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Communication Dans Un Congrès Année : 2023

Decidability of Difference Logic over the Reals with Uninterpreted Unary Predicates

Bernard Boigelot
Baptiste Vergain

Résumé

First-order logic fragments mixing quantifiers, arithmetic, and uninterpreted predicates are often undecidable, as is, for instance, Presburger arithmetic extended with a single uninterpreted unary predicate. In the SMT world, difference logic is a quite popular fragment of linear arithmetic which is less expressive than Presburger arithmetic. Difference logic on integers with uninterpreted unary predicates is known to be decidable, even in the presence of quantifiers. We here show that (quantified) difference logic on real numbers with a single uninterpreted unary predicate is undecidable, quite surprisingly. Moreover, we prove that difference logic on integers, together with order on reals, combined with uninterpreted unary predicates, remains decidable.
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hal-04317419 , version 1 (01-12-2023)

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Bernard Boigelot, Pascal Fontaine, Baptiste Vergain. Decidability of Difference Logic over the Reals with Uninterpreted Unary Predicates. CADE-29 - 29th International Conference on Automated Deduction (2023), Jul 2023, Rome, Italy. pp.542-559, ⟨10.1007/978-3-031-38499-8_31⟩. ⟨hal-04317419⟩
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