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  2. Conjunctive grammar - Wikipedia

    en.wikipedia.org/wiki/Conjunctive_grammar

    They extend the basic type of grammars, the context-free grammars, with a conjunction operation. Besides explicit conjunction, conjunctive grammars allow implicit disjunction represented by multiple rules for a single nonterminal symbol, which is the only logical connective expressible in context-free grammars. Conjunction can be used, in ...

  3. Conjunction (grammar) - Wikipedia

    en.wikipedia.org/wiki/Conjunction_(grammar)

    For example, after is a preposition in "he left after the fight" but a conjunction in "he left after they fought". In general, a conjunction is an invariant (non-inflecting) grammatical particle that stands between conjuncts. A conjunction may be placed at the beginning of a sentence, [1] but some superstition about the practice persists. [2]

  4. Logical conjunction - Wikipedia

    en.wikipedia.org/wiki/Logical_conjunction

    Here is an example of an argument that fits the form conjunction introduction: Bob likes apples. Bob likes oranges. Therefore, Bob likes apples and Bob likes oranges. Conjunction elimination is another classically valid, simple argument form. Intuitively, it permits the inference from any conjunction of either element of that conjunction.

  5. Conjunction introduction - Wikipedia

    en.wikipedia.org/wiki/Conjunction_introduction

    The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if the proposition is true, and the proposition is true, then the logical conjunction of the two propositions and is true. For example, if it is true that "it is raining", and it is true that "the cat is inside", then it is true that "it is ...

  6. Conjunction elimination - Wikipedia

    en.wikipedia.org/wiki/Conjunction_elimination

    The rule makes it possible to shorten longer proofs by deriving one of the conjuncts of a conjunction on a line by itself. An example in English: It's raining and it's pouring. Therefore it's raining. The rule consists of two separate sub-rules, which can be expressed in formal language as: and

  7. Commutativity of conjunction - Wikipedia

    en.wikipedia.org/wiki/Commutativity_of_conjunction

    In propositional logic, the commutativity of conjunction is a valid argument form and truth-functional tautology. It is considered to be a law of classical logic . It is the principle that the conjuncts of a logical conjunction may switch places with each other, while preserving the truth-value of the resulting proposition.

  8. Conjunctive normal form - Wikipedia

    en.wikipedia.org/wiki/Conjunctive_normal_form

    Example As an example, the formula saying "Anyone who loves all animals, is in turn loved by someone" is converted into CNF (and subsequently into clause form in the last line) as follows (highlighting replacement rule redexes in red {\displaystyle {\color {red}{\text{red}}}} ):

  9. Disjunctive syllogism - Wikipedia

    en.wikipedia.org/wiki/Disjunctive_syllogism

    For example, "P or Q" is a disjunction, where P and Q are called the statement's disjuncts. The rule makes it possible to eliminate a disjunction from a logical proof . It is the rule that