PS-rules for the predicate calculus.The predicate calculus offers linguists another kind of expression to describe as a proposition. They may do this in the GT framework using different PS rules. In the predicate calculus a proposition is defined as a predicate expression. The simple predicate expression consists in a predicate symbol together with an argument symbol placed between opening and closing parentheses. The relation is a predicate with two arguments, but predicates could be defined for any number of arguments. The GT linguist (systems designer) writes these two rules as one by using a dashed box to enclose the optional elements and a star to indicate its possible multiplicity. |
| The argument expression may be a single symbol (a single lower-case letter) or by using recursion it may be an (embedded) proposition. |
| Another set of rules redefines the predicate symbol as a series of one or more (n) upper-case letters. |
| The UML diagram for the predicate expression represents recursion by identifying the structure generated by [PSb5] as the initial symbol in [PSb1]. Another recursion captures the structure of multiple arguments in the argument expression of certain predicates. |
Transformations for the predicate calculus.The predicate calculus does not require any additional transformations beyond what the linguist had for the propositional calculus. Since this calculus doesn’t have connectives, however, it is necessary to give the replacement transformations a slightly different form: |
| MODUS PONENDO PONENS (MPP) | |
|---|---|
| base1: | P1 |
| base2: | ENTAIL(P1, P2) |
| transform: | P2 |
| DEFINITION 1 (DEF1) | |
|---|---|
| base1: | P1 |
| base2: | DEFINE(P1,P2) |
| transform: | P2 |
| DEFINITION 2 (DEF2) | |
|---|---|
| base1: | P1 |
| base2: | DEFINE(P2,P1) |
| transform: | P2 |
The first transformation has the Latin name of the mode of inference that it describes.
The linguist in giving specific predicates in these transformations is thereby providing that their own specific meaning be imparted to them.
Remember this is the only way that predicates as symbols in a calculus can acquire meaning.
These replacement transformations are the means whereby the connectives “ ” and “ ” come to have an interpretation. |
