Pith Number

pith:YYYSENF7

pith:2026:YYYSENF7AK4JICOHCE6IGWKYMQ

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Axiomatizing logics of finite G\"odel-Kripke models

Amanda Vidal, Ricardo O. Rodriguez

Natural axiomatic extensions fail to restore completeness for modal Gödel logics over finite Gödel-Kripke models.

arxiv:2605.15810 v1 · 2026-05-15 · math.LO

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The natural candidate axiomatic extensions do not restore completeness with respect to finite Gödel-Kripke models, thereby resolving a 15 year open problem. New axiomatizations are provided that are complete for finite models and characterize intermediate witnessing conditions that hold for the basic logics.

C2weakest assumption

The assumption that the specific modal Gödel logics studied in references [4,11] are the right starting point and that finite Gödel-Kripke models form the intended class of structures for which completeness is sought.

C3one line summary

Resolves open problem by proving natural extensions of modal Gödel logics are incomplete for finite models and supplies new complete axiomatizations.

References

15 extracted · 15 resolved · 1 Pith anchors

[1] M. Baaz and R. Iemhoff. Skolemization in intermediate logics with the finite model property.Logic Journal of the IGPL, 24(3):224–237, 2016 2016

[2] F. Bou, F. Esteva, L. Godo, and R.O. Rodriguez. Possibilistic semantics for a modal KD45 extension of G¨ odel fuzzy logic. In J. P. et. at. Carvalho, editor,IPMU, pages 123–135, Cham, 2016. Springer I 2016

[3] X. Caicedo, G. Metcalfe, R.O. Rodriguez, and J. Rogger. Decidability of order-based modal logics. Journal of Computer and System Sciences, 88:53 – 74, 2017 2017

[4] X. Caicedo and R.O. Rodriguez. Standard G¨ odel modal logics.Studia Logica, 94(2):189–214, 2010 2010

[5] X. Caicedo and R.O. Rodriguez. Bi-modal G¨ odel logic over [0, 1]-valued Kripke frames.Journal of Logic and Computation, 25(1):37–55, 2015 2015

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:19.702337Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6312234bf02b89409c7113c835958640ea841a95ee319ffef00659bb5e19927

Aliases

arxiv: 2605.15810 · arxiv_version: 2605.15810v1 · doi: 10.48550/arxiv.2605.15810 · pith_short_12: YYYSENF7AK4J · pith_short_16: YYYSENF7AK4JICOH · pith_short_8: YYYSENF7

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YYYSENF7AK4JICOHCE6IGWKYMQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c6312234bf02b89409c7113c835958640ea841a95ee319ffef00659bb5e19927

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42e37bce10d8d6dd5a8795cfb57fa98c67013494b2fded1b9ddd2a5e641a18b0",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-15T10:04:29Z",
    "title_canon_sha256": "73472ff1dc87319afd5e32be95d36c61b170d25a04aa40c2b61d173857f4335f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15810",
    "kind": "arxiv",
    "version": 1
  }
}