**617 logic questions.**

The idea I'm thinking of is about a top-down approach for AI. I would like to know if there can be a model for computers so that they can perform causal reasoning. It seems that causal relation can be ...

I have some data in excel that has many formulas in, for ease I have copied and pasted the values into a block range. The formula's give an output of 0 when not applicable and the correct number when ...

It's possible that in some following state you have that $x,y$ are
both true simultaneously.
I have taken a look on Wikipedia: https://en.wikipedia.org/wiki/Computation_tree_logic
and if I ...

Propositional extentionality in the lean theorem prover is stated as the following axiom:
axiom proptext {a b : Prop} : (a $\iff$ b) \to a = b
My confusion about this is as follows: Previously I’...

Sentence: From every reachable state it is possible to reach a state where $p$ is true.
How do you write this sentence as a CTL formula? So far I only dealt with CTL syntax and trees but maybe it ...

I know that there exist type theory based proof-checker, and I know that there are logic/sequent-calculus based automated theorem provers.
But I haven’t heard of a type-theory based automated theorem ...

I originally posted this on math.stackexchange, but then deleted it and moved it here since I think it would fit this site more.
I saw a claim in a slideshow from a basic computer architecture course ...

I am trying to convert the following 2-sat clauses to implications and then draw the implication graph.
The clauses are: ...

Let's say I have a program P, in form of a binary code for x86 architecture.
I want to find a Boolean formula F (in form of CNF, or something like that), such ...

I am somewhat aware of the correspondence between (tuple and domain) relational calculus, relational algebra, and SQL. To the best of my understanding, one should be able to automatically convert a ...

So this was an interview question I had a few weeks back that I just haven't been able to think of how to solve...
Given a random number generator that returns 0 or 1 with a 50% chance of either, ...

I need to create a HDL which will use logic gates to demonstrate if something is a negative number in two's complement. The input is 8 bits, while the output is 1 bit, and if the input is a negative ...

I want to minimize DNF formula which has ~200k products combined into a sum.
The depth of that formula is 2 - first level is the OR, and second level is AND for all conjunctions.
I have tried using ...

Is there an intuitive meaning of XOR of two numbers not involving binary and just decimal? Or is is always converted into binary and then XORed?

I want to detect the non existence of a cycle in a graph using Datalog (which is a declarative logic programming language).
The proposed solution was:
...

What if an $L$-complete problem has $NC^1$ circuits? More generally, what evidence is there against $NC^1=L$?

To find the difference, I'd just encountered with assertions below about temporal logic in Wikipedia:
another variant of modal logic sharing many common features with
dynamic logic, differs from ...

Define a relation $\equiv$ on the set of modal formulas by
$\phi \equiv \psi \Leftrightarrow (\forall M\forall w, M,w \models \phi\Leftrightarrow M,w \models \psi)$ (so it is an equivalence relation)
...

Suppose st: string -> nat and X stands for the string 'X'.
Given the hypothesis ...

Hello I have a slightly unusual question which relates to a definition of filtration structure. The following is my current state of the definition:
$ \mathcal{M} = (W, R, L) $, W is a set of worlds,
...

Given the question below:
Consider that, on the procedure below, the variable X is defined globally and the parameters of the vr function are passed by value
...

So I am studying for an exam which includes unification. I am fairly confident in unifying and calculating the mgu. But I am having trouble understanding how to prove if the following is unifiable or ...

I am trying to simplify the following equation and I am getting stuck on a line and I can't cut it down any further. I'm not sure if certain 'moves' are legal or not.
F(A,B,C,D) = A'B'C' +ACD + A’BCD ...

One can define the semantics of one definite word using the references to real world entities, relationships with the other words and other concepts and represent all this knowledge about this one ...

I found it a little bit difficult and confusing to define the complement language in specific cases. For example, take the next language:
$$L = \left\{\langle M, w\rangle \;\middle|\; \begin{array}{...

It can be easily seen that solving systems of polynomial (i.e. not necessarily linear) equations is NP-Hard via reduction from SAT. Furthermore, because the existential theory of the reals is ...

Is it there any computer or cellular automaton or model of the brain where they could compute logically impossible things and incomputable things?
For example, if we wanted to compute/simulate/think ...

I am trying to understand this program and the respective forest. This is from the book Logic,Programming and Prolog by Ulf Nilsson.
Question:
In the main tree, why from ←off_gound(a) can you ...

Here is the context (Structure and Interpretation of Computer Programs, section 1.1.8, under heading "Local names"):
A formal parameter of a procedure has a very special role in the procedure ...

We define a signature as a triple $$\Sigma\ =\ (S,F,\mathrm{type})$$ where $S$ is a set of sorts, $F$ a set of $n$-ary function symbols $f$ of the type $\mathrm{type}(f)$ $=$ $(M_1,\dotsc,M_n\...

I just and simply want to know if whether or not exist any horn formula that is equisatisfiable to $(p\lor q)$. I would also be interested to know if there also exists equivalent.

