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TAPO-Structured Description Logic for Information Behavior: Procedural and Oracle-Based Extensions
Takao Inoué
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 92%
Last extracted: 7/21/2026, 12:10:44 AM
Summary
The paper introduces TAPO-Structured Description Logic (TAPO-DL), an extension of classical description logic designed to model information behavior as a dynamic, structured process. It extends the standard T-Box/A-Box architecture with a Procedural Box (P-Box) for imperative, concept-driven programs and an Oracle Box (O-Box) for controlled interaction with external sources. The framework utilizes sheaf-theoretic semantics to interpret contexts as local informational states, where truth is defined as stability under repeated agentive interaction rather than correspondence to a fixed global state.
Entities (9)
Relation Signals (8)
TAPO-Structured Description Logic → extends → classical description logic
confidence 95% · TAPO–DL, a formal extension of classical description logic designed to model information behavior
TAPO-Structured Description Logic → includes → Procedural Box
confidence 95% · extends the standard T–Box/A–Box architecture with two additional layers: a Procedural Box (P–Box)
TAPO-Structured Description Logic → includes → Oracle Box
confidence 95% · extends the standard T–Box/A–Box architecture with two additional layers: ... an Oracle Box (O–Box)
TAPO-Structured Description Logic → uses → Sheaf-Theoretic Semantics
confidence 92% · We provide a unified semantic framework for TAPO–DL based on a co-generative, sheaf-theoretic interpretation
Oracle Box → formalizes → interaction with external information sources
confidence 90% · formalizes controlled interaction with external information sources.
Procedural Box → supports → imperative-style programs
confidence 90% · supports concept-driven, imperative-style programs such as conditional and iterative actions
Information Behavior → modeledas → co-generative process
confidence 88% · Information behavior is modeled as a co-generative interaction
Epistemic Agent → →
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Abstract
Abstract:We introduce \emph{TAPO-Structured Description Logic} (TAPO--DL), a formal extension of classical description logic designed to model \emph{information behavior} as a structured, dynamic process. TAPO--DL extends the standard T--Box/A--Box architecture with two additional layers: a \emph{Procedural Box} (P--Box), which supports concept-driven, imperative-style programs such as conditional and iterative actions, and an \emph{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.
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- Source: https://arxiv.org/abs/2602.17242v1
- Canonical: https://arxiv.org/abs/2602.17242v1
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TAPO-Structured Description Logic for Information Behavior: Procedural and Oracle-Based Extensions Takao Inoué (February 19, 2026) Abstract 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. Keywords: Information Behavior, Description Logic, TAPO-Structured Description Logic, Procedural Semantics, Oracle-Based Reasoning, Sheaf-Theoretic Semantics, Knowledge Representation. MSC2020: 03B45, 68T27, 18F20. Contents 1 Introduction 2 Signature and Concept Language 3 T–Box and A–Box 3.1 T–Box (Concept Axioms) 3.2 A–Box (Contextual Assertions) 4 Context as Sheaf Semantics 5 P–Box: A Minimal Imperative Language 5.1 Knowledge States 5.2 Guards 5.3 Program Syntax 5.4 Operational Semantics (Big-step) 6 O–Box: Oracle Interaction Rules 7 An Application to Information Behavior 7.1 Ontological Interpretation of Information 7.2 Information Behavior as a Co-Generative Process 7.3 Stability and Informational Truth 7.4 Minimal Example 8 A Sheaf-Theoretic Interpretation of Information Behavior 8.1 Informational Domains as Sites 8.2 Epistemic Agents as Section-Generating Structures 8.3 Sheaf Condition and Informational Coherence 8.4 Manifestation as Stabilized Global Sections 8.5 Minimal Example: Distributed Sensing 9 Conclusion and the Ruture Work 1 Introduction Classical description logics (DLs) organize knowledge into a T–Box (concept axioms) and an A–Box (individual assertions). This architecture is well–suited for static knowledge representation, but it does not directly model key phenomena of information behavior: iterative search, conditional actions based on partial