Questions tagged [logic]

Questions on use and formulation of logical operations, including both functions for programming and for mathematical operations.

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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. <...
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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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1 vote
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32 views

Reduce works for simple inequalities in Reals but not in Integers

In the domain of Reals Reduce correctly reduces the system to True: ...
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1 vote
2 answers
80 views

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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1 answer
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how to unfolding (expand) logical expression?

How to expand the following expression ...
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0 answers
42 views

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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1 vote
1 answer
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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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6 votes
1 answer
308 views

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 ...
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  • 289
3 votes
1 answer
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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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  • 2,062
2 votes
4 answers
153 views

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 ...
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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....
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1 answer
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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. ...
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1 vote
1 answer
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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 ...
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17 votes
1 answer
986 views

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." ...
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5 votes
0 answers
200 views

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 ...
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3 votes
1 answer
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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 votes
1 answer
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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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2 votes
1 answer
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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 answer
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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). ...
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2 votes
0 answers
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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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1 vote
1 answer
58 views

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 votes
3 answers
253 views

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 ...
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  • 343
1 vote
1 answer
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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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  • 145
2 votes
0 answers
55 views

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 ...
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  • 225
1 vote
1 answer
133 views

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 ...
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15 votes
0 answers
162 views

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 ...
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0 votes
1 answer
114 views

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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  • 145
1 vote
0 answers
68 views

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 ...
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  • 973
5 votes
2 answers
946 views

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 ...
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1 vote
1 answer
87 views

Convert ProofNotes to $ \mathrm\LaTeX $ logic expression

The following code will generate some ProofNotes: ...
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  • 225
7 votes
1 answer
188 views

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}[,]...
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  • 225
1 vote
1 answer
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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 ...
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1 vote
1 answer
66 views

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 ...
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0 votes
0 answers
157 views

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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2 votes
0 answers
84 views

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 ...
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23 votes
0 answers
979 views

Mathematica vs. state-of-the-art SAT solvers

I found some fascinating paper by Marijn Heule and Oliver Kullmann on advances in SAT solvers and automated reasoning. In particular, the authors where able to show (a year earlier) a breakthrough ...
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1 vote
1 answer
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Can I get mapping as output from SatisfiabilityInstances?

Consider the code: SatisfiabilityInstances[Implies[a, b], {a, b}, All] (* output *) {{True, True}, {False, True}, {False, False}} I would like to obtain the ...
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6 votes
3 answers
344 views

How to realize a formal grammar in Mathematica?

This is important because translators and compilers are based on formal grammars. Solid textbooks on algorithmic lanquages include a chapter or an appendix devoted to formal grammars. Let us ...
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0 votes
1 answer
88 views

Why is Resolve not reducing my set?

I tried to run the following code to get the region where (v,b,r) satisfies some complicated set of inequalities. ...
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0 votes
1 answer
86 views

Problem with Resolve

The question is: for which values of the parameter $a$ the equations $$4^{x+1}-3\ 2^{x+3}=2^{x+4}-64 $$ and $$(a+30) \left(-9^x\right)+3^{x+4}+27^x=a \left(81-10\ 3^{x+1}\right) $$ are equivalent? ...
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3 votes
0 answers
167 views

How to implement projective geometry in MMA?

I'd like to implement 2D projective geometry in Mathematica, making use of the FindEquationalProof command. Up to Wiki ru.wikipedia.org (This topic is better ...
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6 votes
1 answer
326 views

FindEquationalProof with Logic in Wolfram Mathematica

I try to "make" proof in Wolfram Mathematica. Thats a proof: if a->b and b->c then a->c I tried ...
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1 vote
1 answer
81 views

How to judge whether a relation is true or false

$x$ is a real number, how to judge $x+1>x$ is true using Wolfram.
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3 votes
0 answers
2k views

Semantic tableaux generator

I would like to use Mathematica to automatically generate a semantic tableaux (truth tree) from a formula in propositional logic). Here is an example formula: $$(a \lor\lnot b )\land b$$ Here is ...
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6 votes
3 answers
328 views

Why Can't Mathematica Resolve this Simple Quantified Expression?

I've been using Mathematica as a hobbyist, off and on, for some time. So while I'm by no means an expert I've used it long enough to know that what might seem obvious to me is not necessarily obvious ...
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3 votes
2 answers
161 views

How to test all possible input for a logic function?

I have a logic expression: f0[a0_, a1_, a2_, a3_] := a0 And Not a1 And Not a2 And a3 Or Not a0 And a2 And a3 Or Not a0 And a1 And a3, I know I should use ...
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1 vote
1 answer
76 views

Logical equivalence of logical propositions that are converted from compact (implicit) notation to Mathematica code

Here is logical formula: $$\bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,j,n)$$ To use it in Mathematica I use that code: ...
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3 votes
1 answer
140 views

Is it possible to resolve this proposition?

Executing this code (see MSE for its background) ...
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4 votes
2 answers
187 views

How can I input a logical proposition using a compact (implicit) notation?

I have: $$\bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,j,n)$$ How can I write it in Wolfram Mathematica code? I tried this way, but it does not work: ...
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