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public interface Symbol
Represents a symbol of a signature.
A symbol is a triple ⟨signifier, type, notation⟩
consisting of a signifier, its type
specification, and its notation.
Each symbol is either a constant symbol or a variable symbol.
Symbols can be names for various kinds of objects in the (logical) universe:
σ→τ
.
A function f of arity (number of arguments) n
is sometimes denoted as f/n.
Functionsymbols especially include
ι
(as functions of arity 0).
(σ)
ο
(as predicates of arity 0).*
and the corresponding type identifier predicates τ of type (⊤)
.
There should never be two equal symbols (i.e. with equal signifier, type, and notation) with one being constant, and the other variable. And it is also recommended not to use symbols of equal signifier and type but with different notations (except perhaps if they have the same semantics).
Signature
,
Naming conventionMethod Summary  

boolean 
equals(java.lang.Object o)
Compares two symbols for equality according to their three components. 
Notation.NotationSpecification 
getNotation()
Get the notation used when this symbol occurs. 
java.lang.String 
getSignifier()
Get the signifier representing this symbol. 
int 
hashCode()
Returns the hash code value for this symbol. 
boolean 
isVariable()
Whether this symbol is a variable symbol. 
void 
setNotation(Notation.NotationSpecification notation)
Set the notation used when this symbol occurs. 
void 
setSignifier(java.lang.String signifier)
Set the signifier representing this symbol. 
void 
setType(Type type)
Set the type specification of this symbol. 
Methods inherited from interface orbital.logic.sign.type.Typed 

getType 
Methods inherited from interface java.lang.Comparable 

compareTo 
Method Detail 

boolean equals(java.lang.Object o)
equals
in class java.lang.Object
int hashCode()
hashCode
in class java.lang.Object
java.lang.String getSignifier()
Synonym(!): sign (C.S.Peirce), signifier (Saussure), token. Depending upon terminology, the "name" of a symbol is known as sign, signifier or token.
Generally the three constituents  according to C.S.Peirce  of a sign are (in their special notations, and with todays most common terminology)
void setSignifier(java.lang.String signifier)
void setType(Type type)
type
 the type specification τ of this symbol.Notation.NotationSpecification getNotation()
void setNotation(Notation.NotationSpecification notation)
notation
 the notation used when this symbol occurs.boolean isVariable()
Note that the distinction between variable symbols and constant symbols is independent of the distinction between variable and constant interpretant functions. Especially, it is independent of the arity of this symbol.
Even though in the case of firstorder logic, only object variables can occur, higherorder logic also provides functionvariable symbols and predicatevariables. Then there truly is the terminologically confusing special case of variable symbols for constant functions (i.e. functions of arity 0).
isVariable
in interface Variable
true
if this symbol is a variable symbol,
and false
if this symbol is a constant symbol.Variable

Orbital library 1.3.0: 11 Apr 2009 

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