Related papers: (Mathematical) Logic for Systems Biology (Invited …
At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has…
We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…
The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…
Single-cell analysis is currently one of the most high-resolution techniques to study biology. The large complex datasets that have been generated have spurred numerous developments in computational biology, in particular the use of…
We propose a conjugate logic that can capture the behavior of quantum and quantum-like systems. The proposal is similar to the more generic concept of epistemic logic: it encodes knowledge or perhaps more correctly, predictions about…
We introduce proof nets for PiL, an extension of first-order multiplicative additive linear logic with new operators allowing a shallow encoding of processes in the {\pi}-calculus as formulas. We provide correctness criterion,…
The computational method of parametric probability analysis is introduced. It is demonstrated how to embed logical formulas from the propositional calculus into parametric probability networks, thereby enabling sound reasoning about the…
I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction…
This paper shows that it is possible to reason about the safety and termination of programs handling potentially cyclic, singly-linked lists using propositional reasoning even when the safety invariants and termination arguments depend on…
Human logic has gradually shifted from intuition-driven inference to rigorous formal systems. Motivated by recent advances in large language models (LLMs), we explore whether LLMs exhibit a similar evolution in the underlying logical…
Physics-Informed Machine Learning (PIML) has successfully integrated mechanistic understanding into machine learning, particularly in domains governed by well-known physical laws. This success has motivated efforts to apply PIML to biology,…
The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process…
A recommendation system assists users in finding items that are relevant to them. Existing recommendation models are primarily based on predicting relationships between users and items and use complex matching models or incorporate…
The behaviour of systems characterised by a closed interaction of software components with the environment is inevitably subject to perturbations and uncertainties. In this paper we propose a general framework for the specification and…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…
The goal of this paper is to advance an extensible theory of living systems using an approach to biomathematics and biocomputation that suitably addresses self-organized, self-referential and anticipatory systems with multi-temporal…
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
Both experimental and computational biology is becoming increasingly automated. Laboratory experiments are now performed automatically on high-throughput machinery, while computational models are synthesized or inferred automatically from…
Recently, symbolic computation and computer algebra systems have been successfully applied in systems biology, especially in chemical reaction network theory. One advantage of symbolic computation is its potential for qualitative answers to…