MODAL LOGIC THEORY FOR PATHOLOGY INFERENCE

http://www.netautopsy.org/modlthry.htm

G. William Moore, MD, PhD
Baltimore VA Medical Center
Pathology and Laboratory Medicine Service
Baltimore, MD USA

G. William Moore, MD, PhD 1
Lawrence A. Brown, MD 1
Robert H. Burger, MD, MPA 1
Grover M. Hutchins, MD 2
Robert E. Miller, MD 2
1 Baltimore VA Medical Center, Baltimore Veterans Affairs Maryland Health Care System, Baltimore, MD USA
2 Department of Pathology, University of Maryland Medical System, The Johns Hopkins Medical Institutions, Baltimore, MD USA


Background: An automated data-mining program for surveying a clinicopathologic database should incorporate the fundamental constraints on data acquisition in routine medical practice. It may be variously unnecessary, uneconomic, technically unfeasible, or unethical to fill in all possible data-items in a rectangular database. Existing clinical databases should include formal considerations for missing values, patient consent, patient risk, and provider alerts. This report proposes a mathematically consistent theory of clinicopathologic inference with the modal concepts of know-whether, need-to-know-whether, and try-to-know-whether.

Technology: Zermelo-Frankel set theory and three modal operators.

Design: The theory employs a set of distinct, atomic statements (atoms, A), each of which has a definite true-false status (no self-reference paradoxes). Quantitative, interval, ranked, and categorical data are reformulated as true-false statements. Each atom is either a datum (complaints, history, physical findings, statements of consent, etc.); or a medical entity (cancer, inflammation, necrosis, etc.). No datum is an entity and no entity is a datum. To each atom, a in set A, there is known-to-the-k-a, for integer k up to a maximum, M; and additionally for each datum, there is need-to-know-d, and try-to-know-d. A datum is d-Hippocratic (do-no-harm) if and only if not-need-d implies not-try-d; and d-conative (try) if and only if (not-know-d and need-d) implies try-d. An entity may be k-vexative (worrisome) or k-ontologic (exists), based upon previously collected data.

Results: The theory is mathematically consistent, and satisfies Occam's Razor, namely, that no entities are known without data. The d-Hippocratic, d-conative, k-vexative, and k-ontologic properties are consistent if data are entered consensually, consecutively, and consistently, i.e., no datum is entered after its negation has been entered. The computer algorithm concludes within polynomial time.

Conclusions: This report introduces a consistent mathematical system for managing medical concepts and data. Modal logic operators expand the purview of classical symbolic logic, to accommodate constraints on clinicopathologic data collection. The theory supports such medical concepts as: do-no-harm; try-if-you-need-to; worrisome findings; disease ontologies; and levels of certainty. Ontologies are organized in ascending certainty versus possible harm to the patient. The theory is completely general, and permits definitions of patient injury that include mortality, morbidity, inconvenience, financial constraints, or loss-of-privacy; and definitions of need-to-know that may differ among observers (patient, physician, insurer, national health policy, research protocol). Mathematical theories can serve to organize medical knowledge and patient data, and improve the scheduling and effectiveness of data collection and surveillance in large clinicopathologic data systems