In the previous notation, we quoted Article
Laws of Thought, published by Keith Devlin in his monthly column
Devlin's Angle. Well, just to mention that he, the author an overview of the main features of Stoic logic (created in the heart of the philosophical school
Stoics, circa 300 BC), which was the real starting point, together with input about Aristotelian logic (which should however be the systematization of the discipline), the contemporary rationale
mathematical logic in general and in particular propositional: "[The Stoics] perform a broadening of the Aristotelian syllogistic using five forms of inference or even hypothetical dilemmas, from which they must be able to obtain any meaningful conclusion. While Aristotelian logic was a logic of terms, Stoic logic is a propositional logic. " [Source: 6.3. Stoicism ] The logic propositional logic statements or , really arises both from the contributions of the Stoics to the field of formal logic (as opposed the latter to the logic or material theory of knowledge), and cultivating a logic based on
propositions (logical statements that associate the values \u200b\u200bof truth and falsity) and not concepts in ( true statements themselves , for example: "All men are mortal, Socrates is a man" needed to infer from them, the demonstration of another, "so therefore Socrates is mortal ") as in the case of Aristotelian logic or syllogistic . A brief look at the main branches of logic has traditionally been considered the remote origin of formal logic or syllogistic logic is classical logic developed by the philosopher Greek Aristotle (384-322 BC), although we have said before to be considered in the development of propositional logic the decisive contribution of Stoic logic. syllogistic logic or Aristotelian , while formalizing common sense, and based on natural language (and therefore not without a certain dose of ambiguity and vagueness) is to establish the truth or falsity of certain philosophical argument. Leaving the field of formalization of logical arguments based on the use of natural language, symbolic or mathematical logic starts with input about the German philosopher GW Leibniz (1646-1717), inspired in turn in the Ars Magna of Ramon Llull (1232-1316) [PDF
], trying to focus the logic from the perspective of algebra, while not actually taken into consideration until the nineteenth century, with the help of George Boole (1815-1864), logical and mathematical ; tico British and Boolean logic which gives an algebraic treatment to the propositions of traditional propositional logic. Boole's work in the field of mathematical logic would allow Claude Shannon [1
] [ 2] [3 ] developed in the 30's of XX century Bá scheme musician of "Logical machine" digital, initially based on the performance of relays that could take two positions: open or closed (binary logic associated with the operation of an electrical circuit) [
1] [2
]. Symbolic logic using symbols representing the concepts, these being interconnected by operators.
In symbolic logic that is developed from the nineteenth century must be distinguished in turn two main branches: propositional logic
the one hand, and the predicate calculus
other. propositional logic [ 1] [2 ] is concerned with establishing truth or falsity of one or more propositions, understood as properly formed sentences that can take a true or false value, being connected proposals by operators. For its part, the predicate calculus, also called predicate logic is an extension of propositional logic that takes as basis for calculating the predicate, a function that returns a value
true or false
depending on their argument. For example, the knowledge bases of
logic programming languages \u200b\u200bsuch as Prolog, are based mainly built of predicates that can take into account one or more arguments, or even other predicates to infer processes results in question. Predicate calculus allows for both separation between an object and its possible attributes, and establish relationships between objects and object classes. Moreover, the generalization of predicates is done using variables.
A step forward in the development of methods of representation knowledge inference based on the use of logical systems, particularly in the development of expert systems on the use that traditionally allowed ló GICA propositional and predicate logic, is the consideration of factors of uncertainty, using probability calculations to that effect from the theory of classical probability, in a first stage of evolution of such systems.
use of uncertainty factors in becomes essential, while many situations within the observable phenomena in the real world situations support a range much broader than just traditional dichotomy between real
and false . A union between logic and uncertainty, often referred to as fuzzy logic or fuzzy , and is the basic starting point and essential to the development of systems and applications of Artificial Intelligence (IA). The application of uncertainty factors (chance) in making decisions in situations where information is taken into account hypothetical , by expert systems, is therefore the gateway basic AI. In all cases is a very basic starting point, totally outclassed today by other approaches to addressing the issue of intelligent systems .
on the subject, and the 
