Tag: OpenLab8
Logic on Math StackExchange
- bisimulation contraction in Logic [closed] August 12, 2022In Java, I am representing an epistemic logic model using an undirected weighted graph, and I would like to ask how to find all the bisimulation contraction models of this logic modelJarod Chen
- Prove $(\cup a)\cup (\cup b)=\cup(a\cup b)$ August 12, 2022I'm learning ZFC set theory and I'm stuck in this question: $$ (\cup a)\cup(\cup b)=\cup(a\cup b). $$ Here $a,b$ are given sets. MY PROGRESS Here are my steps of proof: \begin{equation*} \begin{split} \forall x(x\in (\cup a)\cup (\cup b) &\leftrightarrow x\in \cup a\vee x\in \cup b\\ &\leftrightarrow \exists u(u\in a\wedge x\in u)\vee \exists v(v\in b\wedge x\in […]Evan_Bradley
- Semidecidable algorithm for first order logic invalidity August 12, 2022I was given a task to write an algorithm that would check if the FOL formula is invalid. The algorithm would run, and if the formula is invalid, the algorithm returns TRUE, otherwise algorithm would hung(run indefinitely). I know that there is a semantic tableau method, which checks if a formula is valid. But the […]nutella_eater
- Why do intuitionists think that proving $\neg \neg P$ merely constitutes a proof of the inexistence of a proof for $\neg P$? August 11, 2022In every case of $\neg \neg P$ that I've come across, the statement $\neg P$ has been disproven. Never has such a proof merely been proof for the inexistence of a proof for $\neg P$. Take the proposition $\neg P = 3/2 \in \Bbb Z$. $ P = 3/2 \not \in \Bbb Z$. I am […]user110391
- Exercise 1.1 in introduction to logic stanford coursee August 11, 2022In this exercise in the introduction to logic Stanford course, the last sentence saying : "Abby does not like Cody or Dana.". doesn't that mean that "Abby doesn't like Code or Abby doesn't like Dana" and for the whole sentence to be true there must be at least one sentence of the two to be […]Amr S.
- Negation of The Statement "The sides of the triangle have different lengths" August 11, 2022In exercise 2.13 of page 43 of the book Mathematical Proofs: A Transition to Advanced Mathematics the reader is asked to state the logical negation of some statements. Of these, I find the authors' answer to one of them baffling. The statement to negate is: "Two sides of the triangle have the same length." The […]mali1234
- Can the converse of this predicate axiom be proved a theorem? August 11, 2022In predicate calculus, one of the logical axioms is given like: Let $p,q$ be any formulae in predicate calculus and variable $x$ is not free in $p$ (or doesn't occur), then the formula below is an axiom: $$ \forall x(p\to q)\to (p\to \forall x q). $$ I'm wondering if the formula below is a theorem, […]Evan_Bradley
- How to prove that true statements about the element of a set of size one, hold true for all elements of that set? [closed] August 10, 2022I'm not well versed in formal notation yet, but here's my attempt: $A = \{a\} \rightarrow \left( s(a) \rightarrow \forall x \in A, s(x) \right)$ What is a proof of the above implication?markonius
- How to show $IMP(FO)\equiv IMP(IMP(FO))$? August 10, 2022I am trying to solve exercise 8.5.11 of Finite Model Theory by Ebinghaus and Flum, which asks to show: $IMP(FO)\equiv IMP(IMP(FO))$ Maybe I have some problems with understanding the definition of $IMP$... I supposed that if $log$ is some logic, then $log\leq IMP(log)$ by choosing $m=0$ so $IMP(FO)\leq IMP(IMP(FO))$, for the other part I need […]Arlin
- Is $\forall x(x\in\varnothing)$ true or false? August 10, 2022I know that $$\forall x(x\in\varnothing)$$ is equivelent with "There is no element in Universe such that $x$ is not in $\varnothing$." but, is $\forall x(x\in\varnothing)$ true or false? Is it an example of vacuously true? How about the Univers is the empty set? How about the Univers is not the empty set?Stats Cruncher
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