Spatial Existential Positive Logics for Hyperedge Replacement Grammars

Author Yoshiki Nakamura

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Yoshiki Nakamura
  • Tokyo Institute of Technology, Japan


We would like to thank the anonymous reviewers for their useful comments.

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Yoshiki Nakamura. Spatial Existential Positive Logics for Hyperedge Replacement Grammars. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We study a (first-order) spatial logic based on graphs of conjunctive queries for expressing (hyper-)graph languages. In this logic, each primitive positive (resp. existential positive) formula plays a role of an expression of a graph (resp. a finite language of graphs) modulo graph isomorphism. First, this paper presents a sound- and complete axiomatization for the equational theory of primitive/existential positive formulas under this spatial semantics. Second, we show Kleene theorems between this logic and hyperedge replacement grammars (HRGs), namely that over graphs, the class of existential positive first-order (resp. least fixpoint, transitive closure) formulas has the same expressive power as that of non-recursive (resp. all, linear) HRGs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
  • Existential positive logic
  • spatial logic
  • Kleene theorem


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