Related papers: (Mathematical) Logic for Systems Biology (Invited …
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
Synthetic Biology is an interdisciplinary field that utilizes well-established engineering principles, ranging from electrical, control and computer systems, for analyzing the biological systems, such as biological circuits, enzymes,…
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently…
Biomedical research results are being published at a high rate, and with existing search engines, the vast amount of published work is usually easily accessible. However, reproducing published results, either experimental data or…
Integrative biological simulations have a varied and controversial history in the biological sciences. From computational models of organelles, cells, and simple organisms, to physiological models of tissues, organ systems, and ecosystems,…
Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…
Models of the dynamics of cellular interaction networks have become increasingly larger in recent years. Formal verification based on model checking provides a powerful technology to keep up with this increase in scale and complexity. The…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
Cell injection is an approach used for the delivery of small sample substances into a biological cell and is widely used in drug development, gene injection, intracytoplasmic sperm injection (ICSI) and in-virto fertilization (IVF). Robotic…
Many open problems in biology, as in the physical sciences, display nonlinear and 'chaotic' dynamics, which, to the extent possible, cannot be reasonably understood. Moreover, mathematical models which aim to predict/estimate unknown…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
The paradigm of Tabled Logic Programming (TLP) is now supported by a number of Prolog systems, including XSB, YAP Prolog, B-Prolog, Mercury, ALS, and Ciao. The reasons for this are partly theoretical: tabling ensures termination and optimal…