TAPO-Structured Description Logic for Information Behavior: Procedural and Oracle-Based Extensions

We introduce TAPO-Structured Description Logic (TAPO--DL), a formal extension of classical description logic designed to model information behavior as a structured, dynamic process. TAPO--DL extends the standard T--Box/A--Box architecture with two additional layers: a Procedural Box (P--Box), which supports concept-driven, imperative-style programs such as conditional and iterative actions, and an Oracle Box (O--Box), which formalizes controlled interaction with external information sources. While the terminological and assertional components capture static conceptual and factual knowledge, the procedural and oracle-based components enable the explicit representation of information-generating actions and external validation. We provide a unified semantic framework for TAPO--DL based on a co-generative, sheaf-theoretic interpretation, in which local informational states are modeled as sections and informational stability corresponds to the existence of coherent global structures. Within this setting, informational truth is characterized as stability under repeated agentive interaction rather than correspondence to a fixed global state. By integrating description logic with procedural dynamics, oracle-based reasoning, and sheaf-theoretic semantics, TAPO--DL offers a principled formal framework for analyzing information behavior in contexts involving interaction, uncertainty, and contextuality.