All Questions
Tagged with propositional-calculus boolean-algebra
37
questions with no upvoted or accepted answers
1
vote
0
answers
140
views
Propositional formula proof, general version.
I'm really stuck at proving general versions for any propositional formula for example:
I) Use truth table to prove this De Morgan's law
$$ \lnot (P \land Q) \equiv \lnot P \lor \lnot Q $$
Which ...
- 159
1
vote
0
answers
61
views
Model checking in epistemic logic
I am trying to program a model checker for dynamic epistemic logic, but I am not quite sure how to do it.
As far as I understand, model checking means to take a propositional formula and go through ...
- 819
1
vote
0
answers
112
views
how to determine if formula satisfies without creating a truth table
$(p \wedge q \wedge r) \wedge (\neg p \vee r)$
So far, what I have got is that $(p \wedge q \wedge r)$ satisfies because if $p$, $q$ and $r = 1$ then $(p \wedge q \wedge r)$ also $= 1$. For $(\neg p \...
- 11
1
vote
0
answers
254
views
Monotonic operators in classical logic
Which means monotony for a logical operator, and affinity, in propositional calculus affinity..., here on wiki do not quite understand!!
- 379
1
vote
0
answers
784
views
Dual formula in propositional logic
There's something I don't understand in my course on propositional logic.
In the case of x being a variable, the definition of its dual is x* = x. Right.
However, further in the course, there's a ...
- 11
1
vote
0
answers
737
views
Inverse function in multi-valued logic through the Webb function
Let Webb function in multi-valued logic as $Webb(x, y) = W(x, y) = Inc(Max(x, y))$. There is a theorem about any function in any multi-valued logic can be represented through the Webb function.
Then ...
- 1,211
0
votes
0
answers
34
views
A generalized algorithm to convert a formula in algebraic normal form to an equivalent formula that minimizes the number of bitwise operations
In this question, “bitwise operation” means any operation from the set {XOR, AND, OR}. The NOT operation is not included because ...
- 922
0
votes
0
answers
45
views
Can any finite set of binary sequences be expressed as CNF/DNF
I am new to logic and cannot figure out if there are instances when a given set of binary sequences of equal length is not possible to express as a conjunctive or disjunctive normal form. If such sets ...
- 397
0
votes
0
answers
84
views
Prove $\vdash(A\supset B)\supset C\equiv C\overline{\vee }[A\wedge \neg(B\vee C)]$ using your favorite method
I've been playing with Boolean logic vs ordinary laws of logic like DeMorgan's etc., and I've come up with the following theorem in about 4 lines: $$[(A\supset B)\supset C]\equiv \left\{C\overline{\...
- 1,545
0
votes
0
answers
138
views
Provide a few examples of Boolean algebra where carrier is a finite set of finite sequences (ordered set)
I study Boolean Algebra and it is clear when: (carrier is a power set, union, intersection), (set of all divisors of n, lcm, gcd), (the set of propositional functions of n given variables, conjunction,...
- 435
0
votes
0
answers
103
views
Boolean Algebra Simplification Unknown Step Introduce Variables
I've been trying to interpret a logical proposition for several days. I need to simplify, I can't do it with the laws that I know, but using online tools I can find the result, but in the step by step ...
- 1
0
votes
3
answers
73
views
Why is $ (a \lor b \lor c) \oplus ( a \lor b)$ equivalent to $\lnot a \land \lnot b \land c$?
I'm having a hard time understanding why $(a \lor b \lor c) \oplus (a \lor b)$ (where $\oplus$ stands for XOR) is equivalent to $\lnot a \land \lnot b \land c$ in propositional logic. Any help would ...
- 9
0
votes
0
answers
38
views
How to solve this boolean logic question?
Formalise the following argument in Boolean logic, and decide whether it is correct or not.
Explain your answer.
If the burglar is from France, then he is tall. If he is tall, then he came through ...
- 115
0
votes
0
answers
36
views
Are the statements equal?
Is this true?
$$ \bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p_{i,j,n} \Longleftrightarrow \bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p_{(i,j,n)} \Longleftrightarrow \...
- 368
0
votes
0
answers
70
views
What kind of algebraic structure is the one with NAND?
In her book Model Theory, María Manzano mentions the following kinds algebraic structures:
Group
Rings and fields
Order
Well-order
Peano structures
Boolean algebras
Bolean rings
Nevertheless, it's ...
- 451