Search results
Results From The WOW.Com Content Network
In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives.A clause is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term).
The parallels axiom (P) is independent of the remaining geometry axioms (R): there are models (1) that satisfy R and P, but also models (2,3) that satisfy R, but not P.. In mathematical logic, independence is the unprovability of some specific sentence from some specific set of other sentences.
definition: is defined as metalanguage:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. The notation may occasionally be seen in physics, meaning the same as :=.
The independent clause comprises the entire trees in both instances, whereas the embedded clauses constitute arguments of the respective independent clauses: the embedded wh-clause what we want is the object argument of the predicate know; the embedded clause that he is gaining is the subject argument of the predicate is motivating. Both of ...
A way of expressing a logical formula as a conjunction of clauses, where each clause is a disjunction of literals. connected A property of a graph in which there is a path between any two vertices, or a property of a topological space in which it cannot be divided into two disjoint nonempty open sets.
An independent clause contains a subject and a predicate and makes sense by itself. Independent clauses can be joined by using a semicolon or by using a comma followed by a coordinating conjunction ( and , but , for , or , nor , so , yet , etc.).
An interpretation (or model) of a first-order formula specifies what each predicate means, and the entities that can instantiate the variables. These entities form the domain of discourse or universe, which is usually required to be a nonempty set. For example, consider the sentence "There exists x such that x is a philosopher."
Independence-friendly logic (IF logic; proposed by Jaakko Hintikka and Gabriel Sandu [] in 1989) [1] is an extension of classical first-order logic (FOL) by means of slashed quantifiers of the form (/) and (/), where is a finite set of variables.