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1
vote
0answers
45 views

What is this weird gate?

This came from a picture of something that I'm supposed to make, and I can't find it in the program I'm supposed to use (LogicWorks). It looks like it 'not's only one of its inputs, but that doesn't ...
5
votes
2answers
2k views

Why do ¬, ∀ and ∃ have the same precedence?

I thought the order of precedence of operators and quantifiers was arbitrary, but I don't really understand why those three have the same "strength" in relation to other operators (e.g., ¬ will have ...
-2
votes
1answer
78 views

How to negate this one?

How can I negate the following sentence: For all words x from L with |x|>= n , exists decomposition x = uvw with |uv| <= n and |v| >= 1, so for all i >= 0 , is valid that u(v)^iw in L is.
0
votes
1answer
45 views

Question on interpreting logical notation, relating to alphabets, theoretical comp sci

$\exists x \in \Sigma^* (t=sx)$ Have I interpreted the above into words correctly?: "There exists a symbol 'x', which is a member of the set which contains all possible strings of alphabet sigma, ...
0
votes
0answers
88 views

What does an = sign with an x beneath it mean?

I am studying for a test in Logic right now, and saw the symbol $\underset{x}{=}$, which is used like this: $I \underset{x}{=} I'$. I've seen it in the solutions of questions like this one: Prove ...
1
vote
1answer
22 views

What does $\alpha_r\supset\beta_r$ mean in the tolerance definition of System Z?

I'm reading up on System Z introduced by Judea Pearl (in System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning). A central definition is that of tolerance of a ...
1
vote
2answers
8k views

Operator precedence in propositional logic

there is some kind of priorities for the elements in propositional logic ? for example : p ∧¬q → r , given this ,we there may be two options (p ∧¬q) → r OR p ∧ (¬q → r) , which one is the correct ?...
6
votes
4answers
166 views

Can I use ellipses in first order logic

I ask, because I have to come up with a first-order logic sentence that shows that there are exactly N objects in the universe. What I've been able to come up with is: $$ \forall x \; \exists y_1, ...