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This is a list of mathematical logic topics. For traditional syllogistic logic, see the list of topics in logic . See also the list of computability and complexity topics for more theory of algorithms .
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language .
Mathematical logic is the study of formal logic within mathematics. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. Mathematical logic is divided into four parts: Model theory; Proof theory; Recursion theory, also known as computability theory ...
Logic is often seen as the study of the laws of thought, correct reasoning, valid inference, or logical truth. It is a formal science that investigates how conclusions follow from premises in a topic-neutral manner, i.e. independent of the specific subject matter
For this reason, it neglects many topics of philosophical importance not relevant to mathematics, like the difference between necessity and possibility, between obligation and permission, or between past, present, and future. [5] These and similar topics are given a logical treatment in the different philosophical logics extending classical logic.
A logic that extends first-order logic to allow for more nuanced expressions of quantifier scope and dependence, particularly in contexts of game-theoretical semantics. independent Referring to a pair of propositions that are not contrary , subcontrary , contradictory , logically equivalent , or implied one by the other (either the first by the ...
Language, Proof and Logic is an educational software package, devised and written by Jon Barwise and John Etchemendy, geared to teaching formal logic through the use of a tight integration between a textbook (same name as the package) and four software programs, where three of them are logic related (Boole, Fitch and Tarski's World) and the other (Submit) is an internet-based grading service.
Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. [1] Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths.