The non-logical symbols for the axioms consist of a constant symbol 0 and a unary function symbol " S ".
12.
Just as in first-order logic, second-order logic may include non-logical symbols in a particular second-order language.
13.
It's a term algebra with a signature of 1 unary and 3 binary operations ( depending on my choice of logical symbols ).
14.
It was used in the 19th century by Charles Sanders Peirce as a logical symbol for'un-American'( " unamerican " ).
15.
The traditional approach can be recovered in the modern approach by simply specifying the " custom " signature to consist of the traditional sequences of non-logical symbols.
16.
In other words, as expected and required, " S " is true or false only under an interpretation of all its non-logical symbols.
17.
A "'spider diagram "'is a boolean expression involving unitary spider diagrams and the logical symbols \ land, \ lor, \ lnot.
18.
Logical constants are always given the same meaning by every interpretation of the standard kind, so that only the meanings of the non-logical symbols are changed.
19.
:: : : : I kind of convinced myself that all the steps I was thinkg about don't really necessitate the use of new non-logical symbols, so I guess that's it.
20.
It was used for the universe of sets in 1889 by Peano, the letter " V " signifying " Verum ", which he used both as a logical symbol and to denote the class of all individuals.
