InterlockingLogik

InterlockingLogik is a theoretical framework for modeling and analyzing interdependent logical systems. It focuses on interlocking constraints that bind the truth of multiple propositions, agents, or processes so that their validity emerges only when several conditions are simultaneously satisfied.

At its core, InterlockingLogik uses an interlock graph, where nodes represent propositions or agents and edges encode constraints such as mutual exclusion, dependency, or synchronization. The language extends classical propositional or modal logics with specialized operators that express locking relations, such as an obligation that becomes active only if a set of other propositions holds, or a safety condition that requires two events to co-occur.

Semantics are typically given by labeled transition systems or Kripke-style models augmented with interlock relations. A state satisfies an interlocking formula if the assigned truth values and the interlock constraints satisfy a defined satisfaction relation, which propagates through the network according to the locking rules.

Reasoning in InterlockingLogik involves dedicated inference rules and normal forms that expose decoupled subproblems. Certain fragments admit standard reduction to known logics, while others require constraint propagation or fixpoint computation. The complexity of satisfiability and model checking depends on the fragment; some cases are decidable in polynomial time, others are NP-complete or beyond.

Applications include safety-critical system design, such as interlock circuits and process controls, multi-agent coordination where actions must be synchronized, and architecture verification for concurrent software. The framework helps formalize how local constraints produce global consistency and can assist in detecting deadlocks or unsafe configurations.

See also: modal logic, constraint satisfaction problems, interdependent networks, deontic logic, model checking.