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A term that doesn't contain any variables is called a ground term; a term that doesn't contain multiple occurrences of a variable is called a linear term. For example, 2+2 is a ground term and hence also a linear term, x⋅(n+1) is a linear term, n⋅(n+1) is a non-linear term. These properties are important in, for example, term rewriting.
In mathematical logic, a ground term of a formal system is a term that does not contain any variables. Similarly, a ground formula is a formula that does not contain any variables. In first-order logic with identity with constant symbols a {\displaystyle a} and b {\displaystyle b} , the sentence Q ( a ) ∨ P ( b ) {\displaystyle Q(a)\lor P(b ...
The two terms lie on the outside of the proposition, joined by the act of affirmation or denial. For early modern logicians like Arnauld (whose Port-Royal Logic was the best-known text of his day), it is a psychological entity like an "idea" or "concept". Mill considers it a word. To assert "all Greeks are men" is not to say that the concept of ...
Replacement: (i) the formula to be replaced must be within a tautology, i.e. logically equivalent ( connected by ≡ or ↔) to the formula that replaces it, and (ii) unlike substitution its permissible for the replacement to occur only in one place (i.e. for one formula). Example: Use this set of formula schemas/equivalences: ( (a ∨ 0) ≡ a ).
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Hund's first rule now states that the ground state term is 3 P, which has S = 1. The superscript 3 is the value of the multiplicity = 2 S + 1 = 3. The diagram shows the state of this term with M L = 1 and M S = 1.
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