Abstract
The grand ambition of theorists studying ecology and evolution is to discover the logical and mathematical rules driving the world's biodiversity at every level from genetic diversity within species to differences between populations, communities, and ecosystems. This ambition has been difficult to realize in great part because of the complexity of biodiversity. Theoretical work has led to a complex web of theories, each having non-obvious consequences for other theories. Case in point, the recent realization that genetic diversity involves a great deal of temporal and spatial stochasticity forces theoretical population genetics to consider abiotic and biotic factors generally reserved to ecosystem ecology. This interconnectedness may require theoretical scientists to adopt new techniques adapted to reason about large sets of theories. Mathematicians have solved this problem by using formal languages based on logic to manage theorems. However, theories ecology and evolution are not mathematical theorems, they involve uncertainty. Recent work in Artificial Intelligence in bridging logic and probability theory offers the opportunity to build rich knowledge bases that combine logic's ability to represent complex mathematical ideas with probability theory's ability to model uncertainty. We describe these hybrid languages and explore how they could be used to build a unified knowledge base of theories for ecology and evolution.
Highlights
Theories can be written in some formal language, such as first-order logic or type theory, and algorithms are used to ensure the theories can be derived from a knowledge base of axioms and existing results
Here’s a sample of a knowledge base where the first three formulas were learned directly from our dataset and the last two serve as example for Hybrid Markov logic: predicates to evaluate it; see section 2). This is a strong advantage of this knowledge representation: our little knowledge base here can be used as a basis for any other ecological datasets even if they quite different
We explored hybrid approaches based on first-order logic and, for this section, we’ll briefly discuss Bayesian Higher-Order Probabilistic Programming (BHOPP)
Summary
Researchers have tried to unify probability theory with rich logics to build knowledge bases both capable of the sophisticated mathematical reasoning found in automated theorem provers and the probabilistic reasoning of graphical models. Recent advances moved us closer to that goal (Richardson and Domingos, 2006; Getoor et al, 2007; Wang and Domingos, 2008; Nath and Domingos, 2015; Hu et al, 2016; Staton et al, 2016; Bach et al, 2017) Using these systems, it is possible to check if a mathematical formula can be derived from existing results and possible to ask probabilistic queries about theories and data. Practical representations to unify logic and probability are relatively new, but we argue they could be used to achieve greater synthesis by allowing the construction of large, flexible knowledge bases with a mix of mathematical and scientific knowledge
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