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Topics referred to by the same term
In logic, the term conditional disjunction can refer to: conditioned disjunction, a ternary logical connective introduced by Alonzo Church a rule in classical
Conditional_disjunction
Logical connective
The material conditional (also known as material implication) is a binary operation commonly used in logic. When the conditional symbol → {\displaystyle
Material_conditional
True when either but not both inputs are true
biconditional, by the rules of material implication (a material conditional is equivalent to the disjunction of the negation of its antecedent and its consequence)
Exclusive_or
Type of connective in logic
In logic, conditioned disjunction (sometimes called conditional disjunction) is a ternary logical connective introduced by Church. Given operands p, q
Conditioned_disjunction
Conditional operator in computer programming
In computer programming, the ternary conditional operator is a conditional expression with three parts: the Boolean condition, the then-expression, and
Ternary_conditional_operator
Symbol connecting formulas in logic
negation and contradiction for more). Neither conjunction, disjunction, nor material conditional has an equivalent form constructed from the other four logical
Logical_connective
Graphical symbol or pictogram used to point or indicate direction
conjunction), an downwards arrow indicates the NOR operator (negation of disjunction). Use of arrow symbols in mathematical notation developed in the first
Arrow_(symbol)
Natural-language "if" sentences about what may be the case
An indicative conditional is a natural-language conditional sentence (an "if" sentence) used to talk about what may actually be the case, as in: "If Leona
Indicative_conditional
Pair of logical equivalences
British mathematician. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation. The rules can be expressed
De_Morgan's_laws
In probability theory, a conditional event algebra (CEA) is an alternative to a standard, Boolean algebra of possible events (a set of possible events
Conditional_event_algebra
Binary operator in computer programming
there is no need for the Elvis operator, because the language's logical disjunction operator (typically || or or) is short-circuiting and returns its first
Elvis_operator
British philosopher of language (1913–1988)
might appear one could make these deductions by contraposition and conditional disjunction: ([a] from [ii]) If Yog was white, then 1/2 of the time Yog won
Paul_Grice
11, if/then, Material conditional; 12, p, Projection function; 13, then/if, Converse implication; 14, OR, Logical disjunction; 15, true, Tautology. Each
List_of_rules_of_inference
Type of logical contradiction
formulae involving material conditionals whose translations into natural language are intuitively false when the conditional is translated with English
Paradoxes of material implication
Paradoxes_of_material_implication
Algebraic manipulation of "true" and "false"
algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and negation (not) denoted as ¬. Elementary algebra
Boolean_algebra
Rule of logical inference
premise is a conditional ("if–then") claim, namely that P implies Q. The second premise is an assertion that P, the antecedent of the conditional claim, is
Modus_ponens
Syllogism with conditional premise(s)
hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises. Ancient references point to
Hypothetical_syllogism
Terms to describe a conditional relationship between two statements
terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If P then Q",
Necessity_and_sufficiency
Phenomenon for disjunction in conditional propositions
(SDA) is the phenomenon whereby a disjunction in the antecedent of a conditional appears to distribute over the conditional as a whole. This inference is
Simplification of disjunctive antecedents
Simplification_of_disjunctive_antecedents
Kind of quantifier in logic
clarify the role of conditionals in a first-order language as they relate to other connectives, such as conjunction or disjunction. While they can cover
Conditional_quantifier
Mathematical table used in logic
addition, and as logically equivalent to the exclusive-or (exclusive disjunction) binary logic operation. In this case it can be used for only very simple
Truth_table
Logic gate
The two leftmost transistors mentioned above, perform an optimized conditional inversion of A when B is at a logic high using pass transistor logic
XOR_gate
Logical paradox
.." entirely (reducing to disjunctions), so no protasis and apodosis exist and no counter-argument is needed. Conditional sentences in English Crocodile
