In logic, the form of an argument is **valid** precisely if it cannot lead from true premises to a false conclusion. An argument is said to be valid if, in every model in which all premises are true, the conclusion is true. For example: "All A are B; some A are C; therefore some B are C" is a valid form. Logic, from Classical Greek Î»ÏŒÎ³Î¿Ï‚ (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
In logic, the argument form or test form of an argument results from replacing the different words, or sentences, that make up the argument with letters, along the lines of algebra; the letters represent logical variables. ...
In logic, an argument is an attempt to demonstrate the truth of an assertion called a conclusion, based on the truth of a set of assertions called premises. ...
Look up Premise in Wiktionary, the free dictionary Premise (from the Latin praemisus, meaning placed in front) can refer to: A premise (also premiss in British usage) is a statement presumed true within the context of a discourse, especially of a logical argument. ...
Look up Premise in Wiktionary, the free dictionary Premise (from the Latin praemisus, meaning placed in front) can refer to: A premise (also premiss in British usage) is a statement presumed true within the context of a discourse, especially of a logical argument. ...
A conclusion can have various specific meanings depending on the context. ...
A formula of logic is said to be valid if it is true under every interpretation (also called structure or model). See also model theory or mathematical logic. In logic, WFF is an abbreviation for well-formed formula. ...
In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the models which underlie mathematical systems. ...
Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ...
A tautology, or tautologous formula, is *truth functionally* valid. Not all valid formulas of quantificational logic are tautologies. See also truth table. Tautology refers to a use of redundant language in speech or writing, or, put simply, saying the same thing twice. Within the study of logic, a tautology is a statement that is true by its own definition. ...
Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ...
## Example
Consider the following argument form in which the letters P, Q, and A represent unanalyzed or uninterpreted sentences. - All P are Q
- A is P
- Therefore, A is Q
The validity of an actual argument can be determined by translating it into an argument form, and then analyzing the argument form for validity. (The argument form above is valid; see syllogism.) A syllogism (Greek: ÏƒÏ…Î»Î»Î¿Î³Î¹ÏƒÎ¼ÏŒÏ‚ â€” conclusion, inference), more correctly a categorical syllogism, is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises). ...
- If (all P are Q) and (A is P), then (A is Q).
## See also Look up **Validity** in Wiktionary, the free dictionary. |