Mathematically Structured Programming Group
Next MSP101 seminar
Capucci Logic
Bob Atkey (MSP)
Monday 20 October 2025, 13:00, location TBC
Abstract
For some applications, it is useful for the truth of a logical statement to be approximate instead of merely true or false. Fuzzy Logics are a famous example of such logics, where statements are valued in the interval [0,1], where 1 represents "definitely true" and 0 represents "definitely false".In this talk, I'll talk about a logic which is valued in [0,∞] where implication is interpreted as a ratio between premises and conclusion. The main feature of this logic is that we can formulate a logic where the "sharp" lattice connectives are replaced by smooth ones. Our hope is that this will allow such logics to be used in situations where satisfiability can be learned, or where non-satisfaction is treated as a cost during training.
See the MSP101 seminar page for a full list of future and past talks.
Research Themes
Our vision is to use mathematics to understand the nature of computation, and to turn that understanding into the next generation of programming languages.
We see the mathematical foundations of computation and programming as inextricably linked. We study one so as to develop the other. This reflects the symbiotic relationship between mathematics, programming, and the design of programming languages — any attempt to sever this connection will diminish each component.
To achieve these research goals we use ideas from the following disciplines:
- Functional Programming and Type Theory
- What does the future of programming languages look like? How does one take the logical structure of computation and turn it into a programming abstraction? Type theory allows us to do this by providing a language at an intermediate level of abstraction between a programming language and its logical foundations. Indeed, type theory could be said to be the ideas factory for programming languages.
- Logic
- Different logics are suitable for expressing and verifying different properties of programming languages or systems. We make use of a range of methods such as proof theory and coalgebra to understand the computational nature of proofs and systems intended to run without interruption. Those methods are driven by emerging problems in areas such as AI and security. We have particular strengths in modal logic, quantitative properties of systems, and logics for reasoning about concurrency.
- Category Theory
- How does one understand structure abstractly? How can one build theories that systematically build complex systems by composing descriptions of simpler ones? One uses category theory — that's how! Ideas such as monads and initial algebra semantics attest to the deep contribution that category theory has made to computation.