6 papers · 1 filter
Predicative Ordinal Recursion on the Constructive Veblen Hierarchy
Amirhossein Akbar Tabatabai, Vitor Greati, Revantha Ramanayake
Inspired by Leivant's work on absolute predicativism, Bellantoni and Cook in 1992 introduced a structurally restricted form of recursion called predicative recursion. Using this re…
Proof Complexity and Feasible Interpolation
Amirhossein Akbar Tabatabai
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is…
An Introduction to Categorical Proof Theory
Amirhossein Akbar Tabatabai
These expanded lecture notes are based on a tutorial on categorical proof theory presented at the summer school associated with the conference "Topology, Algebra, and Categories in…
A Cut-free Sequent Calculus for Basic Intuitionistic Dynamic Topological Logic
Amirhossein Akbar Tabatabai, Majid Alizadeh, Alireza Mahmoudian
As part of a broader family of logics, [1, 3] introduced two key logical systems: , which encapsulates the basic logical structure of dynamic topological systems,…
On a Generalization of Heyting Algebras II
Amirhossein Akbar Tabatabai, Majid Alizadeh, Masoud Memarzadeh
A -algebra is a natural generalization of a Heyting algebra, unifying several algebraic structures, including bounded lattices, Heyting algebras, temporal Heyting algebras,…
On Geometric Implications
Amirhossein Akbar Tabatabai
It is a well-known fact that although the poset of open sets of a topological space is a Heyting algebra, its Heyting implication is not necessarily stable under the inverse image…