Mathematica Stack Exchange
Mathematica Stack Exchange

Questions tagged [logic]

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

How to use Logical Operators

Logic and Boolean Algebra

158 questions
7
votes
3 answers

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 consider a formal grammar from the cited Wiki article…
user64494
  • 26,149
  • 4
  • 27
  • 56
6
votes
3 answers

What exactly is Implies? Is it a logical test?

I ran the following to simplify my logical test (expecting something in terms of And and Or ...) FullSimplify[Not[a] || (a && b)] and was surprised to see $a \Rightarrow b$ (*Implies[a, b]*) . I thought "implies" is a statement you deduce from a…
QuantumDot
  • 19,601
  • 7
  • 45
  • 121
5
votes
3 answers

Apply Complement to a list of matrices

With a list of defined matrices list={a,b,c,d} How can I apply Complement to obtain Complement[list,{b,c}]=={a,d}
Phillip Dukes
  • 938
  • 5
  • 18
3
votes
2 answers

Boolean value of proposition assuming previous boolean values of parts of the proposition

Is it possible to ask Mathematica to give us the boolean value of a proposition assuming the boolean value of some parts of it? For instance, give the boolean value of $p\vee q$ assuming that $p$ is true and $q$ is false.
Concept7
  • 139
  • 1
3
votes
1 answer

How can we express more complex logical expressions in Mathematica?

How can we use quantifiers to express something a bit more complex such as - for example - the definition of limit: $$\forall \epsilon >0\hspace{2mm} \exists \delta >0 \hspace{.5mm} :\hspace{.5mm} 0<|x-a|<\delta \implies |f(x)-L|<\epsilon$$ It's not…
Red Banana
  • 5,329
  • 2
  • 29
  • 47
3
votes
1 answer

Is it possible to resolve this proposition?

Executing this code (see MSE for its background) ForAll[{a, b, c}, Implies[ForAll[x, -1 <= x <= 1, RealAbs[a*x^2 + b*x + c] <= 1], ForAll[x, -1 <= x <= 1, RealAbs[c*x^2 + b*x + a] <= 2]]] Resolve[%, Reals] , I obtain Beep:The kernel Local has…
user64494
  • 26,149
  • 4
  • 27
  • 56
2
votes
1 answer

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. P1 = j == i && j < 0 && t >= -j Q = t>0 FullSimplify[ Reduce[ForAll[{i, j, t}, Implies[ P1 , Q]]]] When I run this I get an…
Azzurro94
  • 499
  • 2
  • 9
2
votes
0 answers

Logic - why isn't 'True' doing what I expect it to?

I have the following code test[variable_: 0] := Module[{}, If[variable != True, Print["worked"]]; ]; test2[variable_: 0] := Module[{}, If[variable == True, Print["worked"]]; ]; If I run test2[True] I get "worked" as I expect. But…
Tomi
  • 4,366
  • 16
  • 31
2
votes
2 answers

Discarding a triple because of the absence of monotonicity

Sorry for the title, but I can not think of a better one. Starting informally, monotonicity says that if the number of votes for i is greater that the number of votes for j, the number of seats for i must be greater or equal to the number of seats…
cyrille.piatecki
  • 4,582
  • 13
  • 26
2
votes
0 answers

Translating arguments into Predicate Logic

Consider the paragraph given below. If all the boy friends are either HH or NN, then there are no CC.but Jone is a CC. therefore some boy friends are not NN.. a) translate the following arguments into Predicate Logic b) using the change of…
user48264
  • 21
  • 1
1
vote
1 answer

Resolving a logical statement

I would like to test whether f[n] > 0 and f[n + 1] > 0 implies f[n + 2] > 0. This is what I tried: f[n] == n*f[n - 2] + f[n - 1]; Resolve[ForAll[n, Implies[n > 0 && f[n - 2] > 0 && f[n - 1] > 0, f[n] > 0]], Reals] I was expecting output True, but…
user31953
  • 13
  • 4
1
vote
2 answers

How to unfolding (expand) logical expression?

How to expand the following expression (b == 0 || b == \[Pi] ) && (a == 0 || a == \[Pi])) || (3 a == 2 \[Pi] && 3 b == 4 \[Pi]) || (3 a == 4 \[Pi] && 3 b == 2 \[Pi]) to the following…
M.K
  • 255
  • 1
  • 7
1
vote
1 answer

Checking whether statement A implies statement B

I would like to ask Mathematica "does statement A imply statement B?" and get a yes or no (true or false) answer whenever one exists. I have entered the input Reduce[ Implies[x>0 && y>0 , xy > 0] ]. The output I was expecting was true. The output I…
Ubiquitous
  • 863
  • 2
  • 7
  • 15
0
votes
2 answers

PEANO Integers using successor function

I'd like to define the integers and operations on it by using terms. Starting from zero->init[] and nth->succ[n-1th] where succ[] is the successor function. I believe the operations could be implemented as…
Chris
  • 3
  • 1
0
votes
1 answer

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). While the details of my effort are in development…
TomR
  • 101
  • 2
1
2