Barbershop_paradox
Phenomenon in natural language
Free choice is a phenomenon in natural language where a linguistic disjunction appears to receive a logical conjunctive interpretation when it interacts
Free_choice_inference
Concept in mathematical logic
consequent will be valid. Converse implication is logically equivalent to the disjunction of P {\displaystyle P} and ¬ Q {\displaystyle \neg Q} In natural language
Converse_(logic)
Conditioned disjunction Evasive Boolean function Exclusive or Functional completeness Logical biconditional Logical conjunction Logical disjunction Logical
List of Boolean algebra topics
List_of_Boolean_algebra_topics
Type of formal logic
disjunction introduction but keep disjunctive syllogism and transitivity. In this approach, rules of natural deduction hold, except for disjunction introduction
Paraconsistent_logic
Overview of and topical guide to logic
Conversion (logic) De Morgan's laws Destructive dilemma Disjunction elimination Disjunction introduction Disjunctive syllogism Double negation elimination
Outline_of_logic
Concept in mathematical logic
{\displaystyle \land } ); disjunction ( ∨ {\displaystyle \lor } ); negation ( ¬ {\displaystyle \neg } ); material conditional ( → {\displaystyle \to }
Functional_completeness
Formal proof
A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to
Conditional_proof
Model that describes the programmable interface of a computer processor
cases. Perform bitwise operations, e.g., taking the conjunction and disjunction of corresponding bits in a pair of registers, taking the negation of
Instruction_set_architecture
Method of deriving conclusions
well as the commutative and associative properties of conjunction and disjunction. While rules of implication apply only to complete statements, rules
Rule_of_inference
Kind of non-classical logic
negation, this section will consider only languages with a conditional, conjunction, and disjunction. An operational frame F {\displaystyle F} is a triple
Relevance_logic
Logical rule of inference
three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's
Disjunctive_syllogism
Mathematics notation with operators preceding operands
In this the letters N, A, C, E, K are used in the roles of negation, disjunction, implication, equivalence, conjunction respectively. ... Łukasiewicz
Polish_notation
Algebraic structure modeling logical operations
conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). However, the theory of Boolean rings has an inherent
Boolean_algebra_(structure)
Programming language construct
the basic Boolean operators for logical conjunction AND and logical disjunction OR. Bitwise operators are shown only for languages that allow them to
Short-circuit_evaluation
Style of formal logical argumentation
of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology is inferred
Sequent_calculus
prove a conditional statement. disjunct One of the component propositions in a disjunction, each of which is an alternative to the others. disjunction A logical
Glossary_of_logic
Ancient philosophy
then q"; whereas a conjunction takes the form of "both p and q"; and a disjunction takes the form of "either p or q". The or they used is exclusive, unlike
Stoicism
Greek Stoic philosopher (c.279–c.206 BC)
conjunction, the disjunction, and the conditional, and Chrysippus studied their criteria of truth closely. The first logicians to debate conditional statements
Chrysippus
Possessing negative truth value
implication vacuously true). In most logical systems, negation, material conditional and false are related as: ¬p ⇔ (p → ⊥) In fact, this is the definition
False_(logic)
Polish Dominican and philosopher (1902–1995)
(falsity) Logical disjunction (Disjunction) (F T T T)(p,q) Apq Xpq (T F F F)(p,q) Logical NOR (joint denial) Converse conditional (Converse implication)
Józef_Maria_Bocheński
Branch of logic
expressed by the words "and" (conjunction), "or" (disjunction), "not" (negation), "if" (material conditional), and "if and only if" (biconditional). Examples
Propositional_logic
Symbolic logic system
implication → {\displaystyle \to } , conjunction ∧ {\displaystyle \land } , disjunction ∨ {\displaystyle \lor } , and falsum or absurdity ⊥ {\displaystyle \bot
Minimal_logic
Data having only values "true" or "false"
support for Boolean algebraic operations such as conjunction (AND, &, *), disjunction (OR, |, +), equivalence (EQV, =, ==), exclusive or/non-equivalence (XOR
Boolean_data_type
Concept in first-order logic
the empty conjunction and the empty disjunction. The semantic clauses for, respectively, conjunctions and disjunctions are given by A ⊨ ϕ 1 ∧ ⋯ ∧ ϕ n ⟺ ∀
Empty_domain
