Predicate Declarations

A predicate represents mathematical or logical statements regarding zero or more objects or other statements. To declare a predicate, we write

predicate predicate_name (argument_list)

where

• predicate_name is the name of the predicate, which can be referred to in the Substance and Style schemas; and
• argument_list describes the types of objects that this predicate works with. We will go more into its details below.

The arguments in argument_list contains the types of objects that this predicate accepts, separated by commas. Here is a Domain schema that contains a couple of type declarations and four different, valid, predicate declarations:

type FirstType, SecondType

predicate P1 (FirstType, SecondType)
predicate P2 (SecondType a1, SecondType a2)
predicate P3 ()
predicate P4 (FirstType, SecondType, SecondType)

Notice how some declarations have names associated with the argument types (e.g. P2 with argument names a1 and a2), and some don't. These names to argument types are allowed and encouraged to enhance readability, but are not required.

Symmetric Predicates

Some relations between objects are symmetric: for example, in the set-theory domain, the relations "a intersects b" and "b intersects a" are equivalent. As a recent new feature, Penrose supports symmetric predicates:

symmetric predicate predicate_name (argument_type, argument_type)

For now, Penrose only supports symmetry of binary predicates (taking exactly two arguments), and, the two arguments must be of the exact same type in the Domain schema (not necessarily when the predicate is used in the Substance and Style schemas).

As an example, consider the following valid Domain schema in the chemistry domain:

type Atom
type Hydrogen <: Atom
type Oxygen <: Atom
symmetric predicate Bond (Atom, Atom)

The predicate Bond is declared symmetric. Then, if H is a Hydrogen and O is an Oxygen, then Bond(H, O) and Bond(O, H) are considered equivalent by the Penrose engine. In other words, if Penrose expects to see Bond(H, O) in the Substance or Style schemas, then it will also accept Bond(O, H) even though the order of arguments are different.