**599 logic questions.**

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\...

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 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:
...

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.

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 ...

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 ...

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,
...

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:
...

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)
...

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)

I'm reading a paper about constraint satisfaction problem and found a term "binary Max and binary Min" operations but I dont know the meaning. If someone know could you please explain for me? I ...

Lob's theorem states that:
Let $\textbf{Prov}(n^A)$ be the arithmetic statement such that $PA\vdash$ $A$ iff $\textbf{Prov}(n^A)$, where $PA$ is peano arithmetic, and $n^A$ is the godel number of $A$....

I have a robot that has a start and goal position within a maze. Each point in the maze-grid is simply a Position object containing x and y. I need an algorithm that specifies the robot only moving to ...

Is there any algorithm for converting a DNF boolean expression to CNF and vice versa if it's exists what is time complexity and complexity class for solving this problem?

I am just learning about Scheduling, in particular the Completely Fair Scheduler.
In thinking of specific cases of the types of things that would need to be "prioritized" against each other, there ...

Is it possible to define logic programming for every logic that has implication and conjunction connectives? Does logic programming adds something new to the usual inference process. By usual ...

I'm sure there must be something wrong with the following reasoning because otherwise a lot of P vs. NP research would be curtailed but I cannot determine my error:
For any fixed integer $k>0$ ...

In the book Logic in Computer Science on page 244, there is a proof that $[[E(\phi U\psi)]]$ is the least fixed point of $G(X)=[[\psi]] \cup ([[\phi]]\cap\mathop{\textrm{pre}}_\exists(X))$. I don't ...

You are given an array with $N$ elements. The values of the elements may be any number in the interval $[0,10^9]$. Define $f(a,b)$ as the bitwise or of all the values in the subarray $[a,b]$. Find a ...

I'm confused as to why we can't write formulas of infinite length in FO. For example, to express reachability, I understand the proof that there cannot be a single formula for it, but it is ...

Here is a popular proof of the halting problem theorem:
Suppose there exist a procedure h(x, y) so that for any procedure p(x) and any data d, the execution of h(p, d) will halt, where halt means ...

This answer explains roughly how to convert a nested boolean function into a Binary Decision Diagram (BDD). This question is about how to structure the states for the BDD. Now in this question I am ...

The question is about an operator that transforms any CTL* formula ${\psi}$ into a (not necessarily equivalent) LTL formula ${A\psi^d}$, where $d$ means syntactically removing all $A,E$ quantifiers ...

So in Neil Immerman's book http://books.google.co.kr/books?id=kWSZ0OWnupkC&pg=PA113&lpg=PA113#v=onepage&q&f=false, 3-colorability problem in descriptive complexity fashion is expressed ...

My intuition is that 1) self-awareness (modeled through epistemic modal logics); 2) goal reasoning (e.g. https://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12292) and 3) consciousness (e.g. ...

I'm very new to this so please bear with me.
I found this document describing the PFX language, a stack-oriented language where the instructions act on a stack and replace the arguments with the ...

I would like to apply Hoare Logic to realistic, complex imperative programs that use while loops, if statements, functions, modules, etc. and have side effects (e.g. access the network). In order to ...

I have one or more second-order logic formulas that correct for some finity model. What operation can I perform on them, so that resault is also correct for some finity model?
Just conjunction is ...

I have to simplify A+C'+B'CD but I don't see how.
I had to deduce the expression starting from a logic diagram in which two AND gates were used for the B'CD part. Seeing the diagram all I can think ...

I am going through the following lecture notes by Frank Pfenning :
http://www.cs.cmu.edu/~fp/courses/15317-f17/lectures/02-natded.pdf
In page no 5 I cam across the introduction rule .
The rule ...

I'm writing a logic gate simulator. I would like to prevent user from constructing circuits prone to race condition such as flip-flops, and instead provide them as separate building blocks. Is that ...

Suppose you have to provide a derivation by natural deduction, e.g.
$((A \rightarrow B) \rightarrow A) \rightarrow A$
Is it a good advice to start from backwards on in general?
I mean doing the ...

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

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