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2. Propositional formula - Wikipedia

   en.wikipedia.org/wiki/Propositional_formula

   A propositional formula may also be called a propositional expression, a sentence, or a sentential formula. A propositional formula is constructed from simple propositions, such as "five is greater than three" or propositional variables such as p and q, using connectives or logical operators such as NOT, AND, OR, or IMPLIES; for example:

3. Sentence (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Sentence_(mathematical_logic)

   Sentences without any logical connectives or quantifiers in them are known as atomic sentences; by analogy to atomic formula. 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.

4. Sentence clause structure - Wikipedia

   en.wikipedia.org/wiki/Sentence_clause_structure

   A sentence consisting of at least one dependent clause and at least two independent clauses may be called a complex-compound sentence or compound-complex sentence. Sentence 1 is an example of a simple sentence. Sentence 2 is compound because "so" is considered a coordinating conjunction in English, and sentence 3 is complex.

5. Atomic sentence - Wikipedia

   en.wikipedia.org/wiki/Atomic_sentence

   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.

6. Propositional calculus - Wikipedia

   en.wikipedia.org/wiki/Propositional_calculus

   Compound sentences are formed from simpler sentences and express relationships among the constituent sentences. [30] This is done by combining them with logical connectives : [ 30 ] [ 31 ] the main types of compound sentences are negations , conjunctions , disjunctions , implications , and biconditionals , [ 30 ] which are formed by using the ...

7. Propositional variable - Wikipedia

   en.wikipedia.org/wiki/Propositional_variable

   Given a formula X, the negation ¬X is a formula. Given two formulas X and Y, and a binary connective b (such as the logical conjunction ∧), the expression (X b Y) is a formula. (Note the parentheses.) Through this construction, all of the formulas of propositional logic can be built up from propositional variables as a basic unit.

8. Truth function - Wikipedia

   en.wikipedia.org/wiki/Truth_function

   In logic, a truth function [1] is a function that accepts truth values as input and produces a unique truth value as output. In other words: the input and output of a truth function are all truth values; a truth function will always output exactly one truth value, and inputting the same truth value(s) will always output the same truth value.

9. Well-formed formula - Wikipedia

   en.wikipedia.org/wiki/Well-formed_formula

   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.