Difference between revisions of "Talk:Zeroth order logic"
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==Propositional forms on two variables== | ==Propositional forms on two variables== | ||
| − | By way of initial orientation, Table 1 lists equivalent expressions for the sixteen functions of concrete type <math>X \times Y \to \mathbb{B}</math> and abstract type <math>\mathbb{B} \times \mathbb{B} \to \mathbb{B}</math> in a number of different languages for zeroth order logic. | + | By way of initial orientation, Table 1 lists equivalent expressions for the sixteen functions of concrete type <math>X \times Y \to \mathbb{B}\!</math> and abstract type <math>\mathbb{B} \times \mathbb{B} \to \mathbb{B}\!</math> in a number of different languages for zeroth order logic. |
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Latest revision as of 03:04, 9 November 2015
☞ This page belongs to resource collections on Logic and Inquiry.
Zeroth order logic is an informal term that is sometimes used to indicate the common principles underlying the algebra of sets, boolean algebra, boolean functions, logical connectives, monadic predicate calculus, propositional calculus, and sentential logic. The term serves to mark a level of abstraction in which the more inessential differences among these subjects can be subsumed under the appropriate isomorphisms.
Propositional forms on two variables
By way of initial orientation, Table 1 lists equivalent expressions for the sixteen functions of concrete type \(X \times Y \to \mathbb{B}\!\) and abstract type \(\mathbb{B} \times \mathbb{B} \to \mathbb{B}\!\) in a number of different languages for zeroth order logic.
| \(\begin{matrix}\mathcal{L}_1 \\ \text{Decimal}\end{matrix}\!\) | \(\begin{matrix}\mathcal{L}_2 \\ \text{Binary}\end{matrix}\!\) | \(\begin{matrix}\mathcal{L}_3 \\ \text{Vector}\end{matrix}\!\) | \(\begin{matrix}\mathcal{L}_4 \\ \text{Cactus}\end{matrix}\!\) | \(\begin{matrix}\mathcal{L}_5 \\ \text{English}\end{matrix}\!\) | \(\begin{matrix}\mathcal{L}_6 \\ \text{Ordinary}\end{matrix}\!\) |
| \(x\colon\!\) | \(1~1~0~0\!\) | ||||
| \(y\colon\!\) | \(1~0~1~0\!\) | ||||
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\(\begin{matrix} f_{0} \'"`UNIQ-MathJax1-QINU`"' It may also be noted that \((x, y)\!\) is the same function as \(x + y\!\) and \(x \ne y\), and that the inclusive disjunctions indicated for \((x, y)\!\) and for \((x, y, z)\!\) may be replaced with exclusive disjunctions without affecting the meaning, because the terms disjoined are already disjoint. However, the function \((x, y, z)\!\) is not the same thing as the function \(x + y + z\!\).
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Document historyPortions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.
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