Search results
Results from the WOW.Com Content Network
In logic and deductive reasoning, an argument is sound if it is both valid in form and has no false premises. [1] Soundness has a related meaning in mathematical logic, wherein a formal system of logic is sound if and only if every well-formed formula that can be proven in the system is logically valid with respect to the logical semantics of the system.
In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, for example the amalgamation property and the joint embedding property, among others.
Another form of argument is known as modus tollens (commonly abbreviated MT). In this form, you start with the same first premise as with modus ponens. However, the second part of the premise is denied, leading to the conclusion that the first part of the premise should be denied as well.
[18] [24] But the terms "argument" and "inference" are often used interchangeably in logic. The purpose of arguments is to convince a person that something is the case by providing reasons for this belief. [25] [26] Many arguments in natural language do not explicitly state all the premises.
An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes all the key components of the argument, traditionally called the conclusion and the premises , also called contention and reasons . [ 1 ]
An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism: All men are mortal. (True) Socrates is a man. (True) Therefore, Socrates is mortal. (True) What makes this a valid argument is not that it has true premises and a true conclusion.
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.
In logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system.Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system.