Contextlogica

Contextlogica is a formal framework for representing and reasoning with context-dependent information within logic and computation. It treats context as a first-class object that can influence the meaning of propositions, the validity of inferences, and the behavior of agents operating in a shared information space.

In a typical contextlogica system, contexts are structured entities such as labels or states, and formulas are annotated with context information. Expressions may include standard logical formulas and context operators that specify where a formula is true or how contexts relate (for example, an operator [c]φ meaning 'φ holds in context c'). Context updates describe how the current context can change due to events, actions, or new information.

Semantics extend classical models with a layer for contexts. Models may use Kripke-like structures augmented with a context transition relation or with a context algebra that composes and refines contexts. Truth conditions depend on the active context and on how contexts combine or evolve.

Reasoning in contextlogica involves contextual entailment and update-aware deduction. Inference rules respect the boundaries imposed by contexts and aim to preserve truth under permissible context extensions or reductions.

Applications of contextlogica span natural language interpretation, where context determines truth conditions; knowledge integration from heterogeneous sources; multi-agent systems that negotiate shared context; and software verification for context-specific properties.

Contextlogica draws on ideas from dynamic and modal logics, contextualized semantics, and context-aware computing. It remains an area of theoretical development with ongoing work on standard syntax, semantics, and tool support.