Qualitative-Quantitative Reasoning: Thinking Informally About Formal Things (original) (raw)
2021
Qualitative–quantitative reasoning is the way we think informally about formal or numerical phenomena. It is ubiquitous in scientific, professional and day-to-day life. Mathematicians have strong intuitions about whether a theorem is true well before a proof is found – intuition that also drives the direction of new proofs. Engineers use various approximations and can often tell where a structure will fail. In computation we deal with order of magnitude arguments in complexity theory and data science practitioners need to match problems to the appropriate neural architecture or statistical method. Even in the supermarket, we may have a pretty good idea of about how much things will cost before we get to the checkout. This paper will explore some of the different forms of QQ–reasoning through examples including the author’s own experience numerically modelling agricultural sprays and formally modelling human–computer interactions. We will see that it is often the way in which formal ...
Related papers
Mathematical Foundations of Qualitative Reasoning
Ai Magazine, 2004
■ We examine different formalisms for modeling qualitatively physical systems and their associated inferential processes that allow us to derive quali- tative predictions from the models. We highlight the mathematical aspects of these processes along with their potential and limitations. The article then bridges to quantitative modeling, highlight- ing the benefits of qualitative reasoning-based ap- proaches in the framework of
Reasoning with qualitative models
1994
Qualitative reasoning about physical systems has become one of the most productive areas in AI in recent years, due in part to the 1984 special issue of Artificial Intelligence on that topic. My contribution to that issue was a paper entitled" Commonsense reasoning about causality: deriving behavior from structure"[9]. From my perspective, that paper laid out a research program that has continued to be productive to this day, and promises to continue well into the future.
Quantitative formalism: an experiment
2011
This paper is the report of a study conducted by five people – four at Stanford, and one at the University of Wisconsin – which tried to establish whether computer-generated algorithms could "recognize" literary genres. You take 'David Copperfield', run it through a program without any human input – "unsupervised", as the expression goes – and ... can the program figure out whether it's a gothic novel or a 'Bildungsroman'? The answer is, fundamentally, Yes: but a Yes with so many complications that it is necessary to look at the entire process of our study. These are new methods we are using, and with new methods the process is almost as important as the results.
The need for qualitative reasoning in automated modeling: a case study
1996
This paper demonstrates that qualitative reasoning plays a crucial role for both an efficient and physi- cally correct approach to the automated formulation of an accurate quantitative model which explains a set of observations. The model which "best" repro- duces the measured data is selected within a model space whose elements are constructed by exploiting specific knowledge and techniques of
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.