Theorem in Boolean algebra
логических равенств и об обратном способе [On methods of solving logical equalities and the inverse method of mathematical logic. An essay in construction
Poretsky's_law_of_forms
Analytical philosophical view expounded by Bertrand Russell
Logical atomism is a philosophical view that originated in the early 20th century with the development of analytic philosophy. It holds that the world
Logical_atomism
Standard form of Boolean function
логических равенств и об обратном способе [On methods of solving logical equalities and the inverse method of mathematical logic. An essay in construction
Blake_canonical_form
Type of diagrammatic notation for propositional logic
An existential graph is a type of diagrammatic or visual notation for logical expressions, created by Charles Sanders Peirce, who wrote on graphical logic
Existential_graph
Property involving two mathematical operations
operations is a generalization of the distributive law, which asserts that the equality x ⋅ ( y + z ) = x ⋅ y + x ⋅ z {\displaystyle x\cdot (y+z)=x\cdot y+x\cdot
Distributive_property
Data having only values "true" or "false"
condition evaluates to true or false. It is a special case of a more general logical data type—logic does not always need to be Boolean (see probabilistic logic)
Boolean_data_type
логических равенств и об обратном способе [On methods of solving logical equalities and the inverse method of mathematical logic. An essay in construction
Platon_Poretsky
American political philosopher (1921–2002)
Rawls's theory of "justice as fairness" recommends equal basic liberties, equality of opportunity, and facilitating the maximum benefit to the least advantaged
John_Rawls
"not". ∨ (descending wedge) 1. Denotes logical disjunction, and is read as "or". If E and F are logical predicates, E ∨ F {\displaystyle E\lor F} is
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
System of formal deduction in logic
axioms about & and V #5-10, axioms of negation #11-12, his logical ε-axiom #13, axioms of equality #14-15, and axioms of number #16-17—along with the other
Hilbert_system
Impossible task in computing
functional arity, predicate arity, and equality/no-equality. Having practical decision procedures for classes of logical formulas is of considerable interest
Entscheidungsproblem
In mathematics, a statement that has been proven
of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the
Theorem
Paradox in set theory
axioms of set theory while maintaining a standard logical language, while Russell modified the logical language itself. The language of ZFC, with the help
Russell's_paradox
Standard system of axiomatic set theory
one-sorted theory in first-order logic. The equality symbol can be treated as either a primitive logical symbol or a high-level abbreviation for having
Zermelo–Fraenkel_set_theory
Axioms for the natural numbers
the language of mathematical logic was in its infancy. The system of logical notation he created to present the axioms did not prove to be popular,
Peano_axioms
Concept in functional programming
(2004). "Meta-programming with built-in type equality". Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-languages (LFM'04),
Generalized algebraic data type
Generalized_algebraic_data_type
Mathematical use of "for all" and "there exists"
∈ D P ( x ) {\displaystyle \forall x\in D\;P(x)} is equivalent to the logical conjunction P ( a 1 ) ∧ . . . ∧ P ( a n ) {\displaystyle P(a_{1})\land
Quantifier_(logic)
Inference seeking the simplest and most likely explanation
(also called abduction, abductive inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion from a set
Abductive_reasoning
Programming paradigm based on formal logic
set of sentences in logical form, representing knowledge about some problem domain. Computation is performed by applying logical reasoning to that knowledge
Logic_programming
Quantum error correction code
{S}})\setminus C(C({\mathcal {S}})).} The equality above gives an alternative characterization of an undetectable logical error E: E must commute with all stabilizers
Stabilizer_code
Logic principle
In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands
Extensionality
Austrian–British philosopher of science (1902–1994)
in 1934. Here, he criticised psychologism, naturalism, inductivism, and logical positivism, and put forth his theory of potential falsifiability as the
Karl_Popper
Non-contradiction of a theory
In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T {\displaystyle T} is consistent if there is no
Consistency
1793 French political document
Rights of Man and of the Citizen of 1789 is its egalitarian tendency: equality is the prevailing right in this declaration. The 1793 version included
Declaration of the Rights of Man and of the Citizen of 1793
Declaration_of_the_Rights_of_Man_and_of_the_Citizen_of_1793
Collection of mathematical objects
specific logical framework. For the branch of mathematics that studies sets, see Set theory; for an informal presentation of the corresponding logical framework
Set_(mathematics)
society to function. The theory can be explained as based on two premises, logical and historical. "Every legal relation" proclaims Pashukanis, "is a relation
