Overview

A formal system is broadly defined as any well-defined system of abstract thought based on the model of mathematics. Euclid's Elements is often held to be the first formal system and displays the characteristic of a formal system. The entailment of the system by its logical foundation is what distinguishes a formal system from others which may have some basis in an abstract model. Often the formal system will be the basis for or even identified with a larger theory or field (e.g. Euclidean geometry) consistent with the usage in modern mathematics such as model theory. A formal system need not be mathematical as such; for example, Spinoza's Ethics imitates the form of Euclid's Elements. Each formal system has a formal language, which is composed by primitive symbols. These symbols act on certain rules of formation and are developed by inference from a set of axioms. The system thus consists of any number of formulas built up through finite combinations of the primitive symbols-combinations that are formed from the axioms in accordance with the stated rules. Formal systems in mathematics consist of the following elements: 1.A finite set of symbols (i.e. the alphabet), that can be used for constructing formulas (i.e. finite strings of symbols). 2.A grammar, which tells how well-formed formulas (abbreviated wff) are constructed out of the symbols in the alphabet. It is usually required that there be a decision procedure for deciding whether a formula is well formed or not. 3.A set of axioms or axiom schemata: each axiom must be a w.f.f. 4.A set of inference rules. A formal system is said to be recursive (i.e. effective) if the set of axioms and the set of inference rules are decidable sets or semidecidable sets, according to context. This book gives a thorough overview of The Systems of Formal Logic and is This book is designed to be a general overview of the topic and provide you with the structured knowledge to familiarize yourself with the topic at the most affordable price possible. The level of discussion is that of Wikipedia. The accuracy and knowledge is of an international viewpoint as the edited articles represent the inputs of many knowledgeable individuals and some of the most currently available general knowledge on the topic, based on the date of publication.

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The editor is an Engineer & Former Intelligence Officer for the US intelligence Community. He has authored several books, edited many books and has written numerous Technical, Classified & Unclassified papers, Articles & Essays. He has also written for an International Encyclopedia on Intelligence and Counter-Intelligence and written several award-winning software manuals that have been sold in more than a dozen countries. He has also appeared in Marquis Who's Who in the World & Who's Who in Science & Engineering and continues to edit and write.

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