8 citations · 36 across the 24 of their papers we have counts for
4 papers · 1 filter
Hoops, Coops and the Algebraic Semantics of Continuous Logic
Rob Arthan, Paulo Oliva
Büchi and Owen studied algebraic structures called hoops. Hoops provide a natural algebraic semantics for a class of substructural logics that we think of as intuitionistic analogu…
A Constructive Interpretation of Ramsey's Theorem via the Product of Selection Functions
Paulo Oliva, Thomas Powell
We use Gödel's Dialectica interpretation to produce a computational version of the well known proof of Ramsey's theorem by Erdős and Rado. Our proof makes use of the product of sel…
A Game-Theoretic Computational Interpretation of Proofs in Classical Analysis
Paulo Oliva, Thomas Powell
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive…
(Dual) Hoops Have Unique Halving
Rob Arthan, Paulo Oliva
Continuous logic extends the multi-valued Lukasiewicz logic by adding a halving operator on propositions. This extension is designed to give a more satisfactory model theory for co…