Continuous Fraïssé Conjecture

Beckmann, Arnold; Goldstern, Martin; Preining, Norbert

doi:10.1007/s11083-008-9094-4

Cited by 16 publications

(14 citation statements)

References 22 publications

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“…It is known that there are continuum-many different propositional consequence relations and continuum-many different propositional quantified Gödel logics [10]. In forthcoming work [13], it is shown that there are only countably many first-order Gödel logics (considered as sets of valid formulas). Although this result goes some way toward clarifying the situation, a criterion of identity of Gödel logics using some topological property of the underlying truth value set is a desideratum.…”

Section: Resultsmentioning

confidence: 97%

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First-order Gödel logics

Baaz

Preining

Zach

2007

Annals of Pure and Applied Logic

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First-order Gödel logics are a family of finite-or infinite-valued logics where the sets of truth values V are closed subsets of [0, 1] containing both 0 and 1. Different such sets V in general determine different Gödel logics G V (sets of those formulas which evaluate to 1 in every interpretation into V ). It is shown that G V is axiomatizable iff V is finite, V is uncountable with 0 isolated in V , or every neighborhood of 0 in V is uncountable. Complete axiomatizations for each of these cases are given. The r.e. prenex, negation-free, and existential fragments of all first-order Gödel logics are also characterized.

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Section: Resultsmentioning

confidence: 97%

“…The following simpler proof is inspired by [13]: Proof. If: Every countable non-trivial dense linear order has order type η, 1+η, η +1, or 1+η +1 [25, Corollary 2.9], where η is the order type of Q.…”

Section: Relation To Gödel Logicsmentioning

confidence: 99%

First-order Gödel logics

Baaz

Preining

Zach

2007

Annals of Pure and Applied Logic

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“…However, if we speak of validity and satisfiability in parallel, this representation is useless and we therefore have to refer to the truth-value sets. This is unfortunate, as uncountably many different Gödel logics with respect to truth-value sets correspond to countably many sets of valid sentences (Beckmann et al 2008). The following problem is a particular instance of this phenomenon.…”

Section: Problem 9 Is There a Gödel Logic That Is Undecidable When Rementioning

confidence: 99%

Ten problems in Gödel logic

Aguilera

Baaz

2016

Soft Comput

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“…In fact there are infinitely many different infinite-valued first-order Gödel logics, according to [4]. The conjecture that there are just countable many different Gödel logics has recently been settled in [5]. G [0,1] and G [0,1] are well known to be recursively axiomatizable, see, e.g., [11].…”

Section: Introductionmentioning

confidence: 99%

Monadic Fragments of Gödel Logics: Decidability and Undecidability Results

Baaz

Ciabattoni

Fermüller

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. The monadic fragments of first-order Gödel logics are investigated. It is shown that all finite-valued monadic Gödel logics are decidable; whereas, with the possible exception of one (G ↑ ), all infinitevalued monadic Gödel logics are undecidable. For the missing case G ↑ the decidability of an important sub-case, that is well motivated also from an application oriented point of view, is proven. A tight bound for the cardinality of finite models that have to be checked to guarantee validity is extracted from the proof. Moreover, monadic G ↑ , like all other infinite-valued logics, is shown to be undecidable if the projection operator is added, while all finite-valued monadic Gödel logics remain decidable with .

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Continuous Fraïssé Conjecture

Cited by 16 publications

References 22 publications

First-order Gödel logics

First-order Gödel logics

Ten problems in Gödel logic

Monadic Fragments of Gödel Logics: Decidability and Undecidability Results

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