S4

S4 is an alphanumeric label used in several fields, including mathematics, logic, computing, and transportation. It does not refer to a single entity but to multiple distinct concepts that share the designation.

In logic, S4 is a modal system that extends the basic modal logic K with the axioms T and 4. T states that if something is necessary, then it is true; 4 states that if something is necessary, then it is necessarily true. Semantics use reflexive and transitive Kripke frames. It is used in philosophy and computer science for reasoning about modality and time.

In mathematics, S^4 denotes the four-dimensional sphere, the set of unit vectors in five-dimensional Euclidean space. It is a compact, simply connected 4-manifold, playing a role in topology and geometry.

In consumer electronics, the Samsung Galaxy S4 is a smartphone released in 2013 as part of Samsung's Galaxy S line. It featured a 5-inch display and a 13-megapixel camera, representing a flagship step in early modern smartphones.

In automobiles, the Audi S4 is the performance variant of the A4, introduced in the late 1990s. It offers higher power, sport-tuned suspension, and distinctive styling across several generations.

In enterprise software, SAP S/4HANA, abbreviated S4 or S/4HANA, is SAP's ERP suite built on the HANA in-memory database. It provides real-time analytics and a simplified data model for on-premises or cloud deployments.