Below you will find example sentences with "classical logic". The examples show how this phrase is used in natural context and which words often surround it.

Classical Logic in a sentence

Corpus data

  • Displayed example sentences: 19
  • Discovered as a combination around: classical
  • Corpus frequency in the collocation scan: 5
  • Phrase length: 2 words
  • Average sentence length: 23.1 words

Words in this phrase

classical logic

Meanings of words in this phrase

  • classical can mean: Of or relating to the first class or rank, especially in literature or art. Frequent word
  • logic can mean: logical Frequent word

Sentence profile

  • Phrase position: 8 start, 7 middle, 4 end
  • Sentence types: 18 statements, 1 questions, 0 exclamations

Usage patterns

These patterns show short text windows around the phrase in the example sentences:

assumptions of classical logic to ensure 1× based on classical logic 1× classical logic extends intuitionistic 1× classical logic identifies a 1× classical logic the intended 1× compared with classical logic this combination 1× idempotent in classical logic most varieties 1× implementations of classical logic can choose 1×

Sentence openings and endings

Common sentence openings:

both conjunction and 1× classical logic extends 1× classical logic identifies 1× classical logic the 1× contrapositive arguments rightly 1× despite its simplicity 1×

Common sentence endings:

and intuitionistic logic 1× be surprisingly expressive 1× fact intuitionistically true 1× for classical logic 1× general the intuitionistic 1× imply not c 1×

Context words

These words often appear near this phrase in the example sentences:

intuitionistic 6× programming 3× true 3× proofs 3× truth 3× intuitionist 3× statement 3× linear 2× expressive 2× semantics 2× axiom 2× principle 2×

Related phrases

logic programming classical latin classical music logic gates classical academy classical liberalism formal logic classical theory

Phrases around this combination

Other phrases discovered around classical:

classical academy 7× classical liberalism 6× classical theory 5×

Just before it in the phrase index:

classical liberalism classical latin classical academy classic tale classic gaming classic cars

Just after it in the phrase index:

classical music classical theory classified documents classified information classified material classified records

Other phrases with the same pattern

Same start:

classical latin classical music classical academy classical liberalism classical theory

Same ending:

formal logic

Corpus analysis

  • The phrase "classical logic" has 2 words and usually appears near the start in these examples. The average sentence has 23.1 words and is mostly made up of statements.
  • Around this phrase, patterns and context words such as assumptions of classical logic to ensure, based on classical logic, intuitionistic, programming and true stand out.
  • In the phrase index, this combination connects with logic programming, classical latin, classical music, classical academy, classical liberalism and classical theory, linking the page to nearby combinations.

Example types with classical logic

This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:

Short example sentences

There is no third truth-value, at least not in classical logic. (12 words)

Yet other systems accept classical logic but feature a nonstandard membership relation. (12 words)

Different implementations of classical logic can choose different functionally complete subsets of connectives. (13 words)

Longer example sentences

Results such as the Gödel–Gentzen negative translation show that it is possible to embed (or translate) classical logic into intuitionistic logic, allowing some properties about intuitionistic proofs to be transferred back to classical proofs. (35 words)

However, because the intuitionistic notion of truth is more restrictive than that of classical mathematics, the intuitionist must reject some assumptions of classical logic to ensure that everything he proves is in fact intuitionistically true. (35 words)

However, there are proofs in classical logic that depend upon the law of excluded middle; since that law is not usable under this scheme, there are propositions that cannot be proven that way. (33 words)

Question examples

Still, complementarity does not usually imply that classical logic is at fault (although Hilary Putnam took such a view in " Is logic empirical? (23 words)

Example sentences (19)

Linear logic programming Basing logic programming within linear logic has resulted in the design of logic programming languages that are considerably more expressive than those based on classical logic.

Classical logic The intended semantics of classical logic is bivalent, but this is not true of every semantics for classical logic.

Both conjunction and disjunction are associative, commutative and idempotent in classical logic, most varieties of many-valued logic and intuitionistic logic.

Results such as the Gödel–Gentzen negative translation show that it is possible to embed (or translate) classical logic into intuitionistic logic, allowing some properties about intuitionistic proofs to be transferred back to classical proofs.

Classical logic extends intuitionistic logic with an additional axiom or principle of excluded middle : :For any proposition p, the proposition p ∨ ¬p is true.

Still, complementarity does not usually imply that classical logic is at fault (although Hilary Putnam took such a view in " Is logic empirical?

However, because the intuitionistic notion of truth is more restrictive than that of classical mathematics, the intuitionist must reject some assumptions of classical logic to ensure that everything he proves is in fact intuitionistically true.

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used.

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Contrapositive arguments rightly utilize the transposition rule of inference in classical logic to conclude something like: To the extent that C implies E then Not-E must also imply Not-C.

Despite its simplicity compared with classical logic, this combination of Horn clauses and negation as failure has proved to be surprisingly expressive.

Different implementations of classical logic can choose different functionally complete subsets of connectives.

However, there are proofs in classical logic that depend upon the law of excluded middle; since that law is not usable under this scheme, there are propositions that cannot be proven that way.

In classical logic, the negation of a statement asserts that the statement is false; to an intuitionist, it means the statement is refutable citation (e.

The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.

The classical logic allows this result to be transformed into there exists an n such that P(n), but not in general the intuitionistic..

There is no third truth-value, at least not in classical logic.

This is closer to intuitionist and constructivist views on the material conditional, rather than to classical logic's ones.

Unlike Kripke's theory of truth, revision theory can be used with classical logic and can maintain the principle of bivalence.

Yet other systems accept classical logic but feature a nonstandard membership relation.

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