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In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition , something that must be true or false.
Expressions are commonly distinguished from formulas: expressions are a kind of mathematical object, whereas formulas are statements about mathematical objects. [2] This is analogous to natural language , where a noun phrase refers to an object, and a whole sentence refers to a fact .
Mathematical logic is the study ... share the common property of considering only expressions in a fixed ... It says that a set of sentences has a model if and only ...
Terms, informally, are expressions that represent objects from the domain of discourse. Any variable is a term. Any constant symbol from the signature is a term; an expression of the form f(t 1,...,t n), where f is an n-ary function symbol, and t 1,...,t n are terms, is again a term. The next step is to define the atomic formulas.
First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all men are mortal", in first-order logic one can have expressions in the form "for all x, if x is a man, then x is mortal"; where "for all x" is a quantifier, x is a variable, and "...
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
Evaluation of a propositional formula begins with assignment of a truth value to each variable. Because each variable represents a simple sentence, the truth values are being applied to the "truth" or "falsity" of these simple sentences. Truth values in rhetoric, philosophy and mathematics. The truth values are only two: { TRUTH "T", FALSITY "F" }.
Consider the formal sentence . For some natural number , =.. This is a single statement using existential quantification. It is roughly analogous to the informal sentence "Either =, or =, or =, or... and so on," but more precise, because it doesn't need us to infer the meaning of the phrase "and so on."