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A logical spreadsheet is a spreadsheet in which formulas take the form of logical constraints rather than function definitions.. In traditional spreadsheet systems, such as Excel, cells are partitioned into "directly specified" cells and "computed" cells and the formulas used to specify the values of computed cells are "functional", i.e. for every combination of values of the directly ...
In first-order logic with equality, counting quantifiers can be defined in terms of ordinary quantifiers, so in this context they are a notational shorthand. However, they are interesting in the context of logics such as two-variable logic with counting that restrict the number of variables in formulas. Also, generalized counting quantifiers ...
In the truth table below, d1 is the formula: ( (IF c THEN b) AND (IF NOT-c THEN a) ). Its fully reduced form d2 is the formula: ( (c AND b) OR (NOT-c AND a). The two formulas are equivalent as shown by the columns "=d1" and "=d2". Electrical engineers call the fully reduced formula the AND-OR-SELECT operator.
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
A propositional logic formula, also called Boolean expression, is built from variables, operators AND (conjunction, also denoted by ∧), OR (disjunction, ∨), NOT (negation, ¬), and parentheses. A formula is said to be satisfiable if it can be made TRUE by assigning appropriate logical values (i.e. TRUE, FALSE) to
Free and bound variables of a formula need not be disjoint sets: in the formula P(x) → ∀x Q(x), the first occurrence of x, as argument of P, is free while the second one, as argument of Q, is bound. A formula in first-order logic with no free variable occurrences is called a first-order sentence.