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Everything about Focused proof
In mathematical logic, focused proofs are a family of analytic proofs that arise through goal-directed proof-search, and are a topic of study in structural proof theory and reductive logic. They form the most general definition of goal-directed proof-search—in which someone chooses a formula and performs hereditary reductions until the result meets some condition. The extremal case where reduction only terminates when axioms are reached forms the sub-family of uniform proofs. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Focused proofA 5-minute orientation
- Skim a recent paper: Combination of chemotherapy and focused ultrasound for the treatment of unresectable pancreatic cancer: a proof-of-concept studyInfluential work since 2022
- Pick up a classic book: The Conspirators HierarchyThe most-reprinted book on the subject
- Read the landmark paper: Proof of principle for epitope-focused vaccine designCited 555 times
- Go sideways: Proof theoryA closely related topic
- Go sideways: Linear logicA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Proof of principle for epitope-focused vaccine design
MR-guided focused ultrasound thalamotomy for essential tremor: a proof-of-concept study
Focused Vascular Ultrasound for the Assessment of Atherosclerosis: A Proof-of-Concept Study
Laparoscopic high‐intensity focused ultrasound for renal tumours: a proof of concept study
Deep Neural Network for Navigation of a Single-Element Transducer During Transcranial Focused Ultrasound Therapy: Proof of Concept
A Focused Low-Intensity Pulsed Ultrasound (FLIPUS) System for Cell Stimulation: Physical and Biological Proof of Principle
Low-intensity focused ultrasound to the insula differentially modulates the heartbeat-evoked potential: A proof-of-concept study
A multi-focused proof system isomorphic to expansion proofs
🆕 Influential since 2022
Combination of chemotherapy and focused ultrasound for the treatment of unresectable pancreatic cancer: a proof-of-concept study
Novel treatment system using endoscopic ultrasound-guided high-intensity focused ultrasound: A proof-of-concept study
Comparing written exposure therapy delivered via telehealth to trauma‐focused expressive writing in undergraduates: A proof‐of‐concept trial
Focused electric field (FEF) ablation in a left ventricular and infrared thermal imaging model: a proof-of-concept study
An Analysis of middle school students’ deductive reasoning in proof lessons: Focused on commognition perspective16)
📚 Books worth reading
The Conspirators HierarchyJohn Coleman · 1992
Observational studiesPaul R. Rosenbaum · 1995
How to Deliver Professional Sales Presentations & DemonstrationsMichael McGaulley · 2019
The compassionate-mind guide to overcoming anxietyDennis D. Tirch · 2012- 📕AI Survival Guide : From Zero to Expert · 2025
- 📕Xing shi su song zheng ming quan yan jiuMaoyu Yu · 2010
Romancing the big QLisa M. Walters · 2012- 📕Romancing the big QLisa M. Walters · 2012
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Proof theory Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitati…
- Linear logic Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities…
- Natural deduction In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to…
- Structural proof theory In mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof…
- Intuitionistic logic Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical…
- Sequent calculus In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a…
- Sequent In mathematical logic, a sequent is a very general kind of conditional assertion. A 1 , … , A m ⊢ B 1 , … , B n . {\displaystyle A_{1},\,\dots ,A_{m}\…
- Craig interpolation In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem…