Questions tagged [logic]
Questions on use and formulation of logical operations, including both functions for programming and for mathematical operations.
144
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Symbolic solutions to systems of Boolean constraints?
Is it possible to solve a system of Boolean constraints symbolically? I'm trying to solve systems like the following, where $X$ is the unknown Boolean expression I'm trying to find, $a, b, c$ are the ...
- 440
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1
answer
105
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Is there a function which tests whether a Boolean expression is an inequality?
For something I am doing in Mathematica, it would be very helpful to have a function f[] which, when applied to an atomic Boolean expression, returns True if the Boolean expression is an inequality, ...
- 23
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25
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How can I combine an identity predicate with first-order predicates while using FindEquationalProof
I am trying out some of the automated theorem proving in mathematica, and for my test case am working with Tarski and Sczerba's (mostly) first-order axiomatization of Affine Geometry, which has just ...
2
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1
answer
75
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Implies cannot find an answer
I have a simple relation and I try to find if P implies Q or not. I expect to get True because it is somehow obvious for me.
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31
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How to count the number of disjoint regions covered by a Boolean expression?
Consider the following Boolean expression as an example:
...
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60
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Does applying Reduce result in an equivalence or a oneway implication or both? [closed]
If I type something like this into Mathematica:
...
- 1,149
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148
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Generating language from grammar
To be concrete, consider the following formal grammar:
$$S \rightarrow aSb$$
$$S \rightarrow \varepsilon$$
The language generated by this grammar is $L = \{ a^n b^n | n \geq 0 \}$. How can I implement ...
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1
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Make a plot of the nth prime divided by n*log(n) ,for n from 2to1000 [closed]
ListPlot[Table[RandomReal[n, Prime[1000]]/n*log (n), {n, 2, 1000}]]
this is all i can do.
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Field axioms in Mathematica
I don't understand the result of
AxiomaticTheory["FieldAxioms", "Axioms"]
...
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1
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Need help with Assumptions for an integral
I want to solve this Log, Integrate[2a Log[-a+((A0 + (y-y1)²)^½, {y1, 0,b}]
But Mathematica only gives me long conditional expressions or imaginary numbers. I (my thinking which can be wrong) assume I ...
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6
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2
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110
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How to solve logic problem with a joker sometimes tell truth and sometimes lie?
If there are only truth teller and liar, I used to solve with BooleanConvert or SatisfiabilityInstances. However for this one, ...
- 101
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Evaluation process of And, Or,
Small questions about evaluation process of And, Or.
code 1)
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- 4,037
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What's wrong with or? [closed]
Consider
Clear[x];
x = 2;
x < 2.9 || x > 3.1
This yields
True
So, everything is o. k. (interesting)
But when you replace ...
- 123
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1
answer
99
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Simple way to express disjunction likes x==a || x==b || x==c ||
Is there a simple, shorter way to express x==1||x==2||x==3... ?
For example, suppose that there is a roulette having integers 1 to 10
1> assigin 10% for 1 to 8 ...
- 4,037
2
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3
answers
251
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How to prove or disprove an inequality with Mathematica?
I mean there exist $\lambda>0, x\in \mathbb R$ s.t. the inequality $$ \frac{3^{\lambda } e^x+e^{3 x}+1}{2^{\lambda } e^{2 x}}<\frac{1}{10^{100}}$$ is valid.
Here are my unsuccessful attempts.
<...
- 23.2k
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Logical functions with no arguments
I am trying to understand how logical functions are evaluated if no arguments are passed to them.
{Or[], Nor[], And[], Nand[], Xor[], Xnor[]}
{False, True, True, ...
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Reduce works for simple inequalities in Reals but not in Integers
In the domain of Reals Reduce correctly reduces the system to True:
...
- 1,325
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110
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How to transfer the logical expression to list of list?
As described in the title, I would wondering:
How to transfer the solutions give by the following code
...
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2
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53
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Ordinal arithmetic
How can I compute with ordinals in mathematica? For instance, I'd like to query $2+\omega > 1 + 2 \omega$.
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116
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How to convert this Mathematica expression to another, as described here?
I am working on a function of which the core will consist of something like:
...
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1
answer
330
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How can I self-define a keyboard entry for 3-dot "Because"?
In Mathematica, there already exists a keyboard entry for 3-dot "Therefore", which provides great convenience for input as shown below.
However, I find it a little odd that for its ...
- 453
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1
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58
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Intermediate results from SatisfiabilityInstances
I have a large logical expression, with roughly 100 boolean variables. I am interested in the solution with the smallest numbers of True. It seems there is no such ...
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4
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163
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For all x in {1,2,3}, x is bigger than 4
I am new to ForAll or Exists command.
Resolve[ForAll[x, Element[x, Reals], x > 4]]
gives ...
- 4,037
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0
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38
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LogitModelFit for predicting Categorical Variable
I was wondering how can I use LogitModelFit to predict the probability of a categorical variable based on non-categorially variables ?
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TautologyQ like feature that also works for inequalities
If a=b and b=c, then a=c.
So in mathematica,
TautologyQ[(a == b) && (b == c) \[Implies] a == c, {a, b, c}]
yields 'True'.
If a<b and b<c, then a<c....
- 4,037
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1
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40
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Conditional tab view
I'd like to create a tabview with conditions on it, rather than put the tabview inside an If statement, to reduce the length of my code. i.e.
...
- 53
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1
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204
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How can I change the Mathematica programming for creating a Venn Diagram?
I am working on using Venn diagram to explain logic and logical connections between sets. After coming upon these answers: Create a Venn Diagram,
How to plot Venn diagrams with Mathematica?,
which I ...
