Sign Usage

As in the case of real-time systems, where we distinguish those systems from non-real-time systems by defining an operational criterion as 'observe a deadline for each occurring event', we have to define the concept of 'sign usage' in a way which allows a decision whether a systems does use a sign 'appropriately' or not. This definition of sign usage must be completely independent from the structure of the acting system.

Therefore we need a semiotic framework as a conceptual paradigm which includes as elements distinguishable systems (SYS) in an environment (ENV) where we can identify 'sign material (SM)' (or 'simple expressions (EXP)') which can be 'used' in certain 'situations (SIT)' to 'refer' in 'empirical cases' to some 'properties of the situation (PROP)', which can be identified by this usage as the 'meaning' of the sign material. Any identifiable sign material which can in this sense be related to some meaning is called a 'sign'. Combinations of signs can also be understood as 'meaningful expressions'. We have to presuppose some minimal perception of sign material and characterizing properties by the sign user as well as a minimal response either of expressions or of actions.

In case of learning systems we have introduced the paradigm of task learning: A task is a set of distinguishable states with at least one start and one goal state and at least one minimal solution path.

In the case of sign usage we can define a simple sign-learning task as follows:

Learning the Expression:

  1. The system can perceive an object (OBJ) as a characteristic set of properties (PROP). Within a certain time window (t,t') the system can also perceive some sign material (SM) shortly before, simultaneously, or shortly after the perception of the object. There can be other perceptions than the SM or the O.
  2. The systems responds with some sign material.
  3. If the response is 'similar enough' to the perceived SM, then the systems perceives some reward, otherwise not.
  4. This cycle repeats as often as the system is 'nearby' the object.

Showing the Object:

  1. After the system has 'learned' the right 'response' to the perception it can perceive again an already learned expression.
  2. If the system responds by moving to the object which should not be present while perceiving the expression, the system receives some reward; if it does not respond in this way, it receives no reward.
  3. This cycle repeats as often as the system is 'away' from an object.

Within this simple learning paradigm the system can learn many expression for many objects as well as it can 'translate' an expression into 'appropriate actions' by moving to the object 'designated'.13.2

As stated above all these definitions should be completely independent of special properties of the internal structure of a system. Nevertheless one has to make minimal assumptions related to the participating system as sign user: as a standard input-output system it has to have minimal perceptions and minimal responses. The perceptions have to include all those properties which define the 'objects' of the meaning relations; the responses have to include all those kinds of actions which are necessary to demonstrate an 'appropriate usage' of a sign. The internal states must be able to represent the characterizing perceptions as well as the related objects, both as cognitive entities.Furthermore must the system be able to establish a meaning relation between the cognitive representation of a perception of an expression as well as the cognitve representation of an object.

E.g. the sign material $ 'apple' \in SM$ relates in the English language usually to a certain 'set of properties' (shape, colors, taste,...) which we know from everyday observations. The meaning relation MEANING('apple', 'apple-properties') as such is not given as an observable object. It is only 'given' as a 'knowable relation' between cognitive representations cogn('apple') of the sign material 'apple' and the cognitive representations cogn('apple-properties') of the set of apple-characterizing properties 'apple-properties'.

Furthermore must the system be able to process these cognitive entities in a way that the system can fulfill the above described learning tasks.

Before we continue with more technical details of systems which are using signs we give here a short account of the Saussurian sign concept.

Gerd Doeben-Henisch 2013-01-14