Multi-Perspective Reasoning in Knowledge Representation:
An Introduction to Standpoint Logic
Multi-Perspective Reasoning in Knowledge Representation:
An Introduction to Standpoint Logic
This course introduces students to Standpoint Logics, a novel family of lightweight multi-modal logics designed to represent and reason about knowledge originating from multiple, potentially conflicting perspectives. Many contemporary AI tasks, from ontology engineering to data integration and multi-agent reasoning, require handling context-dependent information without enforcing unification. Standpoint Logic provides a principled and computationally well-behaved framework for this purpose, extending propositional, first-order, and description logics with explicit standpoint-indexed operators and standpoint refinement relations. Across four sessions, students will learn the syntax, and semantics of propositional Standpoint Logic, its first-order extension, and Standpoint Description Logics for ontological modeling. They will also understand what are the main reasoning tasks, algorithms and complexity results in the area.
Instructors: Tim S. Lyon & Hannes Straß
(Acknowledgement: This course was planned jointly with Lucía Gómez Álvarez, whose foundational work on Standpoint Logic underpins this course.)
Participants should have basic familiarity with propositional and first-order logic. Background in modal or description logics, or in proof systems such as tableaux or sequents, is helpful but not required. The content of the course can be learned from a variety of publications, which are listed below.
Lecture 1: [Lecture 1: Video]
Description. We motivate standpoint logic via the knowledge integration problem in KR, introduce the syntax and semantics of propositional standpoint logic, and begin developing the proof theory by defining nested sequents and their formula interpretation.
Lecture 2: [Lecture 2: Video]
Description. We present the nested sequent calculus NS(V) for propositional standpoint logic, establish its soundness, and show how proof search yields a coNP decision procedure with counter-model extraction. We then extend the framework to first-order standpoint logic and identify the sentential fragment, which enjoys a small model property.
Lecture 3: [Lecture 3: Video]
Description. We move beyond the sentential fragment to the monodic setting of standpoint description logics. After a recap on description logics, we introduce Standpoint EL+—its syntax, semantics, refutation-complete calculus, and Datalog implementation—showing that adding standpoints preserves PTime complexity.
Lecture 4: [Lecture 4: Video]
Description. We present expressive standpoint description logics (Standpoint SHIQ, C², and SROIQ), establishing that monodic standpoint extensions preserve the complexity of their base logics via small model properties and polynomial translations. We then introduce non-monotonic standpoint logic based on S4F, covering its semantics of minimal models, Σᴾ₂/Πᴾ₂ complexity, and proof-of-concept ASP implementation.
Standpoint Logic: Multi-Perspective Knowledge Representation. Lucía Gómez Álvarez and Sebastian Rudolph Proceedings of the 12th International Conference on Formal Ontology in Information Systems (FOIS 2021), FAIA vol. 344, pp. 3–17. IOS Press. [Paper]
Automating Reasoning with Standpoint Logic via Nested Sequents. Tim S. Lyon and Lucía Gómez Álvarez Proceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning (KR 2022) [Paper]
How to Agree to Disagree: Managing Ontological Perspectives using Standpoint Logic. Lucía Gómez Álvarez, Sebastian Rudolph, and Hannes Strass Proceedings of the 21st International Semantic Web Conference (ISWC 2022). [Paper]
Pushing the Boundaries of Tractable Multiperspective Reasoning: A Deduction Calculus for Standpoint EL+. Lucía Gómez Álvarez, Sebastian Rudolph, and Hannes Strass. Proceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning (KR 2023), pp. 333–343. IJCAI Organization. [Paper]
Non-Monotonic S4F Standpoint Logic. Piotr Gorczyca and Hannes Strass. Proceedings of the 40th AAAI Conference on Artificial Intelligence (AAAI 2026), pp. 19126–19134. AAAI Press. [Paper]