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Natural deduction at a glance
The strongest research directions include History and Proofs and type theory. Use the connected concepts below as starting points, not as a keyword checklist.
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Explore the main themes, entities and connections around Natural deduction. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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History
27 related topics
Proofs and type theory
18 related topics
Classical and modal logics
16 related topics
First and higher-order extensions
11 related topics
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Topics to explore
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.Browse the full topic structure. Each item opens a new analysis centered on that subject.
Overview
- Logic
- Proof theory
- Proof calculus
- Logical reasoning
- Inference rules
- Hilbert-style systems Hilbert system
- Axioms Axiom
- Deductive reasoning
- Valery Glivenko
- Proved Double-negation translation
- Propositional formula
- Tautology Tautology (logic)
- If and only if
History
- Hilbert David Hilbert
- Frege Gottlob Frege
- Russell Bertrand Russell
- Whitehead Alfred North Whitehead
- Principia Mathematica
- Łukasiewicz Jan Lukasiewicz
- Jaśkowski Stanisław Jaśkowski
- Fitch notation
- Suppes Patrick Suppes
- Lemmon John Lemmon
- Suppes–Lemmon notation
- Gentzen Gerhard Gentzen
- University of Göttingen
- Number theory
- Cut elimination theorem
- Sequent calculus
- Classical Classical logic
- Intuitionistic logic
- Prawitz Dag Prawitz
- Modal Modal logic
- Second-order logic
- Proposition
- Martin-Löf Per Martin-Löf
- Kleene (2002 Natural deduction
- Public copyright license
- Fitch Frederic Fitch
- Quine Willard Van Orman Quine
Notation
- Logical connectives Logical connective
- Propositional logic Propositional calculus
- Modus ponens
- Precedence Order of operations
- As primitives Postulate
- Sequents Sequent
Propositional language syntax
- Formal syntax
- Formal language
- Recursion Recursive definition
- Propositional variable
- Formula Well-formed formula
- Negation
- Falsity False (logic)
- Minimal Minimal logic
- Bostock David Bostock (philosopher)
- Categorial grammar
Gentzen-style propositional logic
- Johansson Ingebrigt Johansson
- Principle of explosion
- Law of excluded middle
Consistency, completeness, and normal forms
- Theory Theory (mathematical logic)
- Model Model theory
- Lambda calculus
- Curry–Howard isomorphism
- Normal form Normal form (abstract rewriting)
- Cut-free Cut elimination
First and higher-order extensions
- Terms Term (logic)
- Countable
- Predicates Predicate (mathematical logic)
- Term algebra
- Atomic formula
- First-order logic
- Quantified Quantifier (logic)
- Universal quantifier
- Existential quantifier
- Decidable Decidability (logic)
- Higher-order logic
Proofs and type theory
- Turnstile Turnstile (symbol)
- Induction Mathematical induction
- Type theory
- Product Product type
- Arrow Function type
- Normalising Normalization property (abstract rewriting)
- Dependent type theory
- Computer-assisted proof
- Extensional type theory
- Intensional type theory
- Parametric polymorphism
- Predicative polymorphism
- Impredicative polymorphism
- Lambda cube
- Henk Barendregt
- Logical framework
- Calculus of constructions
- LF LF (logical framework)
Classical and modal logics
- Excluded middle
- Heyting Arend Heyting
- Parigot Michel Parigot?action=edit&redlink=1
- Λμ Lambda-mu calculus
- Callcc
- LISP
- First class control
- S4 S4 (modal logic)
- S5 S5 (modal logic)
- Linear Linear logic
- Substructural logics Substructural logic
- Analytic tableaux Analytic tableau
- Labelled deduction Labelled deduction?action=edit&redlink=1
- Hybrid logic
- Hypersequents Hypersequent
- Display logic
Comparison with sequent calculus
- Mathematical logic
- Predicate logic
- Kleene Stephen Cole Kleene
- Structural rule
- Meta-theorem
Advanced semantic analysis
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
How this topic connects Entity context
Quick relationship hints grouped by predicate. Useful for spotting recurring semantic connections around the current entity.See the strongest relationship patterns around the current topic before diving into the raw triples.
Natural deduction
Top relations
related to history · 35
Natural deduction → An, Fitch, Frege, Gentzen, Gentzen's, Gerhard Gentzen, German, Göttingen, Hilbert, His, IEP, In, It, Jaśkowski, Kleene, Kleene's, Lemmon, Natural, Notation, Poland
related to Modal substitution theorem · 12
Natural deduction → Avron, Belnap's, However, Kripke, Labels, Pottinger's, S5, Simpson, Stouppa, The, This, To
related to Substitution theorem · 11
Natural deduction → For, If, In, Normalisability, Propositions, Recall, So, The, Thus, To, Type
related to Comparison with sequent calculus · 9
Natural deduction → Gentzen, In, Inference, Introduction, Kleene, Metamathematics, The, Thus, To
related to Cut (substitution) · 7
Natural deduction → For, However, In, Now, Proof, This, Thus
related to Suppes–Lemmon-style inference rules · 6
Natural deduction → Fitch, Gentzen-style, Lemmon, Lemmon-style, Suppes, The
related to Gentzen's tree notation · 5
Natural deduction → Gentzen, In Gentzen's, Let's, Representing, This
related to Proofs and type theory · 5
Natural deduction → Following, The, This, To, We
see also · 4
Natural deduction → Argument, GentzenSystem, Mathematical, Philosophy
is a · 3
Natural deduction → kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the, pair of soundness and completeness theorems, syntactic proof system
Important terminology Word statistics
Frequent words and multi-word phrases across the lead, headings, infobox and body. Useful for terminology coverage.Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
Important terminology
natural deduction rules logic calculus displaystyle proof theory sequent type notation proofs introduction rule inference elimination lemmon one propositions logical
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Natural deduction | is a | kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the | 0.90 | text |
| Natural deduction | is a | syntactic proof system | 0.90 | text |
| Natural deduction | is a | pair of soundness and completeness theorems | 0.90 | text |
| Fitch notation or Suppes' method | instance of | His proposals led to different notations | 0.80 | text |
| for which Lemmon gave a variant now known as Suppes | instance of | His proposals led to different notations | 0.80 | text |
| Patrick Suppes | instance of | where assumptions could be opened within a subderivation and discharged later.Later logicians and educators | 0.80 | text |
| E | instance of | where assumptions could be opened within a subderivation and discharged later.Later logicians and educators | 0.80 | text |
| the calculus of constructions | instance of | Popular modern logical frameworks | 0.80 | text |
| LF are based on higher-order dependent type theory | instance of | Popular modern logical frameworks | 0.80 | text |
| with various trade-offs in terms of decidability | instance of | Popular modern logical frameworks | 0.80 | text |
| expressive power | instance of | Popular modern logical frameworks | 0.80 | text |
| labelling or systems of deep inference.The addition of labels to formulae permits much finer control of the conditions under which rules apply | instance of | extensions | 0.80 | text |
No triples extracted yet.
Related concept clusters Concept neighborhoods
Clusters of nearby vocabulary surrounding the topic. Scan them for adjacent concepts and language you may have missed.These clusters group vocabulary that occurs around closely connected concepts in the source material.
Connections between topic areas Semantic bridges
Bridge nodes connect otherwise separate parts of the map. Expand a row to inspect the topic groups on each side.Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Natural deduction
Nodes126
Edges125
Triples109
Avg. degree1.98
Density0.015873
Components1
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