- 1,653
19
votes
2
answers
1k
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How can I use Mathematica to solve a complex truth-teller/liar logic problem?
I have a logic puzzle I want to convert to Mathematica to solve:
Person A states, "Exactly two people are truth-tellers,"
Person B states, "I and Person C are truth-tellers."
...
- 1,653
5
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0
answers
229
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Incorrect result by DSolve
For real $x$ consider the trivial equation
$$|y'(x)|=-|x|.$$
Since the left side is always positive and the right always negative, there is no solution.
Let's try
...
- 1,005
3
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1
answer
162
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Axiomatizing naturals
Trying to implement the naturals in Mathematica, I follow E. Mendelson, Introduction to Mathematical Logic, Ch. 3, Par. 1.
Here is my code for the axioms (exept the induction axiom)
...
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-1
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2
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156
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How to check if solution to NSolve exists?
I'm trying to created a table where the entries are values of x, either given by x/.NSolve[...][[1]] or a fixed value x0 if there is no numerical solution. Is there a way to find the truth value for ...
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64
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perform logical or on sublist of a list efficiently
Given a huge list x of 0s and 1s and an increasing list i...
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1
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120
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First Order/Higher Order Logical Forward reasoning in Mathematica (Mathematica for FOL/HOL knowledge base)?
I am trying to develop Artificial Intelligence system that can automatically discover and apply reasoning patterns, templates, strategies (there is even theory for that - Cognitive Task Analysis). ...
- 101
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199
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Natural deduction with FindEquationalProof
Out of curiosity, I'm trying to implement a natural deduction prover in Mathematica using FindEquationalProof. So far, I've implemented a few of the easier rules:
<...
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87
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Solving a ForAll optimization problem in Mathematica
I am trying to solve the following optimization problem in Mathematica:
Minimize[{y0 + y2 m2, ForAll[x, y0+y2 x^2 >= Boole[x>0]]}, {y0,y2}]
Unfortunately, ...
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3
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396
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count conditional items in list
I have a list of the form:
{1,1, (1 if x>y, -1 if y>=x), -1}
I want to count the number of 1's in the list. The output I'm looking for is something of the ...
- 343
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1
answer
109
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Applying functions to members of members... of lists of lists..., etc
Suppose that I have a list of depth $k$, and I want to apply a function $f$ to all elements at level $n$ - e.g. $f,\{\{\{a,b\},\{b,c\}\},\{\{c,d\}\}\},3\mapsto\{\{\{f(a),f(b)\},\{f(b),f(c)\}\},\{\{f(c)...
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Determine if a mathematical statement always holds
I know that $\exists a,a\in\mathbb{Z}\land a+1>a$ is always true, and $\forall a,a\in\mathbb{Z}\Rightarrow a+1>a$ is also always true; I try to use function ...
- 225
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1
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How can I show that the equation holds?
Suppose we have the following data:
$ r=\frac{vk}{h^2}$
$u[i,j]$ is a function of two variables with $i,j$ integers.
$\frac{u[i,j+1]-u[i,j]}{k}=v\frac{u[i+1,j]-2u[i,j]+u[i-1,j]}{h^2}$
Then I would ...
- 530
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201
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Reduce[Sin[x]==0,x] splitting odd and even multiples of Pi
as from Title, I'm wondering why Mathematica does not automatically give a single, simple solution for the problem
Reduce[Sin[x] == 0, x]
for which I obtain the ...
- 221
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1
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168
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Defining relations between functions in Mathematica
I would like to find a way to implement the following in Mathematica:
Let $F$ be the set of real functions $f_1,f_2,\ldots f_n$. The function $\min$ is defined as follows...
$$\min F=f_i\iff \forall ...
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0
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75
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Is there simplest and universal way to ask Mathematica to give you in which cases it is True and in which False? [closed]
This question emerged from this comment.
This answer explains how to do that with particular equation with several steps but I am interested if there exists more simple and universal method to just ...
- 1,139
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2
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958
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Why I am not getting True when testing equation?
My input is:
$ \frac{1}{a^x}==(\frac{1}{a})^x $
I want to get output:
True
But getting output:
$ a^{-x}==\left(\frac{1}{a}\right)^x $
Question: How to get ...
- 1,139
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vote
1
answer
94
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Convert ProofNotes to $ \mathrm\LaTeX $ logic expression
The following code will generate some ProofNotes:
...
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214
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Using logical equivalence to prove PL statements
I'm trying to use those Logical equivalence as axioms to prove some PL statements,
In this case I followed the examples in the documentation that didn't use the build-in logic functions$\{\text{And}[,]...
- 225
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1
answer
140
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Using Select and AllTrue to filter elements of a large nested list based on relations between elements of the smaller nested lists
I tried searching but all similar questions seemed to be based around one Boolean logical statement.
I'm dealing with a nested list of pairs partitions of integers, such that the sum of the two ...
- 13
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vote
1
answer
86
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TrueQ returning False on true, non-numerical statement
I'm trying to test the following logical statement:
state = {{1,1,1}};
Or[state != 0, state != Null]
but it's returning False ...
- 13
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0
answers
187
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Completely expand and simplify logical expressions?
Consider a logical expression such as
expr = (a == b + q - w || c == d) && (q + c - d == w || e == r);
I wonder if there is a function that would ...
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How do I transform a 1st order logic formula into Skolem normal form? [closed]
I have a predicate calculus (first-order logic) problem. I have the formula
$\qquad \forall x[\neg P(x) \land \forall y \neg Q(x,y) \rightarrow \forall x \forall y R(x,y,z)]$
I want to express ...
- 141