Project description
Exploring higher dimensions of first-order logic
First-order logic is the foundation of modern mathematics, providing the language to express its core principles. While its study is well-established in 1D category theory, many unexplored aspects remain hidden in 2D category theory. With the support of the Marie Skłodowska-Curie Actions programme, the HiDimAFOL project will explore these higher-dimensional aspects of first-order logic, uncovering new ways to describe its syntax and semantics using advanced algebraic structures called pseudo-monads. By bridging algebraic logic, categorical logic and model theory, the project aims to deepen understanding of mathematical logic and lead to new mathematical applications. Project work will also promote collaboration across different mathematical traditions.
Objective
First-order logic is the foundational formal language used to express almost all of modern mathematics, and improved understanding of this logic is linked to many recent advances in mathematics. Consequently, there is a well-developed framework to study first-order logic within the mathematical discipline of 1-dimensional category theory. However, there are still many important and yet unexplored aspects of first-order logic that only emerge in 2-dimensional category theory. My research has uncovered new descriptions of the syntax and semantics of first-order logic as algebraic structures for a pseudo-monad, a mathematical gadget found in 2-dimensional category theory.
Supported by the Marie Skłodowska-Curie Actions programme, the HiDimAFOL project will establish new results concerning the higher dimensional aspects of first-order logic by investigating the pseudo-monads related to the syntax and semantics of first-order logic. The project will deepen our understanding of first-order logic and lead to new mathematical applications on the interface of algebraic logic, categorical logic and model theory. By highlighting the applications of higher dimensional category theory to mathematical logic, we will promote unity among the various logical traditions that exist in mathematics.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
You need to log in or register to use this function
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2025-PF
See all projects funded under this callCoordinator
Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
601 77 Brno
Czechia
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.