4 papers
Fundamental Logic Through the Lens of Modality
Wesley H. Holliday, Guillaume Massas
Fundamental logic is a non-classical logic based only on the introduction and elimination rules for conjunction, disjunction, negation, and the quantifiers in a Fitch-style natural…
Conditionals and Modalities in Constructive Quantum Logics
Juan P. Aguilera, Guillaume Massas
We investigate logics that generalize both intuitionistic logic and quantum logic. In earlier work, we introduced Ex-logic, an extension of Holliday's fundamental logic that coinci…
Constructive Quantum Logics
Juan P. Aguilera, Guillaume Massas
Following a suggestion of Birkhoff and Von Neumann [Ann. Math. 37 (1936), 23-32], we pursue a joint study of quantum logic and intuitionistic logic. We exhibit a linear-time transl…
A Semi-Constructive Approach to the Hyperreal Line
Guillaume Massas
Using a recent alternative to Tarskian semantics for first-order logic, known as , I introduce an alternative approach to nonstandard analysis that…