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.
This paper develops a refined version of TAPO-description logic for the analysis of information behavior. The framework is treated not as a single homogeneous object logic, but as a layered formalism consisting of a static descriptive layer (TBox/ABox), a procedural layer (PBox), and an oracle-sensitive layer (OBox). To make this architecture mathematically explicit, we introduce a metalevel guard-judgment layer governing procedural branching and iteration. On this basis we formulate a core inference system for TAPO-description logic, covering static TBox/ABox reasoning, guarded procedural transition in the PBox, and validated external import in the OBox. We then give a categorical semantics for the resulting framework and indicate its sheaf-theoretic refinement. The theory is illustrated by examples of information-seeking behavior, including simple search behavior and review-sensitive ordering behavior in a curry restaurant. The aim is to treat not only static knowledge representation but also hesitation, external consultation, and action-guiding update within a unified logical setting.
We investigate a new logic that extends Dynamic Epistemic Logic (DEL), by combining standard epistemic modalities for (individual and distributed) propositional knowledge with operators for (conditional) non-propositional knowledge of a number (in which an agent or a group have knowledge of the value of some variable x, conditional on some additional information). We also generalize these operators, by considering formulas that express the fact that an agent or group can (conditionally) narrow down the possible values of the variable x to at most N possibilities (for some natural number N). In order to name and compare such hypothetical values, we extend the logic further with definite descriptions based on minimization operators, denoting the least of the N possible values of x (according to some fixed order) that are considered possible by the agent or group. On this static base, we consider DEL-style extensions with dynamic modalities for general 'data-exchange events' (covering private and public propositional announcements, but also secret hacking of a private database, or public sharing of one's data via open-source repositories, etc.). In such scenarios, whole 'chunks' of information may be exchanged or modified: once access to a given source is gained, all the 'data' stored at that specific location becomes available. We give complete axiomatizations for the resulting logics, and prove their decidability and co-expressivity.
Alexandru Baltag, Sonja Smets
ILLC, University of Amsterdam · University of Amsterdam, ILLC Amsterdam, Netherlands
Description logic programs are a powerful formalism for combining rules with ontologies. The well-supported semantics for description logic programs ensures that no answer sets rely on cyclic dependencies. Most popular semantics for logic programming have this property of well-supportedness. We recognize two limitations of the current well-supported semantics for DL programs: its increased computational complexity for the consistency problem and its lack of a reduct transformation characterization. In this work, we present a new semantics which evaluates ontological atoms more strictly than the current semantics. This keeps the complexity of its consistency problem NP-complete, rather than increasing it to the second level of the polynomial hierarchy. Additionally, we identify a syntactic class of description logic programs for which our new semantics is equivalent to the current semantics. We characterize our semantics using a fixpoint operator and a reduct-based transformation. Our new semantics is a strict subset of the current well-supported semantics, so it maintains the prior notion of well-supportedness while inducing its own stricter notion. We prefer our new notion of well-supportedness due to its similarities with logic programming.