replaced by the word "not". ∨ (descending wedge) 1. Denotes logical disjunction, and is read as "or". If E and F are logical predicates, E ∨ F {\displaystyle
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
If and only if relation
only case where a logical biconditional is different from a material conditional is the case where the hypothesis (antecedent) is false but the conclusion
Logical_biconditional
should not have affected their decision at all. Conditional probability Contingency Consequentialism Disjunction Decision under uncertainty Game theory Savage's
Non-consequential_reasoning
fallacies: Affirming a disjunct – concluding that one disjunct of a logical disjunction must be false because the other disjunct is true; A or B; A, therefore
List_of_fallacies
Rule of logical inference
premise is a conditional ("if-then") claim, such as P implies Q. The second premise is an assertion that Q, the consequent of the conditional claim, is not
Modus_tollens
Cliché used as a pattern for other expressions
perform or omit". In general usage, "to X or not to X" simply conveys "disjunction between contradictory alternatives", which linguist Arnold Zwicky described
Snowclone
Inference in propositional logic
rules of inference of propositional logic. It allows for one to infer a conditional from a biconditional. If P ↔ Q {\displaystyle P\leftrightarrow Q} is
Biconditional_elimination
Computer science and recursion theory
list of variables), negation (logical NOT), conjunction (logical AND), disjunction (logical OR), bounded universal quantification, or bounded existential
McCarthy_Formalism
Rule of replacement in propositional logic
implication is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states
Material implication (rule of inference)
Material_implication_(rule_of_inference)
Type of Horn clause, a generalization of identities
quasi-identity amounts to a conditional equation for which the conditions themselves are equations. Alternatively, it can be seen as a disjunction of inequations and
Quasi-identity
Typographic symbol
Likewise, the vertical bar is also used singly in many different ways: conditional probability: P ( X | Y ) {\displaystyle P(X|Y)} , read "the probability
Vertical_bar
Rule of replacement in propositional logic
logic. The rule allows conditional statements having conjunctive antecedents to be replaced by statements having conditional consequents and vice versa
Exportation_(logic)
Task to construct a program meeting a formal specification
common subformula p {\displaystyle p} . The resolvent is formed as the disjunction of E {\displaystyle E} , with p {\displaystyle p} replaced by t r u e
Program_synthesis
Mathematical logic concept
contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated
Contraposition
Form of reasoning
valid logical forms or rules of inference, like modus tollens or the disjunction elimination. The syntactic approach then holds that an argument is deductively
Deductive_reasoning
Logical proof involving antecedents and consequents
In mathematical logic, a sequent is a very general kind of conditional assertion. A 1 , … , A m ⊢ B 1 , … , B n . {\displaystyle A_{1},\,\dots ,A_{m}\
Sequent
1879 book on logic by Gottlob Frege
idiosyncratic two-dimensional notation, based on negation, material conditional and universal quantification. Other connectives and existential quantification
Begriffsschrift
Semantic or grammatical assertion of the truth
[[Did you see Mary?]] = { you saw Mary ∨ you didn't see Mary } Because disjunction p ∨ q entails neither p nor q, the context is nonveridical, which explains
Veridicality
Type of logical argument that applies deductive reasoning
when affirming a disjunct – concluding that one disjunct of a logical disjunction must be false because the other disjunct is true; A or B; A, therefore
Syllogism
Branch of metaphysics
e is also a truthmaker for p. The disjunction principle states that if entity e is a truthmaker for the disjunction of proposition p and proposition q
Truthmaker_theory
Logical connective
would infer a biconditional directly. An alternative is to prove the disjunction "(P and Q) or (not-P and not-Q)", which itself can be inferred directly
If_and_only_if
Propositional logic extending intuitionistic logic
There exists a continuum of different intermediate logics with the disjunction property (DP). Intermediate logics form a complete lattice, with intuitionistic
Intermediate_logic
Lattice in universal algebra
(conjunction or meet), ∨, Apq, (disjunction or join), →, Cpq, (implication), ↔, Epq, (biconditional), +, Jpq (exclusive disjunction or Boolean ring addition)
Post's_lattice
List of statements that appear to contradict themselves
