# PSOA KGs: RuleML Technical Group on PSOA Knowledge Graphs

**Authors:** Harold Boley, Theodoros Mitsikas, Mark Thom

This is the root document of one of the RuleML Technical Groups (TGs): About the language Positional-Slotted Object-Applicative RuleML (PSOA RuleML) used to formalize, interoperate, and generalize Knowledge Graphs (KGs). If you are new to PSOA RuleML, you may want to consult Learn PSOA RuleML. If you are new to KGs, you may want to consult Knowledge graph.

## 1 Introduction

In the following, "knowledge" will denote the superconcept for ontologies and rules. Such knowledge can often be derived from data, hence be used, schema-like, to interpret data. In the following, "information" will denote the superconcept for data and knowledge.

PSOA RuleML integrates different notions of "graph", including variants of Directed Labeled Graphs (DLGs), e.g. built from its framepoints -- typed-frame-style atomic formulas aggregated to node-typed DLGs. Also included are generalized notions such as directed hypergraphs, built from PSOA's relationships -- predicate-logic-style atomic formulas aggregated to these (natively n-ary) generalized graphs. This allows (encoding-free) single-language, multi-paradigm information interoperation across a wide spectrum, including between (binary) DLGs and (n-ary) relational tables.

## 2 Topics

The TG explores topics of shared interest, including the following:

- Propose reference KG/KGs for various tests
- Formalism expressivity
- Implementation efficiency (e.g., memory/speed trade-off)
- Expressivity/efficiency trade-off

- Describe community challenges
- Use cases (e.g., PSOA RuleML#Use_Cases)
- Case studies

- Total and partial interoperation
- Define semantics-preserving mappings
- Conduct round-tripping experiments

- Study features of PSOA relevant/novel to KGs
- Atoms combining DLG arcs (slots) with relational hyperarcs (tuples)
- Perspectival information via predicate-dependent slots
- Objectification: Can result in rules with conclusion-existential/Skolemized Object IDentifiers (OIDs)
- Conjunctive-conclusion splitting: Rules derived from conjoined OID-co-referenced conclusion atoms

- Interoperating PSOA and other KG formalisms
- Compatible features amenable to total interoperation
- Incompatible features excluded from subsets for partial interoperation

- Logical reconstruction of graph operations
- Path tracing
- Clustering

## 3 How to Join

Please send an email to any of the above-linked chairs.

## 4 Resources

- Combinations of the Semantic Web, Graph Databases, and Logic Programming are explored, where data are complemented by knowledge, while graphs and relations are integrated
^{[1]} - Both DLGs and three generalized graph definitions can be captured by the PSOA RuleML metamodel for corresponding PSOA RuleML constructs
^{[2]} - The Graph inscribed logic (Grailog) is a systematic combination of generalized graph constructs for visual data & knowledge representation ranging from (binary and n-ary) relational logic to Horn logic, description logic, object/frame logic, higher-order logic, and modal logic
^{[3]} - Illustrate all kinds of atoms in PSOA by their Grailog visualization, aligned with their concrete (symbolic) presentation syntax
^{[4]} - Survey existing Graph Database / KG systems and compare them to PSOATransRun across numerous dimensions, such as expressivity and efficiency
^{[5]}