information, and controlled interaction with external resources. This paper introduces TAPO-Structured Description Logic (for short, TAPO–DL), extending the standard T/A–Box structure with two additional components: • a P–Box, which is not a set of inference rules but a programmable layer where one can write concept–driven procedures using imperative constructs (e.g., if–then and while); • an O–Box, specifying admissible oracle interactions through which the system may incorporate externally obtained information. The four components—Terminological, Assertional, Procedural, and Oracle-based—are integrated via a sheaf–theoretic semantics of contextual information. 2 Signature and Concept Language Let the signature be Σ=(NC,NR,NI,), =(N_C,N_R,N_I,U), where NCN_C is a set of concept names, NRN_R a set of role names, NIN_I a set of individual names, and U a collection of contextual domains (opens, situations, or information states). Concept expressions are generated by the standard ALC grammar: C::=⊤∣⊥∣A∣C⊓D∣C⊔D∣¬C∣∃r.C∣∀r.C,C::= A C D C D C ∃ r.C ∀ r.C, with A∈NCA∈ N_C and r∈NRr∈ N_R. 3 T–Box and A–Box 3.1 T–Box (Concept Axioms) A T–Box T is a finite set of concept inclusions C⊑D.C D. These axioms are interpreted globally and are independent of contextual annotations. 3.2 A–Box (Contextual Assertions) An A–Box A consists of assertions of the form a:C@U(U∈),a:C@U (U ), (and role assertions (a,b):r@U(a,b):r@U). The annotation @U@U indicates that the assertion holds with respect to the contextual domain U. Intuitively, C@UC@U denotes the localization of the concept C to the information available in U. 4 Context as Sheaf Semantics We interpret contexts as objects of a site (or, for simplicity, as opens of a topological space). Concepts are interpreted as sheaves over the partially ordered set (,⊆)(U, ). For each concept C and context U, the interpretation C(U)C(U) denotes the set of individuals satisfying C under the information available in U. If V⊆UV U, there is a restriction map ρUV:C(U)→C(V), _UV:C(U)→ C(V), ensuring contextual monotonicity: a:C@U⇒a:C@V(V⊆U).a:C@U a:C@V (V U). 5 P–Box: A Minimal Imperative Language 5.1 Knowledge States A knowledge state is a pair Σ=(,), =( T, A), where T is a fixed T–Box and A is the current A–Box. 5.2 Guards Guards (conditions) are given by φ::=⊤∣⊥∣α∣¬φ∣(φ∧φ), ::= α ( ), where atomic guards are α::=a:C@U∣(a,b):r@U∣(C⊑D).α::=a:C@U (a,b):r@U (C D). The satisfaction relation Σ⊧φ is defined as follows: • (,)⊧a:C@U( T, A) a:C@U iff a:C@U∈a:C@U∈ A; • (,)⊧(a,b):r@U( T, A) (a,b):r@U iff (a,b):r@U∈(a,b):r@U∈ A; • (,)⊧(C⊑D)( T, A) (C D) iff ⊢DLC⊑D T _DLC D; with Boolean connectives interpreted classically. 5.3 Program Syntax The P–Box language 0P_0 consists of programs generated by P::=∣β∣β∣P;P∣φP∣φP,P::=skip \;β \;β P;P \; \;then\;P\;else\;P \; \;do\;P, where β ranges over A–Box assertions (either a:C@Ua:C@U or (a,b):r@U(a,b):r@U). 5.4 Operational Semantics (Big-step) We write ⟨P,Σ⟩⇓Σ′ P, for the big–step evaluation relation. The core rules are standard. Basic commands. ⟨,(,)⟩ ,( T, A) ⇓(,), ( T, A), ⟨β,(,)⟩ \;β,( T, A) ⇓(,∪β), ( T, A∪\β\), ⟨β,(,)⟩ \;β,( T, A) ⇓(,∖β). ( T, A \β\). Sequencing. ⟨P1,Σ⟩⇓Σ1⟨P2,Σ1⟩⇓Σ2⟨P1;P2,Σ⟩⇓Σ2 P_1, _1 P_2, _1 _2 P_1;P_2, _2 Conditionals. Σ⊧φ⟨P1,Σ⟩⇓Σ′⟨φP1P2,Σ⟩⇓Σ′Σ⊧̸φ⟨P2,Σ⟩⇓Σ′⟨φP1P2,Σ⟩⇓Σ′ P_1, \; \;then\;P_1\;else\;P_2, P_2, \; \;then\;P_1\;else\;P_2, The intended meaning of the first inference rule (left rule) is as follows. • The current state Σ satisfies the condition φ , that is, Σ⊧φ . • Executing the procedure P1P_1 from the state Σ evaluates to the resulting state Σ′ , written as ⟨P1,Σ⟩⇓Σ′ P_1, . Under these assumptions, the execution of the conditional statement φP1P2if\; \;then\;P_1\;else\;P_2 from the state Σ also evaluates to the state Σ′ . In this case, the else branch P2P_2 is not executed. The intended meaning of the second inference rule (right rule) is as follows. • The current state Σ does not satisfy the condition φ , that is, Σ⊧̸φ . • Executing the procedure P2P_2 from the state Σ evaluates to the resulting state Σ′ , written as ⟨P2,Σ⟩⇓Σ′ P_2, . Under these assumptions, the execution of the conditional statement φP1P2if\; \;then\;P_1\;else\;P_2 from the state Σ evaluates to the state Σ′ . In this case, the then branch P1P_1 is not executed. While. Σ⊧̸φ⟨φP,Σ⟩⇓Σ⊧φ⟨P,Σ⟩⇓Σ1⟨φP,Σ1⟩⇓Σ2⟨φP,Σ⟩⇓Σ2 \; \;do\;P, P, _1 \; \;do\;P, _1 _2 \; \;do\;P, _2 The intended meaning of the first inference rule for the while construct