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Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.
In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, [1] or a sentential formula.
In this way, the truth value of the compound sentence is defined as a certain truth function of the truth values of the simpler sentences. The connectives are usually taken to be logical constants , meaning that the meaning of the connectives is always the same, independent of what interpretations are given to the other symbols in a formula.
Propositional logic, as currently studied in universities, is a specification of a standard of logical consequence in which only the meanings of propositional connectives are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.
A sentence is a wff in which any variables are bound. An atomic sentence is an atomic formula containing no variables. It follows that an atomic sentence contains no logical connectives, variables, or quantifiers. A sentence consisting of one or more sentences and a logical connective is a compound (or molecular) sentence.
Compound interest can help turbocharge your savings and investments or quickly lead to an unruly balance, stuck in a cycle of debt. Learn more about what compound interest is and how it works.
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.
The body of an Indian journalist who had reported on alleged corruption in the country has been found in a septic tank in Chhattisgarh state. Mukesh Chandrakar, 32, went missing on New Year's Day ...
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