drinking, everybody in the pub is drinking. Paradox of free choice: Disjunction introduction poses a problem for modal inferences, permitting arbitrary
List_of_paradoxes
List of symbols used to express logical relations
\to } \to or \rightarrow ⊃ {\displaystyle \supset } \supset material conditional (material implication) implies, if P then Q, it is not the case that
List_of_logic_symbols
Mathematical use of "for all" and "there exists"
) {\displaystyle \exists x\in D\;P(x)} is equivalent to the logical disjunction P ( a 1 ) ∨ . . . ∨ P ( a n ) {\displaystyle P(a_{1})\lor ...\lor P(a_{n})}
Quantifier_(logic)
Set of words within the Turkish language
and eğer are Persian; the latter is not generally needed, because the conditional form of the verb is available. The Persian conjunction ki brings to Turkish
Turkish_vocabulary
Approach to the semantics of logic that locates meaning in inferential role
consequence is preserved as new atomic rules are added. The clauses for disjunction, existence, and absurdity merit separate comment, since the most natural
Proof-theoretic_semantics
four or five distinct schools concerning the correct understanding of conditional ("if...then...") statements. Sextus Empiricus described one school as
Connexive_logic
Part of speech that connects two words, sentences, phrases, or clauses
used with conjunctions Genitive connector Logical conjunction Logical disjunction Polysyndeton Relativizer Serial comma – the comma used immediately before
Conjunction_(grammar)
Function in logic
statements. For example, classical logic has ¬P ∨ Q equivalent to P → Q. The conditional operator "→" is therefore not necessary for a classical-based logical
Truth_function
Concept in linguistics
the right indicates its end. { } (Curly Braces): Indicate a logical-disjunction relationship of two expressions. For example, The two expressions, ABD
Phonological_rule
Diagram that shows all possible logical relations between a collection of sets
Venn diagram as a truth table demonstrating logical disjunction
Venn_diagram
Application of logical methods to philosophical problems
which are valid in classical logic: disjunction introduction and disjunctive syllogism. According to the disjunction introduction, any proposition can be
Philosophical_logic
Logical operation
theorem. De Morgan's laws provide a way of distributing negation over disjunction and conjunction: ¬ ( P ∨ Q ) ≡ ( ¬ P ∧ ¬ Q ) {\displaystyle \neg (P\lor
Negation
Compiler optimization of one jump directly to a second jump
conjunction), hence evaluation of expression y || z is not needed (logical disjunction). Therefore, a jump to label jmp is performed. Switch (programming) Spaghetti
Jump_threading
Set of rules defining correctly structured programs
operators: unary negation (NOT = !a) binary disjunction (OR = a || b) and conjunction (AND = a && b) ternary conditional (c ? t : f) In the context of a logical
JavaScript_syntax
Argument whose conclusion must be true if its premises are
sound. The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion
Validity_(logic)
Kind of proof calculus
propositions similar to Γ. Γ was treated as a conjunction, and Δ as a disjunction. This structure is essentially lifted directly from classical sequent
Natural_deduction
operations of Boolean algebra are the conjunction and (denoted as ∧), the disjunction or (denoted as ∨), and the negation not (denoted as ¬). It is thus a
Glossary_of_computer_science
Extension of relational algebra
school). NULL='Spring' will evaluate to MAYBE and so will NULL='Fall'. The disjunction MAYBE OR MAYBE evaluates to MAYBE (not TRUE). Thus Igor will not be part
Imieliński–Lipski_algebra
Set of rules defining correctly structured programs
and represents logical conjunction, and || or or represents logical disjunction. ! represents logical negation, and cannot be substituted with not. Ternary
PHP_syntax_and_semantics
Rule of inference of propositional logic
either P or R is true, then either Q or S has to be true. In sum, if two conditionals are true and at least one of their antecedents is, then at least one
Constructive_dilemma
British philosopher (born 1955)
disjunctivist position of saying that belief can be analysed as the disjunction of knowledge with some distinct, non-factive mental state. Williamson
Timothy_Williamson
\sigma ^{2}} weighted arithmetic mean weighted median XOR, exclusive disjunction Yates's correction for continuity, yules correction z-test Outline of
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Philosophical problem about what constitutes knowledge
owns a Ford". Smith therefore (justifiably) concludes (by the rule of disjunction introduction) that "Jones owns a Ford, or Brown is in Barcelona", even
Gettier_problem
