Everything about Consistency
Non-contradiction of a theory
In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory is consistent if there is no formula such that both and its negation are elements of the set of consequences of. Let be a set of closed sentences and the set of closed sentences provable from under some formal deductive system. The set of axioms is consistent when there is no formula such that and. A trivial theory is clearly inconsistent. Conversely, in an explosive formal system every inconsistent theory is trivial. Consistency of a theory is a syntactic notion, whose semantic counterpart is satisfiability. A theory is satisfiable if it has a model, i.e., there exists an interpretation under which all axioms in the theory are true. This is what consistent meant in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: ConsistencyA 5-minute orientation
- Skim a recent paper: Interpolation consistency training for semi-supervised learningInfluential work since 2022
- Pick up a classic book: Theological IncorrectnessThe most-reprinted book on the subject
- Read the landmark paper: The Columbia–Suicide Severity Rating Scale: Initial Validity and Internal Consistency Findings From Three Multisite Studies With Adolescents and AdultsCited 4,822 times
- Go sideways: Gödel's completeness theoremA closely related topic
- Go sideways: Theory (mathematical logic)A closely related topic
📖 Definitions
Noun Local coherence.
Noun Correspondence or compatibility.
Noun Reliability or uniformity; the quality of being consistent.
Noun The degree of viscosity of something.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The Columbia–Suicide Severity Rating Scale: Initial Validity and Internal Consistency Findings From Three Multisite Studies With Adolescents and Adults
From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation
Starting at the Beginning: An Introduction to Coefficient Alpha and Internal Consistency
Structural models of primary cell walls in flowering plants: consistency of molecular structure with the physical properties of the walls during growth
A scoping review of scoping reviews: advancing the approach and enhancing the consistency
Lower Extremity Function and Subsequent Disability: Consistency Across Studies, Predictive Models, and Value of Gait Speed Alone Compared With the Short Physical Performance Battery
The rank-order consistency of personality traits from childhood to old age: A quantitative review of longitudinal studies.
Checking consistency in mixed treatment comparison meta‐analysis
🆕 Influential since 2022
Interpolation consistency training for semi-supervised learning
Prompt engineering in consistency and reliability with the evidence-based guideline for LLMs
Semi-supervised medical image segmentation via uncertainty rectified pyramid consistency
Mutual consistency learning for semi-supervised medical image segmentation
Consistency Indices in Analytic Hierarchy Process: A Review
📚 Books worth reading
Theological IncorrectnessJason Slone · 2007- 📕Theories of cognitive consistencyRobert P. Abelson · 1968
Is there value in inconsistency?Engel, Christoph, Lorraine Daston · 2006- 📕Stage analysis of response programmingGeorge A. Frekany · 1980
- 📕Sequential response biasWillem Albert Wagenaar · 1972
- 📕Reaktionsversuche bei durchgangsbeobachtungenFriedrich Günther · 1911
- 📕Log-based recovery in asynchronous distributed systemsKenneth P. Kane · 1990
- 📕The effect of response error on SES, ethnic, and sex differences in reported symptoms of psychological distressDiana Carol Cook · 1980
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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