is as follows. • The current state Σ does not satisfy the condition φ , that is, Σ⊧̸φ . Under this assumption, the execution of the loop φPwhile\; \;do\;P from the state Σ terminates immediately and evaluates to the same state Σ . In this case, the loop body P is not executed. The intended meaning of the second inference rule for the while construct is as follows. • The current state Σ satisfies the condition φ , that is, Σ⊧φ . • Executing the loop body P from the state Σ evaluates to an intermediate state Σ1 _1, written as ⟨P,Σ⟩⇓Σ1 P, _1. • Executing the loop again from the updated state Σ1 _1 evaluates to the final state Σ′ , written as ⟨φP,Σ1⟩⇓Σ′ \; \;do\;P, _1 . Under these assumptions, the execution of the loop φPwhile\; \;do\;P from the initial state Σ evaluates to the state Σ′ . The while construct is therefore generally partial (non–termination is possible), matching the open–ended nature of iterative information behavior. 6 O–Box: Oracle Interaction Rules The O–Box specifies admissible interactions with external information sources (oracles). An oracle call may introduce new contextual assertions into the A–Box, representing openness of the system to the environment. Formally, an O–Box can be treated as a relation ⟦⟧⊆(×)×(×), O ( T× A)×( T× A), whose transitions are externally justified (e.g., by an API response, a human judgment, or a sensor reading), rather than internally derivable. 7 An Application to Information Behavior In this section, we present a simple application of the co-generative ontological framework to the analysis of information behavior. Here, information behavior refers to the structured actions by which an epistemic agent selects, interprets, and stabilizes informational entities from a latent informational domain. 7.1 Ontological Interpretation of Information Within the present axiomatization, informational entities are not assumed to exist as fully determined objects a priori. Instead, they are treated as elements of the domain of structural potential, which become manifest through interaction with epistemic agents. Let P denote the domain of structural potential, ℰE the class of epistemic agents, and ℳM the domain of manifested existents, as introduced in previous sections. An informational object i initially belongs to P as a latent structure, such as an uninterpreted signal, data stream, or symbolic pattern. 7.2 Information Behavior as a Co-Generative Process An information behavior is modeled as a co-generative interaction (e,i)⟼m,(e,i) m, where e∈ℰe is an epistemic agent, i∈i is a latent informational structure, and m∈ℳm is a manifested informational object. This process does not merely reveal pre-existing information, but actively constitutes the informational object as meaningful for the agent. Different agents, or different internal states of the same agent, may generate distinct manifested informational objects from the same latent structure. Remark. This interpretation aligns with the view that information is not ontologically primitive, but emerges through structured interaction. The same data may remain informationally nonexistent for one agent, while becoming a stable informational entity for another. For the author’s co-generative theory of existece, refer to Inoué [8]. 7.3 Stability and Informational Truth According to the co-generative axioms, truth is interpreted as a stability phenomenon. In the context of information behavior, an informational object m∈ℳm is said to be informationally stable if repeated interactions between e and i consistently regenerate m. Such stability corresponds to the agent’s recognition of the information as reliable, meaningful, or true. This allows informational truth to be agent-relative without collapsing into arbitrariness, since stability is constrained by the structure of P. 7.4 Minimal Example As a minimal example, consider a sensor system acting as an epistemic agent. Raw sensor signals exist initially as latent structures in P. Through interpretive protocols implemented by the agent, certain signal patterns are repeatedly stabilized as specific informational objects, such as “obstacle detected” or “temperature exceeds threshold”. Within the present framework, these informational objects exist precisely insofar as they are co-generatively stabilized through agent–structure interaction. 