Commodity_form_theory
Notion of equality in type theory
represents the concept of equality. It is also known as propositional equality to differentiate it from "judgemental equality". Equality in type theory is a
Identity_type
Undecidability of equality of real numbers
mathematics, Richardson's theorem establishes the undecidability of the equality of real numbers defined by expressions involving integers, π, ln 2, and
Richardson's_theorem
Axiom used in set theory
predicate is the set of all things for which the predicate is true. The logical term was introduced to set theory in 1893, Gottlob Frege attempted to use
Axiom_of_extensionality
System of formal mathematical logic
free occurrences. The only primitive constants are Q((oα)α), denoting equality of members of each type α, and ℩(i(oi)), denoting a description operator
Q0_(mathematical_logic)
Relationship between programs and proofs
function (i.e., the type of values returned by a function) is analogous to a logical theorem, subject to hypotheses corresponding to the types of the argument
Curry–Howard_correspondence
Impossibility for separate objects to have all their properties in common
regarded this principle as essential to identity and equality: Alfred Tarski listed it among the logical axioms governing the notion of identity, and Rudolf
Identity_of_indiscernibles
Productive prefix in English derived from Greek
given if different logical statements or theories are put together in contradiction, thus distorting the meaning and generating logical paradoxes. One example
Meta_(prefix)
Indian actor (born 1983)
egalitarian ideals. He has championed causes related to caste abolition, gender equality, LGBTQIA rights, tribal welfare, and environmental justice. His initiatives
Chetan_Kumar
Overview of and topical guide to discrete mathematics
descriptions of redirect targets Venn diagram – Diagram that shows all possible logical relations between a collection of sets Empty set – Mathematical set containing
Outline of discrete mathematics
Outline_of_discrete_mathematics
of algebraic logic, whose aim was to provide algebraic counterparts of logical systems. Another approach relating first-order logic to algebra is provided
Polyadic_algebra
Mathematical-logic system based on functions
substitution, as used in β-reduction Harrop formula – A kind of constructive logical formula such that proofs are lambda terms Interaction nets Kleene–Rosser
Lambda_calculus
Form of logic that allows quantification over predicates
and a variety of other powerful logical theories could be formulated axiomatically without appeal to any more logical apparatus than first-order quantification
Second-order_logic
Topics referred to by the same term
a logical quantifier Complex variable, the argument or value of a function of a complex number in complex analysis Variable (research), a logical set
Variable
Rule, guide or inevitable consequence
principles,” from higher-order “guiding” or “exemplary” principles, such as equality, justice, and sustainability. Higher-order, “superordinate” principles
Principle
Liberty and the pursuit of Happiness Logical consequence Logical constant Logical form Logical possibility Logical truth Logos Love Loyalty Magnificence
List of philosophical concepts
List_of_philosophical_concepts
Empiricist philosophical theory
phase of humanity as the time since the Enlightenment, a time steeped in logical rationalism, to the time right after the French Revolution. This second
Positivism
Formalization of the natural numbers
equality symbol =, the constant symbol 0, and the successor symbol S (meaning add one); A symbol for each primitive recursive function. The logical axioms
Primitive recursive arithmetic
Primitive_recursive_arithmetic
Approach to formal semantics
as the existence of a winning strategy for a player. In this framework, logical formulas are interpreted as defining games between two players. The term
Game_semantics
Set of the elements not in a given subset
(X\times Y)\setminus R.} Here, R {\displaystyle R} is often viewed as a logical matrix with rows representing the elements of X , {\displaystyle X,} and
Complement_(set_theory)
Symbol with multiple meanings
this meaning, while ≡ is used for the higher-level metalogical notion of logical equivalence, according to which two formulas are logically equivalent when
Triple_bar
Proof assistant program
simplified BSD license. HOL Light is based on a formulation of type theory with equality as the only primitive notion. The primitive rules of inference are the
HOL_Light
Index of articles associated with the same name
predicate symbols guaranteeing that a unique formal interpretation of a logical theory exists. Specifically, we say that a set of clauses of the form Q
Stratification_(mathematics)
Distribution of income or wealth between different groups
accounts for inequality. Important concepts of equality include equity, equality of outcome, and equality of opportunity. Historically, there has been a
Economic_inequality
Mathematical model of the physical space
stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved
Euclidean_geometry
Intelligence of machines
