Logic References

• Slice: logic
• Source: slices/core/logic/design/LOGIC-REFERENCES.md

GMEOW Logic — References

Status: bibliography appendix for the GMEOW Logic design set. The logic: design relies on a substantial body of external standards, foundational theory, and engines; this appendix names them so the claims in the other documents are cited, not merely name-dropped.

Relationship to the citation ledger

Per docs/CITATIONS.md, the canonical citation record is the Turtle ledger metadata/references.ttl; Markdown, CSL JSON, and BibTeX are generated lossy projections (Principle 4). This appendix is therefore a staging surface: correct, identifiable references with stable URLs that gmeow references-backfill harvests from authored files, after which precise DOIs and venue metadata are curated into the ledger. When the ledger lands, each entry here becomes a gmeow:CreativeWork cited by a gmeow:CitationAct, with gmeow:viaSelector pointing at the design file (and section) that cites it. The two groupings below map directly to the two citation intents:

• Standards, vocabularies, and engines → gmeow:intentBridgedByReference (aligned to or built on, never copied in — Principle 5).
• Foundational theory → gmeow:intentCitesAsDataSource (relied on as the source for a design claim — AGM revision, decidability-as-projection, the chase, and so on).

Internal references (GTS conformance design, references ledger, the statement layer, the slices) are not bibliography items unless they themselves cite an external work; they are cross-references within GMEOW.

Standards and specifications (intentBridgedByReference)

• W3C. RDF 1.2 Concepts and Abstract Syntax. https://www.w3.org/TR/rdf12-concepts/ (Full vs Basic conformance; triple terms in object position).
• W3C. OWL 2 Web Ontology Language — Document Overview (2012) and Profiles (EL, QL, RL). https://www.w3.org/TR/owl2-overview/, https://www.w3.org/TR/owl2-profiles/
• W3C. Shapes Constraint Language (SHACL) (2017). https://www.w3.org/TR/shacl/
• W3C. SPARQL 1.1 Query Language (2013). https://www.w3.org/TR/sparql11-query/
• W3C. SWRL: A Semantic Web Rule Language Combining OWL and RuleML (Member Submission, 2004). https://www.w3.org/submissions/SWRL/
• W3C. RIF (Rule Interchange Format) Overview (2013). https://www.w3.org/TR/rif-overview/
• ISO/IEC 24707:2018. Information technology — Common Logic (CL).
• ISO/IEC 21838-2:2021. Basic Formal Ontology (BFO). See also Arp, Smith & Spear, Building Ontologies with Basic Formal Ontology (MIT Press, 2015).
• Berners-Lee, T., Connolly, D., Kagal, L., Scharf, Y. & Hendler, J. (2008). N3Logic: A logical framework for the World Wide Web. Theory and Practice of Logic Programming 8(3).

Foundational ontologies (intentBridgedByReference; cited as source for UFO⁺)

• Guizzardi, G. (2005). Ontological Foundations for Structural Conceptual Models (UFO). PhD thesis, University of Twente.
• Almeida, J. P. A., Falbo, R. A. & Guizzardi, G. gUFO: A Lightweight Implementation of the Unified Foundational Ontology. https://nemo-ufes.github.io/gufo/
• OntoUML — Guizzardi et al.; anti-pattern catalogue: https://ontouml.readthedocs.io/
• Masolo, C., Borgo, S., Gangemi, A., Guarino, N. & Oltramari, A. (2003). Ontology Library (WonderWeb Deliverable D18) — DOLCE; Gangemi, A. & Mika, P. (2003). Understanding the Semantic Web through Descriptions and Situations (DnS). ODBASE.
• Niles, I. & Pease, A. (2001). Towards a Standard Upper Ontology (SUMO). FOIS.

Foundational theory (intentCitesAsDataSource)

