Language

Predicate Logic Semantics – Models



David Agler

In this video, I give a brief overview of the notion of a model in predicate logic. This video sets the stage for a discussion of predicate logic valuations.

Predicate Logic Symbols: https://youtu.be/PTwGnYh0nS4
Predicate Logic Syntax: https://youtu.be/AQWeTrFBaXw

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17 thoughts on “Predicate Logic Semantics – Models
  1. 23:10
    For interpretations of predicates, are you allowed to use the letters in RL used to denote elements in the domain instead of the original domain objects.
    In other words, can we write ?(C) = {a,b,c} instead of ?(C) = {1,2,3}.
    Does it matter?

  2. ("_" means subscript, quantifiers are specified in brackets)
    Hi David, I am having trouble with an unsure conclusion that i share with Gamut's Logic, Language and Meaning. Chapter 3, exercise 9: Prove that ( [for all]x(fi) → [t/x](fi) ) is universally valid (using valuations under a model M and an assignment function g). The demonstration that the book gives (pp. 249) goes like this.
    "Suppose V_M,g([for all]x(fi)) = 1. It is to be proven that V_M,g([t/x](fi)) = I. That
    V_M,g([for all]x(fi)) = I means that for all d [in] D, V_M,g((fi)) = 1. In particu-
    lar, [[t]]_M,g is such an element of D. From this it follows that V_M,g([t/x](fi)) = 1 (strictly, this should be proven
    with induction on the length of (fi))."
    My concern is: from where does it comes the assumption that every name or variable "t" member of L is defined for the interpretation function I? Couldn't just exist a term t such that I(t) = undefined? In such a case, I(t) [not member of] D, where it follows that there is a counter-example to the universal validity of the initial formula.
    Nevertheless, great videos and promulgation of logic to youtube 😀

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