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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., ).
In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs.
A clause is a disjunction of literals (or a single literal). A clause is called a Horn clause if it contains at most one positive literal. A formula is in conjunctive normal form (CNF) if it is a conjunction of clauses (or a single clause). For example, x 1 is a positive literal, ¬x 2 is a negative literal, and x 1 ∨ ¬x 2 is a clause.
Formulas in logic are typically built up recursively from some propositional variables, some number of logical connectives, and some logical quantifiers.Propositional variables are the atomic formulas of propositional logic, and are often denoted using capital roman letters such as , and .
The consensus or consensus term of two conjunctive terms of a disjunction is defined when one term contains the literal and the other the literal ¯, an opposition. The consensus is the conjunction of the two terms, omitting both a {\displaystyle a} and a ¯ {\displaystyle {\bar {a}}} , and repeated literals.
ALF was designed to be genuine integration of both programming paradigms, and thus any functional expression can be used in a goal literal and arbitrary predicates can occur in conditions of equations. ALF's operational semantics is based on the resolution rule to solve literals and narrowing to evaluate functional expressions. To reduce the ...
The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" [4] 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)).
This is a list of equations, by Wikipedia page under appropriate bands of their field. Eponymous equations The following equations are named after researchers who ...