Logic System

A Logic System is a formal system composed of a logic system grammar and Logic Operation Set.

• AKA: Logic Theory, Formal Logic, Logic Formalism, Logic Framework, Logic Calculus.
• Context:
  • It can be proposed by a Logic Discipline.
  • It must have a Logic System Grammar and its corresponding Logic System Language.
  • It must have a Logic Operation Set composed of Logic Operations (such as Modus Ponens and Modus Tollens).
  • It can used to formulate a Logic Argument.
  • It can range from being a Deductive Logic System to being an Inductive Logic System to being an Abductive Logic System.
• Example(s):
  • A Deductive Logic System, such as a Boolean Logic System, Propositional Logic System, or Predicate Logic System.
  • A Inductive Logic System, such as: Generative Model, or Discriminative Model.
  • a Abductive Logic System, such as ...
  • …
• Counter-Example(s):
  • a Probabilistic Formal System.
  • a Formal Language.
• See: Reasoning, Mathematical System, Logic Task.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Mathematical_logic Retrieved:2014-6-29.
  • Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. Topically, mathematical logic bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.

    Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those.

    Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems (as in reverse mathematics) rather than trying to find theories in which all of mathematics can be developed.

2009

• WordNet.
  • the branch of philosophy that analyzes inference
  • reasoned and reasonable judgment; "it made a certain kind of logic"
  • the principles that guide reasoning within a given field or situation; "economic logic requires it"; "by the logic of war"
  • the system of operations performed by a computer that underlies the machine's representation of logical operations
  • a system of reasoning

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Logic
• Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical trivium.
  • The word derives from Greek λογική (logike), fem. of λογικός (logikos), "possessed of reason, intellectual, dialectical, argumentative", from λόγος logos, "word, thought, idea, argument, account, reason, or principle".
  • Logic concerns the structure of statements and arguments, in formal systems of inference and natural language. Topics include validity, fallacies and paradoxes, reasoning using probability and arguments involving causality. Logic is also commonly used today in argumentation theory.
• Mathematical logic is a subfield of logic and mathematics. It consists both of the mathematical study of logic and the application of this study ...

• • (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Logic_(math)
• A method of human thought that involves thinking in a linear, step-by-step manner about how a problem can be solved. ...

• http://www.uky.edu/~rosdatte/phi120/glossary.htm
  • logic: the study of arguments.

• http://www.logic-classroom.info/glossary.htm
  • logic is the science of necessary inference.

• http://www.philosophy.uncc.edu/mleldrid/logic/logiglos.html
  • Logic: Logic is the study of correct reasoning. It both describes and evaluates the way in which we draw inferences. Inferences are formulated as arguments and then evaluated as to their validity and soundness. The aim is to find generally reliable (see inductive) or always reliable (see deductive) arguments.

• http://www.britannica.com/EBchecked/topic/213716/formal-logic
  • formal logic theory: the abstract study of propositions, statements, or assertively used sentences and of deductive arguments.

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