Sentence examples for closure operation from inspiring English sources

The direct/indirect precedence P total relation between operators can be inferred by applying the transitive closure operation to the P direct(n, n) matrix: P total = P direct ∪ P direct 2 ∪ ⋯ ∪ P direct i ∪ ⋯ ∪ P direct n, (2)  .

The notation and denote the closure operation and convex hull operation on set, respectively.

We adopt the convention that the empty class ∅ is c-closed for every closure operation c.

We introduce a new closure operation on natural numbers involving candelabra systems.

The conditions given earlier for C's being a closure operation can be recast as conditions definitive of a consequence relation, conditions we do not give explicitly here.

These two facts imply that the reflexive transitive closure of >sc is reduction when the tonicity of the reflexive transitive closure operation (denoted by *) is taken into account.

Closure operations as defined in the opening section are sometimes called closure operators.

Gödel started with three very simple functions, the initial functions, and two natural closure operations, composition and primitive recursion, each of which take some already defined functions and use them to define a new one.

Some authors discuss matters of logical theory placing a particular emphasis on closure operations and their systems of closed sets (sets X with C X) = X); see Pollard and Martin (1996) and references there cited.

In this case the derived closure operations Th ○ Mod (mapping S0 to Th(Mod(S0))) and Mod ○ Th (understood analogously) on S and T respectively deliver the set of first-order consequences of S0 and the set of all models verifying all the sentences verified by every M ∈ T0.

EVOMINER's increased speed is the result of an efficient phylogenetic tree-specific constant-time candidate generation scheme in the candidate generation step, and a novel fingerprinting based scheme for the downward-closure operation in the frequency counting step.