Logicsuch

Logicsuch is a term used in speculative discussions to designate a family of logical formalisms intended to capture the semantics of the phrase "such that" as it appears in logic and natural language. The central idea is to provide a unified account of how a base condition and a qualifying constraint interact within a single expression. In logicsuch, a typical construct takes a form such as φ such that ψ, where φ specifies a primary condition or class and ψ imposes a secondary constraint that may depend on the same domain or on related domains. The framework treats such constructs as enriched predicates that can be analyzed with standard tools from first-order, modal, or description logics, possibly augmented with a specialized satisfaction relation.

Semantics are usually given by relational or possible-world models. A model M satisfies φ such that ψ with an assignment a if M satisfies φ under a and, in the same context, the constraint ψ holds for the chosen objects under a. This allows logicsuch to express restricted quantification, conditional selection, and cross-domain constraints such as those encountered in database queries or linguistic generalizations. The approach generalizes set-builder notation {x | φ(x) ∧ ψ(x)} and can be extended to support modalities, temporal operators, or type-theoretic features.

Relation to existing logics: logicsuch is intended as a bridging framework that can be instantiated in variants paralleling first-order logic, modal logic, description logics, or constraint programming. Potential applications include natural language semantics, formal ontology design, and expressive query languages.

Status: The term logicsuch is not widely standardized; described mainly in speculative discussions. Ongoing work examines its expressivity, decision procedures, and computational costs, as well as its interoperability with existing logical systems.