• Alchourrón, C., Gärdenfors, P. & Makinson, D. (1985). On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. Journal of Symbolic Logic 50(2). (AGM belief revision.)
• Gärdenfors, P. & Makinson, D. (1988). Revisions of Knowledge Systems Using Epistemic Entrenchment. TARK. (Entrenchment ↔ revision; deterministic revision.)
• Lewis, D. (1973). Counterfactuals. Harvard University Press. (Closeness ordering; ties.)
• Stalnaker, R. (1968). A Theory of Conditionals. In Studies in Logical Theory. (Unique closest world.)
• Ramsey, F. P. (1931). General Propositions and Causality. (The Ramsey test.)
• Church, A. (1936). An Unsolvable Problem of Elementary Number Theory. American Journal of Mathematics 58. — Turing, A. M. (1936). On Computable Numbers, with an Application to the Entscheidungsproblem. Proc. London Math. Soc. (Undecidability / the halting problem.)
• Blackburn, P., de Rijke, M. & Venema, Y. (2001). Modal Logic. Cambridge University Press. (The standard translation of modal logic into first-order logic.)
• Gelfond, M. & Lifschitz, V. (1988). The Stable Model Semantics for Logic Programming. ICLP.
• Van Gelder, A., Ross, K. & Schlipf, J. (1991). The Well-Founded Semantics for General Logic Programs. Journal of the ACM 38(3).
• Chen, W., Kifer, M. & Warren, D. S. (1993). HiLog: A Foundation for Higher-Order Logic Programming. Journal of Logic Programming. (Second-order-as-first-order reification.)
• Kifer, M., Lausen, G. & Wu, J. (1995). Logical Foundations of Object-Oriented and Frame-Based Languages (F-logic). Journal of the ACM 42(4).
• Fagin, R., Kolaitis, P., Miller, R. & Popa, L. (2005). Data Exchange: Semantics and Query Answering. Theoretical Computer Science 336. (The chase; weak acyclicity / termination.)
• Calì, A., Gottlob, G. & Lukasiewicz, T. (2012). A general Datalog-based framework for tractable query answering over ontologies (Datalog±). Journal of Web Semantics.
• Bancilhon, F., Maier, D., Sagiv, Y. & Ullman, J. (1986). Magic Sets and Other Strange Ways to Implement Logic Programs. PODS. (Goal-directed materialization.)
• Chen, W. & Warren, D. S. (1996). Tabled Evaluation with Delaying for General Logic Programs. Journal of the ACM 43(1). (SLG resolution / tabling.)
• Green, T., Karvounarakis, G. & Tannen, V. (2007). Provenance Semirings. PODS. (Why-provenance; proof-trace provenance.)
• de Kleer, J. (1986). An Assumption-Based TMS. Artificial Intelligence 28. — Doyle, J. (1979). A Truth Maintenance System. Artificial Intelligence 12. (Contradiction witnesses / ATMS·JTMS.)

Engines and tools (intentBridgedByReference)

• Oxigraph — an RDF store with SPARQL and RDF 1.2 support (Rust). https://oxigraph.org/
• Nemo — a Datalog-based rule engine with existential rules and stratified negation (knowsys, Rust). https://knowsys.github.io/nemo/
• Soufflé — Jordan, H., Scholz, B. & Subotić, P. (2016). Soufflé: On Synthesis of Program Analyzers. CAV. https://souffle-lang.github.io/
• RDFox — Nenov, Y., Piro, R., Motik, B., Horrocks, I., Wu, Z. & Banerjee, J. (2015). RDFox: A Highly-Scalable RDF Store. ISWC. (Cited as prior art only; not a dependency — Principle 5.)
• Scryer Prolog — an ISO Prolog system in Rust. https://www.scryer.pl/
• Trealla Prolog — a compact ISO Prolog in C/Rust bindings. https://trealla-prolog.github.io/
• ProbLog — De Raedt, L., Kimmig, A. & Toivonen, H. (2007). ProbLog: A Probabilistic Prolog and Its Application in Link Discovery. IJCAI.
• EYE — the Euler Yet another proof Engine (N3 reasoning). https://eyereasoner.github.io/eye/
• cwm — the Closed World Machine (N3 rules). https://www.w3.org/2000/10/swap/doc/cwm.html
• ELK — Kazakov, Y., Krötzsch, M. & Simančík, F. (2014). The Incredible ELK. Journal of Automated Reasoning 53.
• HermiT — Glimm, B., Horrocks, I., Motik, B., Stoilos, G. & Wang, Z. (2014). HermiT: An OWL 2 Reasoner. Journal of Automated Reasoning 53.
• OWL-RL — a Python OWL 2 RL/RDFS reasoner (cross-check oracle). https://owl-rl.readthedocs.io/
• PyO3 / maturin — Rust bindings for Python. https://pyo3.rs/
• WebAssembly. https://webassembly.org/

Design influence (intentCitesAsDataSource)

• Quijada, J. (2011). A Grammar of the Ithkuil Language. https://ithkuil.net/ (Orthogonal factorization; obligatory evidentiality; precision without a usable surface.)