Propositional representation is the psychological

Cognitive psychology

Cognitive psychology is a subdiscipline of psychology exploring internal mental processes.It is the study of how people perceive, remember, think, speak, and solve problems.Cognitive psychology differs from previous psychological approaches in two key ways....

 theory, first developed in 1973 by Dr. Zenon Pylyshyn, that mental relationships between objects are represented by symbols and not by mental images of the scene.

Examples

A propositional network describing the sentence "John believes that Anna will pass her exam" is illustrated below.
Each circle represents a single proposition, and the connections between the circles describe a network of propositions.

Another example is the sentence "Debby donated a big amount of money to Greenpeace, an organization which protects the environment", which contains the propositions "Debby donated money to Greenpeace", "The amount of money was big" and "Greenpeace protects the environment". If one or more of the propositions is false, the whole sentence is false. This is illustrated in Figure 2:
Propositional representations are also:

• Language-like only in the sense that they manipulate symbols as a language does. The language of thought
  Language of thought
  In philosophy of mind, the language of thought hypothesis put forward by American philosopher Jerry Fodor describes thoughts as represented in a "language" that allows complex thoughts to be built up by combining simpler thoughts in various ways...
  
   cannot be thought of as a natural language
  Natural language
  In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...
  
  ; it can only be a formal language
  Formal language
  A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
  
   that applies across different linguistic subjects, it therefore must be a language common to mind rather than culture, must be organizational rather than communicative. Thus Mentalese is best expressed through predicate and propositional calculus
  Propositional calculus
  In mathematical logic, a propositional calculus or logic is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules and axioms allows certain formulas to be derived, called theorems; which may be interpreted as true...
  
  .

• Made up of discrete symbols; each symbol has a smallest constituent part; i.e. limit to how far units of rep. can be broken down.

• Explicit; each symbol represents something (object, action, relation) specifically and thus explicitly.

• Grammatical; symbolic manipulation follows (requires?) syntactical rules and semantical rules.

• Abstract and amodal; symbols may represent any ideational content irrespective of which sensory modality
  Stimulus modality
  Stimulus modality also sensory modality is one aspect of a stimulus or what we percieve after a stimulus. For example the temperature modality is registered after heat or cold stimulate a receptor. There are many modalities: temperature, taste, pressure...
  
   was involved in its perception. (Unlike a pictorial representation which must be modality specific to the visual sensory mode).

Each proposition consists of a set of predicates and arguments which are represented in the form of predicate calculus. For instance:

An event; (X) John hit Chris with a unicycle, the unicycle broke, because of this John started to cry, which caused Chris to be happy.

A propositional representation

• P [hit (John, Chris, unicycle)]

• Q [broke (unicycle)]

• R [cry (John)]

• S [happy (Chris)]

• Cause (Q,R)

• Cause (R,S)

Each set of predicates (words like hit, broke, cry, happy are first order-predicates; Cause is a second-order predicate

Second-order predicate

In mathematical logic, a second-order predicate is a predicate that takes a first-order predicate as an argument. Compare higher-order predicate....

) and arguments (often consisting of an agent/subject (e.g. John in ‘P’), a recipient/object (e.g. Chris in ‘P’) and an instrument (e.g. the unicycle in ‘P’)) are in turn manipulated as propositions: event/statement “John hit Chris with the unicycle” is represented as proposition ‘P’.

Also, features of particular objects may be characterized through attribute lists. ‘John’ as a singular object may have the attributes ‘plays guitar’, ‘juggles’, ‘eats a lot’, ‘rides a unicycle’ etc. Thus reference to ‘John’ identifies him as the object of thought in virtue of his having certain of these attributes. So in predicate calculus

First-order logic

First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...

, if “John (F) has the property of being ‘rides a unicycle’ (x)” we may say salva veritate

Salva veritate

Salva veritate is the logical condition in virtue of which interchanging two expressions may be done without changing the truth-value of statements in which the expressions occur. The phrase occurs in two fragments from Gottfried Leibniz's General Science...

: (x)(Fx). These elements have been called semantic primitives or semantic markers/features. Each primitive may in turn form part of a propositional statement, which in turn could be represented by an abstract figure e.g. ‘P’. The primitives themselves play a crucial role in categorizing and classifying objects and concepts.

The meaningful relations between ideas and concepts expressed between and within the propositions are in part dealt with through the general laws of inference. One of the most common of these is Modus Ponens Ponendum (MPP), which is a simple inference of relation between two objects, the latter supervening on the former (P-›Q). Thus if we have two propositions (P, Q) and we assume a law of inference that relates to them both (P-›Q), then if we have P we must necessarily have Q. Relations of causation and may be expressed in this fashion, i.e. one state (P) causing (-›) another (Q)

So a purely formal characterization of the event (X) written above in natural language would be something like:

• P, Q (A)

• Q -› R (A)

• Q (A1)

• R (2,3 MPP)

• R -› S (A)

• S (4,5 MPP)