What does first order mean in logic?

First-order logic is symbolized reasoning in which each sentence, or statement, is broken down into a subject and a predicate. The predicate modifies or defines the properties of the subject. In first-order logic, a predicate can only refer to a single subject.

Is first-order logic complete?

Perhaps most significantly, first-order logic is complete, and can be fully formalized (in the sense that a sentence is derivable from the axioms just in case it holds in all models). First-order logic moreover satisfies both compactness and the downward Löwenheim-Skolem property; so it has a tractable model theory.

What is the difference between zero first and second-order reactions?

A zero-order reaction proceeds at a constant rate. A first-order reaction rate depends on the concentration of one of the reactants. A second-order reaction rate is proportional to the square of the concentration of a reactant or the product of the concentration of two reactants.

Is there third-order logic?

No. It is not. In the sense that you can express every mathematical statement as a sentence of a standardized first-order language math is not based on FOL. This means that there are some mathematical statements that cannot be derived from «pure» logic simply because one doesn’t have enough expressive power.

Is FOL complete?

First order logic is complete, which means (I think) given a set of sentences A and a sentence B, then either B or ~B can be arrived at through the rules of inference being applied to A. If B is arrived at, then A implies B in every interpretation.

Is first-order logic Axiomatizable?

Standard textbooks in mathematical logic will assume an infinite supply of variables. Their axiomatization of first order logic will typically contain an axiom of the form ∀xϕ1→ϕ1[y/x] with varying qualifications on what the term y is allowed to be, along the lines of ‘y is free for x in ϕ1’.

What is the difference between propositional and first-order logic?

Propositional logic deals with simple declarative propositions, while first-order logic additionally covers predicates and quantification. A proposition is a collection of declarative statements that has either a truth value “true” or a truth value “false”.