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of 213
pro vyhledávání: '"03f55"'
Autor:
Nezhad, Babak Jabbar
Bishop's constructive mathematics school rejects the Law of Excluded Middle, but instead vastly makes use of weaker versions of the Choice. In this paper we pioneer an example, which shows that this road is not consistent, as our example provides a p
Externí odkaz:
http://arxiv.org/abs/2412.08667
Autor:
Pacheco, Leonardo
We prove that the constructive and intuitionistic variants of the modal logic $\mathsf{KB}$ coincide. This result contrasts with a recent result by Das and Marin, who showed that the constructive and intuitionistic variants of $\mathsf{K}$ do not pro
Externí odkaz:
http://arxiv.org/abs/2408.16428
Autor:
Deakin, Jonte, de Groot, Jim
Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic logic by m
Externí odkaz:
http://arxiv.org/abs/2408.12030
Autor:
Visser, Albert, Litak, Tadeusz
We study the principle phi implies box phi, known as `Strength' or `the Completeness Principle', over the constructive version of L\"ob's Logic. We consider this principle both for the modal language with the necessity operator and for the modal lang
Externí odkaz:
http://arxiv.org/abs/2404.11969
We show that there is a constant $k$ such that Buss's intuitionistic theory $\mathsf{IS}^1_2$ does not prove that SAT requires co-nondeterministic circuits of size at least $n^k$. To our knowledge, this is the first unconditional unprovability result
Externí odkaz:
http://arxiv.org/abs/2404.11841
Autor:
Bauer, Andrej, Hanson, James E.
We construct a topos in which the Dedekind reals are countable. To accomplish this, we first define a new kind of toposes that we call parameterized realizability toposes. They are built from partial combinatory algebras whose application operation d
Externí odkaz:
http://arxiv.org/abs/2404.01256
The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation of mathematics. In this paper, we carry out a metathe
Externí odkaz:
http://arxiv.org/abs/2311.11032
Autor:
Pacheco, Leonardo
We define game semantics for the constructive $\mu$-calculus and prove its equivalence to bi-relational semantics. As an application, we use the game semantics to prove that the $\mu$-calculus collapses to modal logic over the modal logic $\mathsf{IS
Externí odkaz:
http://arxiv.org/abs/2308.16697
Autor:
Berg, Benno van den, Otten, Daniël
We investigate how much type theory is able to prove about the natural numbers. A classical result in this area shows that dependent type theory without any universes is conservative over Heyting Arithmetic (HA). We build on this result by showing th
Externí odkaz:
http://arxiv.org/abs/2308.15288
Autor:
Filippov, Dmitry
This dissertation gives an overview of Martin Lof's dependant type theory, focusing on its computational content and addressing a question of possibility of fully canonical and computable semantic presentation.
Comment: Dissertation submitted in
Comment: Dissertation submitted in
Externí odkaz:
http://arxiv.org/abs/2308.09621