step-by-step reasoning that humans use when they solve puzzles or make logical deductions. By the late 1980s and 1990s, methods were developed for dealing
Artificial_intelligence
Subfield of automated reasoning and mathematical logic
showed that the first-order theory of the natural numbers with addition and equality (now called Presburger arithmetic in his honor) is decidable and gave an
Automated_theorem_proving
Topics referred to by the same term
effect of European Union law Logical equivalence, where two statements are logically equivalent if they have the same logical content Material equivalence
Equivalence
American sociologist (1926–1995)
theories, and his works The Adolescent Society (1961) and "Coleman Report" (Equality of Educational Opportunity, 1966) were two of the most cited books in educational
James_Samuel_Coleman
Social identity movements
differences in approach, many activists share liberal political goals of equality and freedom, seeking to integrate into the political mainstream alongside
LGBTQ_movements
Technology designed to persuade
recently, Lieto and Vernero have also shown that arguments reducible to logical fallacies are a class of widely adopted persuasive techniques in both web
Persuasive_technology
life on this very class basis. The demand for real equality of women with men, if taken to its logical conclusion, would dislodge the patriarchal structure
Capitalist Patriarchy and the Case for Socialist Feminism
Capitalist_Patriarchy_and_the_Case_for_Socialist_Feminism
Reasoning about equations with free variables
contrary to function theory. A given relation may be represented by a logical matrix; then the converse relation is represented by the transpose matrix
Algebraic_logic
Physical lower limit to energy consumption of computation
physics have established that there is not a prior relationship between logical[further explanation needed] and thermodynamic reversibility. It is possible
Landauer's_principle
Government system where political power lies with the people
reflect the first two principles of upward control and political equality. Legal equality, political freedom and rule of law are often identified by commentators
Democracy
LOGICAL EQUALITY
LOGICAL EQUALITY
Girl/Female
Danish, Hindu, Indian, Japanese
Ray of Light; Logical
Girl/Female
Australian, French, Swedish
Elf; Magical Counsel
Boy/Male
Hindu
Love and kindness, Analytical, Logical
Boy/Male
Indian, Sanskrit
Logician
Boy/Male
Indian, Sanskrit
Endowed with Mind; Logical
Boy/Male
German, Swedish
Elf; Magical Army; Warrior
Girl/Female
Tamil
Give light to others
Boy/Male
Hindu, Indian
A Magical Sword
Boy/Male
Gujarati, Hindu, Indian, Sanskrit
Logical Science
Boy/Male
Tamil
Intelligent, Logical
Girl/Female
Indian, Modern, Sanskrit
Magical
Girl/Female
Indian, Tamil
King Rama's Wife
Boy/Male
Tamil
Love and kindness, Analytical, Logical
Boy/Male
Indian
Intelligent, Logical
Girl/Female
Indian
Successful; Logical Thinkers
Girl/Female
Native American
Magical dancer.
Boy/Male
Hindu, Indian
Logical
Girl/Female
African, Arabic, French, Indian, Muslim, Swahili, Tamil
Intelligent; Logical; Intelligent One who Reasons; Wise
Girl/Female
Hindu, Indian
Give Light to Others
Girl/Female
Hindu
LOGICAL EQUALITY
LOGICAL EQUALITY
Girl/Female
Bengali, Hindu, Indian, Tamil
Goddess Durga
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
A Flower; Name of a Flower
Girl/Female
Hebrew
Close to God.
Girl/Female
American, Australian, British, Chinese, English
From the Hedged Valley; The Rosy Meadow
Biblical
in fellowship; in envy
Boy/Male
Tamil
Black horse
Girl/Female
Tamil
Provided with nectar, Wealthy, Remembered
Boy/Male
Gaelic Scottish
Wealthy or stubborn.
Boy/Male
Hindu, Indian
Ocean
Boy/Male
Indian, Punjabi, Sikh
Limitless; Bound-free
LOGICAL EQUALITY
LOGICAL EQUALITY
LOGICAL EQUALITY
LOGICAL EQUALITY
LOGICAL EQUALITY
a.
Skilled in logic; versed in the art of thinking and reasoning; as, he is a logical thinker.
a.
Of or pertaining to logic; used in logic; as, logical subtilties.
a.
Logical.
adv.
In a logical manner; as, to argue logically.
a.
Exciting mirth; droll; laughable; as, a comical story.
a.
Having the form of, or resembling, a geometrical cone; round and tapering to a point, or gradually lessening in circumference; as, a conic or conical figure; a conical vessel.
a.
Half logical; partly logical; said of fallacies.
n.
A person skilled in logic.
v. t.
Consistent; logical.
n.
A treatise on logic; as, Mill's Logic.
a.
Having a mixture of seriousness and sport; serious and comical.
a.
Of or pertaining to the nodes; from a node to the same node again; as, the nodical revolutions of the moon.
a.
Ignorant or negligent of the rules of logic or correct reasoning; as, an illogical disputant; contrary of the rules of logic or sound reasoning; as, an illogical inference.
n.
See Logic.
n.
Of or pertaining to a place; limited; logical application; as, a topical remedy; a topical claim or privilege.
a.
Having or observing logical sequence; logically consistent and rigorous; consecutive in development or transition of thought.
a.
Excessively logical; adhering too closely to the forms or rules of logic.
pl.
of Lorica
a.
According to the rules of logic; as, a logical argument or inference; the reasoning is logical.
n.
A logical deduction.