Formal logical systems: consequence relations, proof systems, and model-theoretic semantics that define what follows from what. A logical system specifies a language, a notion of well-formed formula, and either a derivability relation (⊢) via inference rules or a satisfaction relation (⊨) via models—or both, with soundness and completeness connecting them.
The collection is organized along structural axes. Algebraic/ collects logics individuated by the variety of algebras they are complete for. Modal/ adds operators beyond truth-functional connectives. Structural/ varies which structural rules hold. Type/ tracks the structure of terms and judgments. Team/ evaluates formulas on sets of assignments rather than on single ones. Hyperintensional/ replaces the possible world with something finer, so that necessary equivalents come apart. Theories/ collects systems individuated by a non-logical signature and its axioms, with the consequence relation inherited rather than defined—a signature axis rather than an apparatus one. Metatheory/ contains results about systems. Applications/ houses systems designed for specific domains; unlike the six apparatus axes above it individuates by the domain that shaped a system's apparatus rather than by the apparatus itself, and its criteria accordingly requires both a consequence relation and that domain orientation.
Every entry answers the same seven questions in the same order, and the template is not arbitrary. Where did this come from (Origin); what structures realize it (Models); how do you write it down (Formalism); what does the notation mean (Symbols); what can you prove (Metatheory); what problems does it solve (Applies to); and where does it fail (Limitations). The order is the forcing function: a system cannot reach Limitations without having committed to Models, and cannot state Applies to without having said in Metatheory what is actually established rather than hoped for. A system that cannot answer all seven cleanly is probably not ready for an encyclopedic reference — not because the questions are hard, but because a system whose realizing structures are unclear, or whose limits no one has stated, is still being invented rather than described. Answering cleanly does not mean answering positively: an entry whose Metatheory records that nothing has been proved has answered the question, and the criteria admit such systems on the apparatus test alone.
What the collection gives is precise, citable, bounded information, quickly — what a system is, what it is called, what is known about it, and where the edge of that knowledge lies. What it does not give is instruction. It will not teach a system from scratch, walk through an implementation of a calculus, work a proof line by line, or develop the quantified extension of a propositional system. Each entry states what is established and points at the work that establishes it. The entries are references, not lessons; they tell you where to go and do not take you there.