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Propositional formula: History, Historical development & An algebra of propositions, the propositional calculus

In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula.

Language: English [EN]
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Propositional formula topic overview

The analysis highlights History, Historical development and An algebra of propositions, the propositional calculus as prominent areas in the source structure around Propositional formula.

Related topics
123
Source areas
13
Connected nodes
136
Extracted relationships
62
Related term clusters
37
Bridge connections
136

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Historical development · 30 topics
Overview · 22 topics
An algebra of propositions, the propositional calculus · 19 topics
Propositional connectives · 14 topics
Propositions · 10 topics
Propositional formula with "feedback" · 7 topics
Well-formed formulas (wffs) · 7 topics
Inductive definition · 3 topics
Normal forms · 3 topics
Parsing formulas · 3 topics
Impredicative propositions · 2 topics
Reduced sets of connectives · 2 topics
More complex formulas · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

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Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Propositions

An algebra of propositions, the propositional calculus

Propositional connectives

More complex formulas

Inductive definition

Parsing formulas

Well-formed formulas (wffs)

Reduced sets of connectives

Normal forms

Impredicative propositions

Propositional formula with "feedback"

Historical development

For the semantics nerds

You can skip this section if you’re here for content ideas and keyword inspiration.

Advanced semantic analysis

How Propositional formula connects Entity context

The extracted context around Propositional formula shows recurring relationship patterns in the source. For example, Propositional formula → AND IF, Bender, Different, Goodstein, Hamilton, I'm, IDENTITY, Leibniz's, Logical, One, Principia Mathematica, Robbin, Suppes, Translated, Typically, Williamson Another extracted example is Propositional formula → Arbitrary, Constant, ELSE, EQUALS, Examples, IDENTITY, NAND, Thus, XORThe. Use these groups to spot repeated connection types before inspecting the individual relationships.

Propositional formula

Top relations

related to IDENTITY and evaluation · 16
Propositional formula → AND IF, Bender, Different, Goodstein, Hamilton, I'm, IDENTITY, Leibniz's, Logical, One, Principia Mathematica, Robbin, Suppes, Translated, Typically, Williamson
related to Propositional connectives · 9
Propositional formula → Arbitrary, Constant, ELSE, EQUALS, Examples, IDENTITY, NAND, Thus, XORThe
related to Well-formed formulas versus valid formulas in inferences · 8
Propositional formula → Another, Bertrand Russell, Convert, Example, Quite, Reichenbach, Saying, THEN NOT-a
related to Connectives of rhetoric, philosophy and mathematics · 3
Propositional formula → FALSITY, IMPLIES, TRUTH
related to Propositional formula with "feedback" · 3
Propositional formula → Begin, Either, Observe
related to Propositional variables · 3
Propositional formula → Monday, Propositions, Saturday
is a · 2
Propositional formula → propositional variable, type of syntactic formula which is well formed
related to Connective seniority (symbol rank) · 2
Propositional formula → IDENTITY, Thus
related to Oscillation · 2
Propositional formula → Analysis, Oscillation
related to Truth-value assignments, formula evaluations · 2
Propositional formula → Evaluation, Truth

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

formula propositional truth one connectives variables formulas example logic connective two form table use logical calculus propositions isbn symbols notion

Propositional formula relationships Subject–Predicate–Object triples

TTTA extracted 62 structured relationships around Propositional formula. Examples in this analysis include Propositional formula → is a → type of syntactic formula which is well formed and Propositional formula → is a → propositional variable. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Propositional formulais atype of syntactic formula which is well formed0.90text
Propositional formulais apropositional variable0.90text
pinstance ofor propositional variables0.80text
qinstance ofor propositional variables0.80text
using connectives or logical operators such as NOTinstance ofor propositional variables0.80text
or IMPLIESinstance ofor propositional variables0.80text
parenthesesinstance ofis a method by which a collection of symbols called variables together with some other symbols0.80text
the law of contradiction or laws of identityinstance ofSome formal systems specify these valuation axioms at the outset in the form of certain formulas0.80text
nullityinstance ofSome formal systems specify these valuation axioms at the outset in the form of certain formulas0.80text
commutationinstance oftogether with laws0.80text
distributioninstance oftogether with laws0.80text
is up to the system's designer as long as the set of axioms is completeinstance oftogether with laws0.80text

Related concept clusters Related term clusters

The concept neighborhoods around Propositional formula bring nearby vocabulary together. In this analysis, examples include Propositional, Calculus and Formulas. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Propositional formula
    • Propositional
    • Calculus
    • Formulas
    • Variables
    • Connectives
    • Notion
    • Logical
    • Truth
    • One
    • Propositions
    • Simple
    • Variable
  • propositional formula
    • Propositional
    • Calculus
    • Formulas
    • Variables
    • Form
    • One
    • Connectives
    • Truth
    • Notion
    • Logical
    • Use
    • Variable
  • formula
    • Propositional
    • Variables
    • Form
    • One
    • Truth
    • Use
    • Variable
    • Set
    • Logical
    • Connectives
    • Connective
    • Table
  • propositional variables
    • Calculus
    • Formulas
    • Formula
    • Propositional
    • Variables
    • Truth
    • Symbols
    • Connectives
    • Notion
    • Logical
    • Set
    • One
  • propositional function
    • Calculus
    • Formulas
    • Variables
    • Connectives
    • Notion
    • Logical
    • Truth
    • One
    • Propositions
    • Simple
    • Variable
    • Use
  • predicate calculus
    • Propositional
    • Propositions
    • Simple
    • Notion
    • Symbols
    • Use
    • Following
    • Identity
    • Two
    • Logic
    • Values
    • Etc
  • propositional calculus
    • Calculus
    • Propositional
    • Propositions
    • Simple
    • Formulas
    • Notion
    • Symbols
    • Variables
    • Connectives
    • Logical
    • Use
    • Truth
  • truth tables
    • Table
    • Values
    • Variables
    • Use
    • Example
    • Following
    • Formulas
    • Simple
    • Connectives
    • Logical
    • Connective
    • Two

Connections between topic areas Semantic bridges

For Propositional formula, one of the stronger structural bridges in this analysis connects Propositional formula with Historical development. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Propositional formula — Historical development · splits 106 ⟂ 31
Propositional formula — Overview · splits 114 ⟂ 23
Propositional formula — An algebra of propositions, the propositional calculus · splits 117 ⟂ 20
Propositional formula — Propositional connectives · splits 122 ⟂ 15
Propositional formula — Propositions · splits 126 ⟂ 11
Propositional formula — Well-formed formulas (wffs) · splits 129 ⟂ 8
Propositional formula — Propositional formula with "feedback" · splits 129 ⟂ 8
Propositional formula — Inductive definition · splits 133 ⟂ 4
Propositional formula — Parsing formulas · splits 133 ⟂ 4
Propositional formula — Normal forms · splits 133 ⟂ 4
Propositional formula — Reduced sets of connectives · splits 134 ⟂ 3
Propositional formula — Impredicative propositions · splits 134 ⟂ 3

Map overview Semantic statistics

Propositional formula

Nodes137
Edges136
Triples62
Avg. degree1.99
Density0.014599
Components1

Source & methodology

TTTA analyzes the structure around Propositional formula to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History, Historical development & An algebra of propositions, the propositional calculus, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Propositional formula · EN edition · Analysis: TopicsToTalkAbout

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