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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.
A formal expression is a kind of string of symbols, created by the same production rules as standard expressions, however, they are used without regard to the meaning of the expression. In this way, two formal expressions are considered equal only if they are syntactically equal, that is, if they are the exact same expression.
Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [3] also used for denoting Gödel number; [4] for example “āGā” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...
The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" [3] It breaks a simple sentence down into two parts (i) its subject (the object (singular or plural) of discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)).
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
Expression (linguistics), a word, phrase, or sentence; Expression (mathematics), Symbolic description of a mathematical object; Fixed expression, a form of words with a specific meaning; Idiom, a type of fixed expression; Metaphorical expression, a particular word, phrase, or form of words that has a different meaning than its literal form
This generates sentences such as "the cat eats the bat", "a bat eats the cat". One can generate all of the valid expressions in the language generated by this grammar at a Prolog interpreter by typing sentence(X,[]). Similarly, one can test whether a sentence is valid in the language by typing something like sentence([the,bat,eats,the,bat],[]).
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