Skip to main content
-
-
2.7.1: Overview
-
First-order logic is not the only system of logic of interest: there are many extensions and variations of first-order logic.
-
-
2.7.2: Many-Sorted Logic
-
In first-order logic, variables and quantifiers range over a single domain. But it is often useful to have multiple (disjoint) domains. Many-sorted logic provides this kind of framework.
-
-
2.7.3: Second-Order logic
-
The language of second-order logic allows one to quantify not just over a domain of individuals, but over relations on that domain as well.
-
-
2.7.4: Higher-Order logic
-
Passing from first-order logic to second-order logic enabled us to talk about sets of objects in the first-order domain, within the formal language. Why stop there? For example, third-order logic should enable us to deal with sets of sets of objects, or perhaps even sets which contain both objects and sets of objects. And fourth-order logic will let us talk about sets of objects of that kind. As you may have guessed, one can iterate this idea arbitrarily.
-
-
2.7.5: Intuitionistic Logic
-
In constrast to second-order and higher-order logic, intuitionistic first-order logic represents a restriction of the classical version, intended to model a more “constructive” kind of reasoning.
-
-
2.7.6: Modal Logics
-
One obtains modal propositional logic from ordinary propositional logic by adding a box operator; which is to say, if \(A\) is a formula, so is \(\Box A\). Intuitively, \(\Box A\) asserts that \(A\) is necessarily true, or true in any possible world.
-
-
2.7.7: Other Logics
-
Recent decades have witnessed a veritable explosion of formal logics.