8 A Sheaf-Theoretic Interpretation of Information Behavior In this section, we strengthen the interpretation of information behavior by making explicit use of sheaf-theoretic structures. The central claim is that information behavior is naturally modeled as the generation and stabilization of local sections, together with their coherent gluing into global informational entities. 8.1 Informational Domains as Sites Let (,J)(C,J) be a site, where objects of C represent informational contexts (e.g. temporal windows, sensor modalities, linguistic perspectives), and J is a Grothendieck topology encoding admissible coverings. We interpret informational potential as a presheaf ℐ:op→,I:C^op , where ℐ(U)I(U) is the set of latent informational structures available in context U. 8.2 Epistemic Agents as Section-Generating Structures An epistemic agent e∈ℰe is modeled as a structure that assigns, to each context U∈U , a (possibly partial) selection of sections sU∈ℐ(U),s_U (U), subject to interpretive constraints internal to the agent. Information behavior is thus the process by which an agent extracts, refines, or stabilizes local sections from the presheaf ℐI. 8.3 Sheaf Condition and Informational Coherence The sheaf condition plays a central ontological role. Given a covering Ui→U∈J\U_i→ U\∈ J, a family of local informational sections sUi∈ℐ(Ui)\s_U_i (U_i)\ represents distributed informational behavior. If these sections agree on overlaps, they admit a unique gluing sU∈ℐ(U),s_U (U), which we interpret as the emergence of a coherent informational object at the global level. This gluing operation corresponds precisely to the transition from fragmented, context-dependent information to stabilized, meaningful informational existence. 8.4 Manifestation as Stabilized Global Sections Within the co-generative ontology, manifested informational entities correspond to globally stabilized sections of ℐI. That is, an informational object exists in ℳM if and only if it arises as a glued section that remains stable under further contextual refinements. Remark. This interpretation explains why informational existence is neither purely subjective nor purely objective. Local sections depend on agents and contexts, while global coherence is constrained by the topology J. 8.5 Minimal Example: Distributed Sensing Consider a distributed sensor network. Each sensor modality or time slice defines a context U∈U , with raw sensor readings forming local sections in ℐ(U)I(U). Information behavior consists in extracting these local sections and verifying their compatibility across overlaps. When coherence is achieved, a global section emerges, corresponding to an informational object such as “an obstacle is present.” In this framework, informational truth is identified with the stability of glued sections under refinement, rather than with correspondence to a pre-given global state. 9 Conclusion and the Ruture Work TAPO–DL extends description logic beyond static representation by introducing a programmable procedural layer (P–Box) and explicit oracle interaction (O–Box). In the future, we hope to develop TAPO-DL in a more sheaf-theoretic manner (cf. Inoué [9]). References [1] F. Baader et al., The Description Logic Handbook, Cambridge University Press, 2003. [2] T. D. Wilson, Models in information behaviour research, Journal of Documentation, 1999. [3] D. O. Case and L. M. Given, Looking for Information, Emerald, 2016. [4] C. C. Kuhlthau, Inside the search process, JASIS, 1991. [5] S. Mac Lane and I. Moerdijk, Sheaves in Geometry and Logic, Springer, 1992. [6] Takao Inoué, On the TBox-derivation of “Murderer is included in Human” in certain description logic T2⊧Murderer⊑HumanT_2 , and more, ResearchGate preprint, 2025. https://w.researchgate.net/publication/393475729 [7] Takao Inoué, On Brain as a Mathematical Manifold: Neural Manifolds, Sheaf Semantics, and Leibnizian Harmony, arXiv:2601.15320, 2026. [8] Takao Inoué, On the Co-Generative Theory of Existence Derived from My Definitions of Existence. Forthcoming. [9] Takao Inoué, Lectures on TAPO-Structured Description Logic. Forthcomming. (The title is temporal.) [10] K. Kaneiwa, Description Logic and Web Ontology Language (in Japanese), Ohm-sya, Tokyo, 2009. [11] K. Kaneiwa, Semantic Web and dscription logic (in Japanese), pdf slide, p. 46. http://w.sw.cei.uec.ac.jp/kaneiwa/SemWeb.pdf Takao Inoué Faculty of Informatics Yamato University Katayama-cho 2-5-1, Suita, Osaka, 564-0082, Japan inoue.takao@yamato-u.ac.jp (Personal) takaoapple@gmail.com (I prefer my personal mail)