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In addition to the traditional Kripke-style 'universal' reading of \ \Box F\) as F holds in all possible situations, there is now a rigorous 'existential' semantics for \ \Box F\) that can be read as there is a witness (proof, justification) for F. Justification semantics plays a similar role in Modal Logic to that played by Kleene realizability in Intuitionistic Logic.
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Proofs (justifications) are represented by proof terms which do not contain individual variables.
Production of dynamic gestures during proof and justification will predict student performance on mathematical insights.
These two points of view the 3D histograms and the co-occurrence matrices are a first validity proof and justification for a fractal approach.
Probability and possibility are critical to understand what can be accepted as an analytical proof, a justification, a probation, a critique, or a falsification [12].
Gödel's so-called Dialectica intepretation (Gödel 1958) delivers a relative consistency proof and justification for Heyting arithmetic by means of a concrete interpretation involving a system T of computable functionals of finite type.
This study provides scientific proof and justification for further evaluation of irreversible electroporation as a promising non-thermal, non pharmacological, ultra short modality for the treatment of VSMC proliferation and the clinical problem of in-stent restenosis.
GEMC theory, along with findings from Nathan et al. (2014), served as the basis for the design of a scalable video game environment that would guide directed actions in service of players' proofs and justifications for mathematical conjectures.
"The Southbank Centre argues that the commercial revenue from developing the existing undercroft is essential for funding the project, yet there has been no proof or financial justification that this funding gap can't be met elsewhere".
More recently, other kinds of proof procedures for Justification Logics have been created.
A different explanation is that Moore's proof does transmit justification but is dialectically ineffective (see mainly Pryor 2004).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com