LOGIC TYPES:
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		    By: Jan Lubek, PHD

Roughly speaking, logic is the study of prescriptive 
systems of reasoning, that is, systems proposed 
as guides for how people (as well, perhaps, 
as other intelligent beings/machines/systems) 
ought to reason. Logic says which forms of 
inference are valid and which are not. 
Traditionally, logic is studied as a branch of philosophy, 
but it can also be considered a branch of mathematics. 
Logic assumes that something can not be both true and not true
but I digress, there are exceptions to every rule..

Modal logic is a form of logic which deals with sentences/statements that 
are qualified by modalities such as possibly, necessarily,
contingently, actually, can, could, might, etc. 
Unlike more traditional forms of first-order logic, 
which can only work with assertoric sentences/statements 
(such as "Socrates is mortal," "This dog is a terrier," 
"All cats are reptiles," etc.), modal logic 
also deals with the logical relationships 
between problematic statements, such as 
"It's possible that it will rain on Thursday" 
or "I can choose to go to the movies tomorrow," 
and apodictic statements like "Every planet must 
have an orbit in the form of a conic section" or 
"if you add 2 and 2, the answer is necessarily 4." 
	The basic modal operators are usually given to be possibility, 
actuality, necessity, and contingency. A sentence is said to be 
actual if it is true; it is said to be possible if it might be 
true (whether it is actually true or actually false). 
A necessary statement is one which could not possibly 
be false; by contrast, a contingent statement is one 
that might be true and also might be false. 
(This is not the same, of course, as saying that it is a statement which might 
be both true and false; there are no statements of that sort) 

Informal (inductive) logic is the field of philosophy that attempts to 
describe the logic of natural language arguments that occur 
in for example, legal pleadings and newspaper opinion pieces. 
The treatment is necessarily less analytical than formal logic. 

Formal logic is a set of rules for making deductions that seem 
self evident. Syllogisms like the following occur in every day conversation: 

	All humans are mortal. 
	Socrates is a human. 
	Therefore Socrates is mortal. 

Mathematical logic formalizes such deductions with rules precise 
enough to program a computer to decide if an argument is valid. 

Dynamic logic, commonly called fuzzy logic (used in mathematics) 
is a system by which value states may contain the added property 
of degrees in relation to other known or unknown values. 
The concept of "degrees of belief" in dynamic logic is 
similar to that found in the Bayesian school of statistics. 
Fuzzy logic establishes a matrix (place where something is embedded, originates)
relationship between known factors. 
Fuzzy logic is a way of dealing with uncertain information (partial truth) 
and variables that do not permit simple yes/no categorisations (e.g. colour)
Aka in Latin: "exemplum gratii."
Fuzzy logic can be used to make decisions where uncertainty occurs. 
Fuzzy logic is the process of reaching conclusions based on information 
and facts that are not 100 percent certain. 
	As an analogy, in nature there are far more shades of gray than 
black or white. These represent an important concept that says there 
are values not black nor white. Taking this further, 
just like in the Platonic ideal... everything is colored to some degree 
by the mere presence of the other. 
	The exception to this is the need for the analogy of direct opposites, 
which is what Binary logic is essential for. Dynamic logic attempts 
to transcend the limitations of a binary system 
(Unlike the decimal system, only two digits 0, 1 suffice to 
represent a number in the binary system. The binary system 
plays a crucial role in computer science and technology)
by allowing distinct values to have the possibility of degrees, 
while still maintaining the necessary 'switch' 
for performing computing functions. 

		Terms:

Modalities-
The classification of logical propositions according to their asserting or 
denying the possibility, impossibility, contingency, or necessity 
of their content.
-One of the main avenues of sensation (aas vision).

Bayesian School-
A method of combining the likelihood ratio with additional information 
to produce an overall estimate of the strength of a piece 
of evidence, named after the Reverent Bayes. 

Platonic Idealism (Ideal) -
The theory that the substantive reality around us is only a reflection of a
higher truth. That truth Plato argues is Abstraction. A particular tree, with
a branch or two missing, possibly alive or not and names of two people
carved in its bark is distinct from the concept of a untouched tree.
A tree is the ideal that each of us holds that allows us to identify
the imperfect reflections of trees (world) around us.