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  2. Multiple subset sum - Wikipedia

    en.wikipedia.org/wiki/Multiple_subset_sum

    The maximum sum is 1, attained by giving one agent the item with value 1 and the other agent nothing. But the max-min allocation gives each agent value at least e, so the sum must be at most 3e. Therefore the POF is 1/(3e), which is unbounded. Alice has two items with values 1 and e, for some small e>0. George has two items with value e. The ...

  3. Logical disjunction - Wikipedia

    en.wikipedia.org/wiki/Logical_disjunction

    Because the logical or means a disjunction formula is true when either one or both of its parts are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as exclusive or, or XOR).

  4. Disjunctive normal form - Wikipedia

    en.wikipedia.org/wiki/Disjunctive_normal_form

    In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or — in philosophical logic — a cluster concept. [1] As a normal form, it is useful in automated theorem proving.

  5. Conjunctive normal form - Wikipedia

    en.wikipedia.org/wiki/Conjunctive_normal_form

    In Boolean algebra, 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.

  6. Exclusive or - Wikipedia

    en.wikipedia.org/wiki/Exclusive_or

    This field can represent any logic obtainable with the system (,) and has the added benefit of the arsenal of algebraic analysis tools for fields. More specifically, if one associates F {\displaystyle F} with 0 and T {\displaystyle T} with 1, one can interpret the logical "AND" operation as multiplication on F 2 {\displaystyle \mathbb {F} _{2 ...

  7. If and only if - Wikipedia

    en.wikipedia.org/wiki/If_and_only_if

    Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).

  8. Logic programming - Wikipedia

    en.wikipedia.org/wiki/Logic_programming

    Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical form, representing knowledge about some problem domain. Computation is performed by applying logical reasoning to that knowledge, to solve problems in the domain.

  9. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    The statement is true if and only if A is false. A slash placed through another operator is the same as ¬ {\displaystyle \neg } placed in front. The prime symbol is placed after the negated thing, e.g. p ′ {\displaystyle p'} [ 2 ]