Tagged Questions
0
votes
1answer
36 views
Confusing symbol in papers on hybrid logic
In literature about hybrid logic I'm reading for my thesis I've come across the following symbol:
::=
Now, I've never seen this notation before. I can also not ...
1
vote
3answers
54 views
Using $p\supset q$ instead of $p\implies q$
I saw that a use for the notation $p\supset q$ instead of $p\implies q$
that got me a bit confused.
One occurrences is in this Wikipedia link.
It seems to me opposite than what it should be, let me ...
2
votes
1answer
39 views
Is it a standard to say that $a \oplus a_{\small 1}=0$ or $a \veebar a_{\small 1}=0$?
I am trying to express the following:
$a$ or $a_{\small 1}=0$ but only one of them equals zero.
so if $a=0$ then $a_{\small 1}\neq 0$ and if $a\neq 0$ then $a_{\small 1}=0$.
And I'm ...
3
votes
0answers
34 views
Definition(s) for variable binding in first-order logic
The following statement made me realize that variable binding can be defined in first-order logic:
The same holds for λ terms to define functions. There is no reason that they could not be ...
6
votes
1answer
241 views
What are $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$?
Sometimes reading on wikipedia or in this site (and in very different context like topology, arithmetic and logic) I have found these symbols $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$. They are ...
2
votes
1answer
90 views
In Logic is ⇒, →, and ⊃ basically the same symbol?
I need to create a few truth tables and I got confused by the logic symbols as some of the questions use either one or the other which is really confusing especially if they all mean the same thing.
...
4
votes
6answers
152 views
Negating A Mathematical Statement
Regard this statement $ x \ge 0$. According to my teacher, by negating this statement, it will become $ x < 0$. Why is this so; why does the $\ge$ morph into $<$, and not into $\le$?
12
votes
5answers
388 views
Notation Question: What does $\vdash$ mean in logic?
In a "math structures" class at the community college I'm attending (uses the book Discrete Math by Epp, and is basically a discrete math "light" edition), we've been covering some basic logic.
I've ...
1
vote
1answer
119 views
Logic about systems?
In Godel's Incompleteness Theorem, his theorem is about a system of logic. Where can I find more about this study, especially the notation?
EDIT
I mean logic about systems in general. I worded the ...
1
vote
2answers
94 views
Logic Notation question (specifically about logical equivalences)
$$\text{Equivalence}$$
$p \land T \equiv p\tag{Identity law 1}$
$$p\lor F \equiv p\tag {Identity law 2}$$
$$p\lor T \equiv T\tag{Domination law 1}$$
$$p\land F \equiv F\tag{Domination law 2}$$
...
1
vote
1answer
57 views
ZFC Union axiom
Maybe I'm just need to buff up on my logic notation, but I don't fully understand the following:
$$\exists y\forall z \left(\exists w(z\in w\wedge w\in x)\implies z\in y\right)$$
How should I ...
6
votes
3answers
342 views
Difference between $\implies$ and $\;\therefore\;\;$?
I've seen both symbols used to mean "therefore" or logical implication. It seems like $\therefore$ is more frequently used when reaching the conclusion of an argument, while $\implies$ is for ...
0
votes
2answers
76 views
$\leq$ operation and logical error
We define $x \leq y$ operation as '$x<y \ \ or \ \ x=y$'. But this is false when both $x<y$ and $x=y$ as both can not be true at the same time. But I read text books that use this expression in ...
1
vote
3answers
124 views
Simple predicate calculus
All I want to do is write the following things into notation.
My trouble is in inserting the correct order and understand where to use the same variables.
The predicates are Students, Answers, and ...
0
votes
0answers
151 views
Questions regarding set theory notation
I’ve got some questions regarding set theory. I am struggling to find the right notation in order to express a number of conditions. I have a set named A that ...
