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Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [4] also used for denoting Gödel number; [5] for example “⌜G⌝” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...
A formula in first-order logic with no free variable occurrences is called a first-order sentence. These are the formulas that will have well-defined truth values under an interpretation. For example, whether a formula such as Phil(x) is true must depend on what x represents.
One property type that can be added to Databases is a Formula property. Formula properties can leverage Notion Formulas [35] code, a JavaScript-like language. Formula properties receive a row in a database as context. The language can be utilized to write code that outputs custom data based on the data and relations in the database row.
A closed formula, also ground formula or sentence, is a formula in which there are no free occurrences of any variable. If A is a formula of a first-order language in which the variables v 1, …, v n have free occurrences, then A preceded by ∀v 1 ⋯ ∀v n is a universal closure of A.
Ground formulas may be defined by syntactic recursion as follows: A ground atom is a ground formula. If φ {\displaystyle \varphi } and ψ {\displaystyle \psi } are ground formulas, then ¬ φ {\displaystyle \lnot \varphi } , φ ∨ ψ {\displaystyle \varphi \lor \psi } , and φ ∧ ψ {\displaystyle \varphi \land \psi } are ground formulas.
In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. [1] [2] The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. Literals can be divided into two types: [2] A positive literal is just an atom (e.g., ).
According to model theory, a logical system may be given interpretations which describe whether a given structure - the mapping of formulas to a particular meaning - satisfies a well-formed formula. A structure that satisfies all the axioms of the formal system is known as a model of the logical system.
Symbol Name Meaning SI unit of measure nabla dot : the divergence operator often pronounced "del dot" per meter (m −1) : nabla cross : the curl operator often pronounced "del cross"