Formal system in mathematical logic
denoting abstraction and scope, as well as four constants: negation, disjunction, universal quantification, and selection respectively; and also, a finite
Simply_typed_lambda_calculus
Algebraic ring that need not have additive negative elements
a ring is the two-element Boolean algebra, for instance with logical disjunction ∨ {\displaystyle \lor } as addition. A motivating example that is neither
Semiring
Opposite of a probability event
× ... × (5/6) = 1 − (5/6)8 = 0.7674... Logical complement Exclusive disjunction Binomial probability Robert R. Johnson, Patricia J. Kuby: Elementary
Complementary_event
Theory of logic to account for observations from quantum theory
quantum logic as a basis for reasoning, because it lacks a material conditional; a common alternative is the system of linear logic, of which quantum
Quantum_logic
Type of logical system
conjunctions or disjunctions with less than κ constituents is known as Lκω. For example, Lω1ω permits countable conjunctions and disjunctions. The set of
First-order_logic
Robot programming language
involve conjunctions and disjunctions (Rich ∧ (Beautiful ∨ Smart)). In STRIPS the effects are conjunctions, but in ADL conditional effects are allowed: when
Action_description_language
Type of residuated Boolean algebra with extra structure
Boolean operations of conjunction x ∧ y {\displaystyle x\wedge y} , disjunction x ∨ y {\displaystyle x\vee y} , and negation x − {\displaystyle x^{-}}
Relation_algebra
CONDITIONAL DISJUNCTION
CONDITIONAL DISJUNCTION
Girl/Female
Hindu
Good or Happy condition, Solution, Fortune
Boy/Male
Bengali, Indian
Sleepless; Condition of Being Awake; One who Conquers Sleep
Boy/Male
African, Arabic, Australian, Greek, Swahili
Unique; Graceful; Kind; Sweet; The Beautiful Ocean; Loving; Forgiving; Content; Delighted; Beauty; Perfect; State; Handsome; Condition; The Sea
Girl/Female
Tamil
Good or Happy condition, Solution
Boy/Male
African, Arabic, Australian, French, Indian, Muslim, Sindhi
Sacrifice; Unconditional Love; Love
Girl/Female
Tamil
Circumstance, Period of life, Wick, Condition, Degree
Boy/Male
Arabic
State; Condition
Girl/Female
Tamil
Good or Happy condition, Solution, Fortune
Girl/Female
Indian
Circumstance, Period of life, Wick, Condition, Degree
Boy/Male
Indian
Can Travel in All Climatic Conditions
Girl/Female
Hindu
Good or Happy condition, Solution
Boy/Male
Tamil
Can travel in all climatic conditions
CONDITIONAL DISJUNCTION
CONDITIONAL DISJUNCTION
Boy/Male
Hindu, Indian
Successful
Boy/Male
Indian
Pertaining to mecca
Surname or Lastname
English
English : habitational name from a place in Lancashire, so named from the Old English personal name Æ{dh}elsige (see Elston) + wīc ‘dairy farm’.
Girl/Female
Sikh
Knowledge, Learning
Boy/Male
Arabic, Farsi, Iranian, Muslim, Parsi
Name of King
Boy/Male
Indian
Famous
Girl/Female
Australian, Jamaican
Enclosed Meadow
Female
Dutch
, a Saxon woman.
Boy/Male
Hindu, Indian, Kannada, Traditional
Another Name of Vishnu
Girl/Female
Indian, Punjabi, Sikh
Surprise
CONDITIONAL DISJUNCTION
CONDITIONAL DISJUNCTION
CONDITIONAL DISJUNCTION
CONDITIONAL DISJUNCTION
CONDITIONAL DISJUNCTION
n.
A limitation.
a.
Not conditioned or subject to conditions; unconditional.
a.
Not conditional limited, or conditioned; made without condition; absolute; unreserved; as, an unconditional surrender.
n.
To put under conditions; to require to pass a new examination or to make up a specified study, as a condition of remaining in one's class or in college; as, to condition a student who has failed in some branch of study.
v. t.
To qualify by conditions; to regulate.
a.
Unconditional.
n.
To invest with, or limit by, conditions; to burden or qualify by a condition; to impose or be imposed as the condition of.
v. t.
Conditional.
imp. & p. p.
of Condition
n.
A conditional word, mode, or proposition.
a.
Of the nature of a proviso; containing a proviso or condition; conditional; as, a provisory clause.
v. i.
To impose upon an object those relations or conditions without which knowledge and thought are alleged to be impossible.
adv.
In a conditional manner; subject to a condition or conditions; not absolutely or positively.
v. t.
To put under conditions; to render conditional.
a.
Containing, implying, or depending on, a condition or conditions; not absolute; made or granted on certain terms; as, a conditional promise.
a.
Surrounded; circumstanced; in a certain state or condition, as of property or health; as, a well conditioned man.
a.
Expressing a condition or supposition; as, a conditional word, mode, or tense.
a.
Having, or known under or by, conditions or relations; not independent; not absolute.
adv.
Conditionally.
n.
train; acclimate.