A model is finite. How to replace an some predicate $P$ with a formula $\varphi$?
Example: $\{a, b, c\}$, $A = \{a, b\}$,
$\psi = (\exists P)((\exists x) (A(x) \wedge P(x)) \wedge ((\exists x) (A(x) ...

As I understand, everyone can create logic programming language and system by declaring that the valid program of some logic programming language is the set of statements in the form: ...

The following formulas are said to be defined in WS1S logic.
$Closed(Z, R) := ∀x ∀y(x ∈ Z ∧ R(x, y) → y ∈ Z)$
$(z_1, z_2) ∈ R^∗
:= ∀Z.(z_1 ∈ Z ∧ Closed(Z, R) → z_2 ∈ Z)$
However since WS1S formula ...

xor gate, now I need to construct this gate using only 4 nand gate
...

I am not sure if the names of these logics are right, but I saw that you can generalize logic with probability theory. Then I found 3 ways of reasoning with probabilistic/smooth logic, Fuzzy, Bayes/...

I need to draw a combinatorial circuit that when an integer is greater than 7 and is an odd number, the output will be 1. There are 4 inputs representing 4 bits and 1 output wire. The output wire is ...

I have following unfinished proof of a lemma:
...

I came across this circuit that swaps logical signals:
However I don't understand why would you need to use logic gates. Would it be possible to just connect the A on the left to the B on the right ...

I am stuck on how to progress with this proof; i cannot see my next move.
The task is to show $S \to \exists x Q(x) \vdash \exists x (S \to Q(x))$ using natural deduction for predicate logic.
My ...

I tried solving past exam question but there is this one that I haven't been able to solve.
The question states that a suitable precondition should be found for the statement.
$$
a= i +2; i++\{(a = ...

Suppose there are 2 workers w1 and w2 who can cool a hot iron. So if iron is hot (denoted by atomic proposition ...

Wikipedia says the following (and more) about the logical characterization of the P versus NP problem here:
Thus, the question "is P a proper subset of NP" can be reformulated as "is existential ...

My question is a very basic one. It seems feasible to believe that $\mathsf{P = NP}$, because there is some "pathological" good algorithm for SAT, yet it is impossible to prove that the algorithm is ...

I'm currently looking into Japridze's computability logic. It looks great, but I was wondering whether any programming languages or systems implement it.
Does anyone know of any implementation?
...

How to represent in first order logic the expression:
"there are infinitely many"
To be honest I'm confused and not even sure whether you can represent them in first order logic.

A simple optimization problem is of form $\max_{x\in\mathcal R}f(x)$.
We can quantify as $\exists x\in\mathcal R\forall y\in\mathcal R f(y)\leq f(x)$.
The quantification here is $\exists\forall$.
...

Let's say we have given two numbers $x, z$, and we need to find another number $y$ such that $x \text{ xor } y = z$. The xor ( exclusive or ) is bitwise operation: xor table
.
I know that this can be ...

I'm currently looking into computability logic.
Japaridze explain that a game !P v P like !Chess v Chess is always winnable thanks to the copycat strategy (http://www.csc.villanova.edu/~japaridz/CL/3....

How do I fill a truth table from the following expression? I can't decide whether it is SOP or POS.Y=(A+B)C+AB`+(A+C)C`+(`AB)

- first-order-logic
- propositional-logic
- satisfiability
- complexity-theory
- algorithms
- lambda-calculus
- linear-temporal-logic
- terminology
- computability
- boolean-algebra
- proof-techniques
- type-theory
- reference-request
- programming-languages
- model-checking
- temporal-logic
- computation-tree-logic
- circuits
- proof-assistants
- undecidability
- formal-methods
- hoare-logic
- automated-theorem-proving
- formal-languages
- software-verification

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- Should I send professors 10 dollars for illegally downloading their books?
- Why shouldn't a bank robbery without threats be legal?
- Were there any CAPCOMs who were not astronauts?
- Why is there no permutation in Regexes? (Even if regular languages seem to be able to do this)
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- Make slimes great again, but how?
- 2 x 2 lines equation on a single line separated by a text in the middle
- Why did Dormammu keep his promise?
- Why is the EU concerned about the UK "unilaterally withdrawing" from a proposed Irish backstop?
- Is it ever okay to use lists in a relational database?
- How old is the use of "steal" for non-rival goods?
- Allowing late comers to enter into class
- Are there any indications why Roddenberry chose to make Star Trek a "battleship universe"?
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- Why does O(n^2) code execute faster than O(n)?
- Explaining made up card game
- Does this cantrip have a fair risk/reward balance?
- Replying to professor who say that I can join his research group as a PhD student next year
- How should a big universe be introduced without being boring?
- Tikz and Secant Line diagram
- Could people of the 14th century create an inline engine for use in aircraft and vehicles?
- How can I unscrew this nut with little clearance?
- Why Did God Directly Command Abraham to Sacrifice Isaac but Sent Angels to Stop Him?