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Material conditional

The material conditional (also known as material implication) is a binary operation commonly used in logic. When the conditional symbol → {\displaystyle \to } is interpreted as material implication, a formula P → Q {\displaystyle P\to Q} is true unless P {\displaystyle P} is true and Q {\displaystyle Q} is false.

History, Semantics & Discrepancies with natural language

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0-preserving
no
1-preserving
yes
Affine
no
Conjunctive
x ¯ + y {\displaystyle {\overline {x}}+y}
Definition
x → y {\displaystyle x\to y}
Disjunctive
x ¯ + y {\displaystyle {\overline {x}}+y}

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Overview

Notation

History

Semantics

Syntactical properties

A selection of theorems (classical logic)

The relationship between the material conditional and logical consequence

Discrepancies with natural language

Conditionals

Bibliography

Advanced semantic analysis

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Map overview Semantic statistics

Material conditional

Nodes88
Edges87
Triples46
Avg. degree1.98
Density0.022727
Components1

How this topic connects Entity context

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Material conditional

Top relations

related to Discrepancies with natural language · 14
Material conditional → For, France, Frank Jackson, Grice, Grice's, If, In, Material, On, Paris, Recent, Similarly, These, Thus
related to Notation · 9
Material conditional → Conditional, Cpq, In, Polish, Rightarrow, RIGHTWARDS ARROW, RIGHTWARDS DOUBLE ARROW, SUPERSET OF, The
related to The relationship between the material conditional and logical consequence · 2
Material conditional → It, The
0-preserving · 1
Material conditional → no
1-preserving · 1
Material conditional → yes
Affine · 1
Material conditional → no
Conjunctive · 1
Material conditional → x ¯ + y {\displaystyle {\overline {x}}+y}
Definition · 1
Material conditional → x → y {\displaystyle x\to y}
Disjunctive · 1
Material conditional → x ¯ + y {\displaystyle {\overline {x}}+y}
Monotone · 1
Material conditional → no

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Important terminology

material conditional displaystyle logic implication conditionals ed natural language doi isbn classical also 10 truth expressed true false logical proposition

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Material conditional0-preservingno1.00infobox
Material conditional1-preservingyes1.00infobox
Material conditionalAffineno1.00infobox
Material conditionalConjunctivex ¯ + y {\displaystyle {\overline {x}}+y}1.00infobox
Material conditionalDefinitionx → y {\displaystyle x\to y}1.00infobox
Material conditionalDisjunctivex ¯ + y {\displaystyle {\overline {x}}+y}1.00infobox
Material conditionalMonotoneno1.00infobox
Material conditionalSelf-dualno1.00infobox
Material conditionalTruth table( 1011 ) {\displaystyle (1011)}1.00infobox
Material conditionalZhegalkin polynomial1 ⊕ x ⊕ x y {\displaystyle 1\oplus x\oplus xy}1.00infobox
Material conditionalis asentential connective within a formal language0.90text
the strict conditionalinstance ofmany logics replace material implication with other operators0.80text

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