Sentence examples for order logic from inspiring English sources

That is, P is equal to NP iff every property expressible in second order logic is already expressible in first-order logic plus inductive definitions.

Indeed, this basic idea is familiar from standard first order logic.

Modal logic as a fragment of first order logic is made algebraic via Boolean modules.

Central algebraic notions in first order logic are ultraproducts, elementary equivalence, and elementary and pseudoelementary varieties.

The fundamental point is the same as in the move from first to second order logic.

Second order logic is a logic with variables for both individuals and properties of individuals.

It was restricted to just the universally acknowledged logical operators of first-order logic: ¬, ∧, ∨, →, ∃ and ∀.

Note that implication is not among the logical symbols of IF first-order logic.

This gives rise to second-order logic.

First-order logic requires the system to be consistent or complete, not both.

Independence friendly logic (IF logic, IF first-order logic) is an extension of first-order logic.