All Questions
Tagged with propositional-calculus boolean-algebra
37
questions with no upvoted or accepted answers
3
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0
answers
102
views
Do the integers 1 and 0 mean different things in Boole's original logic and modern Boolean algebra?
I understand that the modern notion of Boolean algebra was adapted by Peirce, Schroder and others from Boole's logic of classes. Boole spoke of 1 and 0 as representing the Universe of Discourse and ...
- 79
2
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0
answers
37
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When are two propositional formulas dependent?
The following question has arisen when considering dependencies induced by probabilistic logic programs:
Let $A_1, \dots, A_n$ be proposition symbols, and let $\Omega_n$ be the set of all truth value ...
- 31
2
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60
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Are ultrafilters precisely the designated sets in semantics(es) for classical logic?
I'm messing around with ultrafilters to try to understand them better. It seems as if ultrafilters work well as sets of designated truth values in matrix semanticses for classical logic.
This also ...
- 11.8k
2
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253
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How can I find the CNF of ($A$ and $B$ or $C$) and ($B$ or not $C$) using a Karnaugh map?
$$(A\land B \lor C) \land (B \lor \lnot C)$$
I know how to create the truth table and Karnaugh map of a logic expression. But I couldn't find exactly how to calculate the simplified CNF of it using ...
2
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0
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68
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why does a closed circuit represent a false proposition? (Claude Shannon thesis)
In reading through Claude Shannon's paper: A Symbolic Analysis of Relay and Switching Circuits.
As a software engineer, I got confused by Shannon's choice to have 0 as representing a closed circuit, ...
- 277
2
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0
answers
149
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How many distinct subsets of binary boolean operators are closed under composition?
Question:
There are $2^4=16$ distinct binary boolean operators. Two operators are regarded the same if one can be obtained from the other by exchanging the operands (input). It is easy to see only $...
- 4,223
2
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142
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Boolean algebras as models of (quantifier-free) monadic predicate logic
Suppose we have a Boolean algebra over $n$ bits, meaning when viewed as a vector space over $F_2$, the dimension is $n$.
Then we can define $n$ unary predicates $P_n$ which return the value of the $n$...
- 7,950
1
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73
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How to show $\{0, \vee, \leftrightarrow \}$ is functionally complete/ incomplete?
I'd like to provide an attempt, but all I can think off is trying to construct one of the following complete set of boolean functions and have been unsucessful in that. I can only get an additional ...
- 871
1
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0
answers
92
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How do I prove this logical equivalence?
$\phi$ is a well formed formula.
f($\phi$) is given by replacing ∧ with ∨ (and vice versa) and 1 with 0 (and vice versa) in $\phi$.
g(f($\phi$)) is given by replacing all literals in f($\phi$) (...
- 111
1
vote
1
answer
257
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Rewriting a boolean expression using different literals
I'd like to implement an algorithm to rewrite a boolean expression as a sum of products of different boolean expressions (expressed as new literals).
Example
Let's say that I have some literals $A_0,...
- 111
1
vote
0
answers
68
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can you help me find the dnf of this expression ? i got messy
I want to find the DNF of the following expression but it got all messy.
I also tried it in wolfram alpha, and of course it showed i really need the steps you need to make to get there $\dots$
This ...
- 11
1
vote
0
answers
1k
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A reduction of 3-CNF down to 2-CNF for boolean satisfiability
Could you please review the following candidate solution for the boolean satisfiability problem?
It is known that 2-CNF has a polynomial solution.
Now consider we have a 3-CNF (AFAIK, it's proven ...
- 153
1
vote
0
answers
284
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How to prove something is not a logical consequence of 2 propositions.
I have a question where I have to show that the third statement is not a logical consequence of the 1st two using a truth table. I've seen how you'd do if there are only two (How to prove logical ...
1
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0
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51
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Is this a Boolean algebra? (proof)
Let $B=\{0,1\}$ and the binary operations $\oplus,\cdot$
We define a bijection $\varphi$ s.t.:
$$
\varphi:B \longrightarrow L=\{\mathbf{False},\mathbf{True}\},
$$
$$
\varphi(x):=
\begin{cases}
\...
- 2,031
1
vote
2
answers
194
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SOP expression simplify
I wanted to know how to simply this SOP expression using Boolean Algebra :
F= A'BC'+A'BC+ABC
I got this answer using K - Map: (A'B+BC), but I want to know how do get it using Boolean Algebra Rules.
...
