Metalogic- EASY definition question, but crucial

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The discussion centers on the distinction between the expressions "P is T on α" and "α(P)=T" within the context of Sentential Logic metatheory. Participants clarify that both expressions convey the same relationship between a function and its input, specifically regarding truth-values. The conversation emphasizes the importance of understanding the difference between a truth-function, which maps truth-values to truth-values, and a truth-value assignment, which assigns truth-values to atomic formulas. This understanding is crucial for students preparing for exams in metalogic.

PREREQUISITES
  • Understanding of Sentential Logic
  • Familiarity with truth-functions and truth-value assignments
  • Basic knowledge of metatheory concepts
  • Experience with logical expressions and valuations
NEXT STEPS
  • Research the definitions and examples of truth-functions in logic
  • Study truth-value assignments and their applications in metalogic
  • Explore the role of valuations in logical frameworks
  • Review metatheoretical concepts relevant to Sentential Logic
USEFUL FOR

Students of metalogic, educators teaching logic courses, and anyone seeking a deeper understanding of the relationships between truth-functions and truth-value assignments in Sentential Logic.

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Metalogic-- EASY definition question, but crucial!

In the metatheory of Sentential Logic, what is the difference between saying

P is T on [tex]\alpha[/tex]

vs.

[tex]\alpha[/tex](P)=T

and is it related to the diff between a truth-function and a truth-value assignment?

This is NOT homework or for a grade btw, although it is baffling me as I take a metalogic course, and I would like to know ASAP as we have an exam coming up.

S
 
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I am more used to saying that a formula is true (or whatever) under a given valuation, but I suppose P is T on α makes enough sense. Your two expressions both express the same relationship to me: the value assigned by a function to an input. If you are asking about a definition, though, then the definer (your book or instructor, I imagine) is the only one that can give you a definitive answer.

What is the difference (to you) between a truth-function and a truth-value assignment? The truth-function is from truth-values to truth-values and based on an assignment (which is from (atomic) formulas to truth-values)?
 

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