What's the difference between predicate and propositional logic?
Propositional logic (also called sentential logic) is logic that includes sentence letters (A,B,C) and logical connectives, but not quantifiers. The semantics of propositional logic uses truth assignments to the …
Scope of Assumptions in Propositional Logic.
Feb 5, 2019 · In the calculus there are different types of rules; some allow us to "discharge" assumptions, like e.g. $\to$ -intro; others do not. The "mechanism" is quite simple: we can made …
The translations of "unless" and "except" into symbolic logic.
In above examples, we see "unless" can have different meanings in different context. However for propositional logic, we don't have any context. No one knows what a proposition symbol represents. …
Is a propositional function a proposition in propositional logic ...
Jul 7, 2024 · In propositional logic there are no propositional functions because there are no predicates and variables in the syntax. See Mendelson's example: the two mathematical statements "x is prime" …
definition - Interpretations and models in propositional logic ...
It's possible that considering propositional logic is making this too simplified, and that, at the cost of some additional complexity, the distinctions would be clearer in predicate logic. For example, you …
Propositional Logic Proof using I.P. or C.P or rules of inference
Apr 26, 2017 · I'm attempting to solve a proof my professor asked. We are able to use any of the rules of inference, Indirect Proof or Conditional Proof. Every time I think am making progress I run into a brick …
What is the logical operator for but? - Mathematics Stack Exchange
An alternative way of conveying the same information would be to say "I am fine and he has flu.". Often, the word but is used in English to mean and, especially when there is some contrast or conflict …
discrete mathematics - When a proposition is satisfiable and valid ...
Feb 18, 2021 · The statement of the problem is confusing me. I don't understand whether it is asking for the definition of satisfiable proposition and valid proposition separately, or it is asking when a proposit...
Expressing "there is exactly one" - Mathematics Stack Exchange
I'm trying to express ∃!x: (P(x)) ∃! x: (P (x)) in a different way. i want to know how to express it with the other quantifiers. Here is what I have tried: ∃!x(P(x)) = ∃x:(P(x)∧∀y,y≠ x(¬P(y))) ∃! x (P (x)) = ∃ x: (P …
incompleteness - What is the difference between Completeness and ...
From the perspective of trying to write down axioms for first-order logic that satisfy both completeness and soundness, soundness is the easy direction: all you have to do is make sure that all of your …