The Guarded Fragment with Nested Equivalences
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913129860956160 |
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| author | Fiuk, Oskar |
| author_facet | Fiuk, Oskar |
| contents | The Guarded Fragment (GF) is a well-established decidable fragment of first-order logic. We study an extension of GF with nested equivalence relations, namely a family of distinguished binary predicates $E_1, E_2, \dots$ interpreted as equivalence relations such that $E_{k+1}$ is coarser than $E_k$ for every $k$. We show that the equality-free GF with nested equivalence relations enjoys the finite model property and has a decidable satisfiability problem. Moreover, we establish tight complexity bounds for satisfiability: TOWER-completeness in general, and $(K{+}2)$-ExpTime-completeness when the number of distinguished predicates is fixed to $K$. Finally, we show that satisfiability becomes undecidable if either the nesting condition is dropped (already with two equivalence relations) or equality is admitted (already with a single equivalence relation). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15072 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Guarded Fragment with Nested Equivalences Fiuk, Oskar Logic in Computer Science F.4.1 The Guarded Fragment (GF) is a well-established decidable fragment of first-order logic. We study an extension of GF with nested equivalence relations, namely a family of distinguished binary predicates $E_1, E_2, \dots$ interpreted as equivalence relations such that $E_{k+1}$ is coarser than $E_k$ for every $k$. We show that the equality-free GF with nested equivalence relations enjoys the finite model property and has a decidable satisfiability problem. Moreover, we establish tight complexity bounds for satisfiability: TOWER-completeness in general, and $(K{+}2)$-ExpTime-completeness when the number of distinguished predicates is fixed to $K$. Finally, we show that satisfiability becomes undecidable if either the nesting condition is dropped (already with two equivalence relations) or equality is admitted (already with a single equivalence relation). |
| title | The Guarded Fragment with Nested Equivalences |
| topic | Logic in Computer Science F.4.1 |
| url | https://arxiv.org/abs/2605.15072 |