Questions tagged [logic]

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

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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 votes
2 answers
101 views

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, ...
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2 votes
1 answer
76 views

Evaluation process of And, Or,

Small questions about evaluation process of And, Or. code 1) ...
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2 votes
1 answer
289 views

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 ...
2 votes
1 answer
89 views

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 ...
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2 votes
3 answers
226 views

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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0 answers
60 views

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
0 answers
33 views

Reduce works for simple inequalities in Reals but not in Integers

In the domain of Reals Reduce correctly reduces the system to True: ...
1 vote
2 answers
81 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 ...
0 votes
1 answer
78 views

How to unfolding (expand) logical expression?

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

Ordinal arithmetic

How can I compute with ordinals in mathematica? For instance, I'd like to query $2+\omega > 1 + 2 \omega$.
1 vote
1 answer
107 views

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: ...
6 votes
1 answer
314 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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3 votes
1 answer
56 views

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 votes
4 answers
157 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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0 answers
31 views

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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1 vote
0 answers
82 views

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 vote
1 answer
32 views

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
173 views

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 ...
19 votes
2 answers
1k 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." ...
5 votes
0 answers
205 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
147 views

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
75 views

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 ...
2 votes
1 answer
60 views

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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0 votes
1 answer
69 views

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
137 views

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
63 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, ...
3 votes
3 answers
297 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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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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2 votes
0 answers
56 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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1 vote
1 answer
144 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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16 votes
0 answers
164 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 ...
0 votes
1 answer
126 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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1 vote
0 answers
70 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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5 votes
2 answers
948 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
88 views

Convert ProofNotes to $ \mathrm\LaTeX $ logic expression

The following code will generate some ProofNotes: ...
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7 votes
1 answer
195 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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1 vote
1 answer
114 views

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 ...
1 vote
1 answer
69 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
166 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
85 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
1k 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
59 views

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 ...
6 votes
3 answers
361 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
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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. ...
0 votes
1 answer
87 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
172 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
346 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 ...