Perceiving and observing by a sentient being (and in many non-sentient mechanisms) produce output having some relationship to the state of the world outside the observer. The characteristics of the output of the process serve as input to memory structures that store beliefs. A belief is an idea, or statement, that has one or more characteristics' values that match the values for representandums. Belief may thus be understood as a representation that is not necessarily fully justified and is not necessarily completely true, but must be true in part. A belief is an idea that is held based on some support. Thus, Swinburne has suggested that if a person believes proposition p then p must be more probable than [Hel94]. Unfortunately, this implies that if there is a proposition, one holds a belief either in the proposition or in its negation. The holding of incorrect or weak beliefs becomes problematic, as does the imposition of a logical formulation on this sort of problem.
A statement of belief contains one or more characteristics' values matching in full or in part the values for representandums. The output of a process or set of processes provides a representation of the input to the processes. We can therefore describe a percept as the set of values in this output; it is essentially the information in the output of a process about the input. A perceiving function, f(),provides a percept, f(x), about input x. Belief is thus transmitted through the hierarchy.
Knowledge has been frequently described as ``justified true belief," a belief held by an individual that is both true and for which they have some justification. Thus, for a belief to be knowledge, it must be the case that the belief is, in fact, true, and the believer must have justification for the belief. A belief that is true but for which we have no evidence cannot be described as knowledge. If there are homunculi inside computers performing operations, those who have long believed in their presence cannot be said to have had knowledge of this, since their belief, while true, has never been justified (we assume.)
It had become common to describe knowledge as ``justified true belief" when Gettier [Get63] wrote a brief article that raised a problem with this definition. As a result of Gettier's work, we can be certain that ``knowledge is not, or is not merely, justified true belief" [Dre81]. There have been several responses to Gettier's argument against accepting knowledge as being only justified true belief. One possible approach is to add a condition requiring that the grounds for believing a proposition do not include any false beliefs [Pol86], to the requirements of justification, truth, and belief. However, this addition and several other modifications that have been proposed fail to avoid counterexamples in which ``knowledge is lacking despite the believer's not inferring his belief from any false beliefs" [Pol86]. Other approaches to understanding knowledge have been proposed and supported, such as having a disposition to behave or a disposition to feel a certain way [Ack72,Hel94].
We accept here that knowledge is something like ``justified true belief." A belief is an internally accepted statement, the result of an observation or an inferential or deductive product combining observed facts about the world with reasoning processes. To understand knowledge in a way consistent with a hierarchical notion of information, it becomes necessary to understand the notions of ``truth" and ``justification" in a manner consistent with the hierarchical context.
A statement may be understood as ``true" if it exactly represents what it is describing. This is referred to as the ``correspondence" theory of truth [All93,Joh92]. This applies not only to statements but to the representation and belief. The coherence theory of truth, on the other hand, suggests that truth is essentially derived from a system. A statement is true when it is consistent with a system of accepted statements. Truth may also be viewed as a representation that is learned and that will not be altered, even given additional experiences. William James thus defined truth as the vanishing point toward which we imagine that all our temporary truths will some day converge.
The justification of a belief is based on internal considerations concerning the qualities of the function producing the belief. A belief is ``justified" if and only if the input to the function is accurately represented in the output. Consider a handheld calculator which accepts the keystrokes ``2" ``+" ``2" ``=" and then displays the digit ``4." We note that the digit displayed is not of the same form as the input, e.g., a keystroke. Instead, an accurate function takes keystrokes and produces a displayed number. If the calculator is broken and produces the digit ``3" given the above set of keystrokes, we clearly don't have knowledge that 2+2=4.Consider a different case where the calculator is broken but the above set of keystrokes produces, through erroneous subprocesses, the digit ``4" in the display. While the output is correct or ``true" and may be interpreted as a belief, it is not justified--the function is not accurate in that it does not operate as the user intends or understands the calculator to operate.
Other models of knowledge have been proposed, such as the notion that knowledge is one's ``image," what one subjectively believes to be true [Bou56]. This is close to what we have referred to as a belief, and choosing to call it ``knowledge" appears to only confuse the issue. Yet, like the more conventional philosophical idea of knowledge, it can be understood as the values in the output of a process, actually, the hierarchical series of processes that range from low level atomic processes up to sophisticated intellectual processes.
Perception and observation can be understood as conveying information about the input to certain processes (for humans, sensory processes such as seeing, hearing, smelling, etc.) The output of such a process may be understood as a belief. Such a belief may constitute knowledge about the input when the process or set of processes producing the belief operate in a manner consistent with the understanding of the process. These definitions of knowledge and belief are broader than the common language notions of the terms and less human-centered, in the case of belief, making the concepts more objective and more easily studied. We note that knowledge is information that is both true and justified. These perceptual, observational, and processing functions take as input sensory data from the real world, as well as personal beliefs and cultural biases, when producing information bearing output. This conceptual framework for understanding information provides a mechanism for understanding both the cultural influence on information, as well as the most minute phenomena studied by physicists.