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Related puzzles involving disjunction include free choice inferences, Hurford's Constraint, and the contribution of disjunction in alternative questions. Other apparent discrepancies between natural language and classical logic include the paradoxes of material implication , donkey anaphora and the problem of counterfactual conditionals .
Disjunction has also been given numerous non-classical treatments, motivated by problems including Aristotle's sea battle argument, Heisenberg's uncertainty principle, as well as the numerous mismatches between classical disjunction and its nearest equivalents in natural languages. [1] [2] An operand of a disjunction is a disjunct. [3]
A logical formula is considered to be in DNF if it is a disjunction of one or more conjunctions of one or more literals. [2] [3] [4] A DNF formula is in full disjunctive normal form if each of its variables appears exactly once in every conjunction and each conjunction appears at most once (up to the order of variables).
In logic, mathematics and linguistics, and is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as ∧ {\displaystyle \wedge } [ 1 ] or & {\displaystyle \&} or K {\displaystyle K} (prefix) or × {\displaystyle \times } or ⋅ {\displaystyle \cdot } [ 2 ] in ...
In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs.
[4] [5] [6] It is the most widely known example of duality in logic. [1] The duality consists in these metalogical theorems: In classical propositional logic, the connectives for conjunction and disjunction can be defined in terms of each other, and consequently, only one of them needs to be taken as primitive. [4] [1]
It deals with propositions [1] (which can be true or false) [10] and relations between propositions, [11] including the construction of arguments based on them. [12] Compound propositions are formed by connecting propositions by logical connectives representing the truth functions of conjunction, disjunction, implication, biconditional, and ...
The dual of a formula is obtained by replacing each connective by its dual, [110] [111] e.g., for a formula containing only conjunction, disjunction, and negation (such as a formula in disjunctive normal form), its dual is the result of replacing each conjunction with a disjunction, and each disjunction with a conjunction.
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