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Questions tagged [logic]

Questions related to mathematical logic and its use in computer science

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1answer
45 views

D flip flop : How does it work in depth

I'm coming to you today because I have some trouble to understand how works D flip flop in depth. Two weeks ago we started at school learning sequential logic and so register and everything that come ...
5
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2answers
46 views

Topology vs sigma-algebra's as a framework for approximate information?

In the book "topology via logic" by Steven Vickers, topology is introduced for computer scientists, with the idea that topology captures the idea of approximate information. I am somewhat confused ...
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2answers
83 views

Decidability of equivalence to existential formulas

I'm looking for an algorithm to recognise if a given first order formula over a fixed vocabulary admits a logically equivalent existential one (i.e. a formula in prenex form where all quantifiers are ...
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1answer
39 views

How to evaluate dynamical conditioning/pseudo code

I am having a hard time even to formulate my question, so here it is: I have an application that the user can go in and define on a webpage the logic one wants to evaluate for the student to comply ...
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1answer
38 views

What is the signature of a formal language?

I will briefly state the context where my doubts arise. I know the following definitions. A formal language is a set of well-formed formulas. It's a tuple constituited by an alphabet and a formal ...
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0answers
16 views

Can I use the Quine-McCluskey to simplify a CNF which is not a product of maxterms?

As I understand it the Quine-McCluskey method allows you to start with a set of maxterms (or minterms), and combine them pairwise in a systematic way into a smaller set of clauses with a smaller set ...
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0answers
13 views

KB implication vs and

i m doing KB from sentence to model. I m stuck on this sentence that say this : The packages stored in room1 are smaller than those stored in room 2. I m created this vocabulary Package X ...
2
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2answers
64 views

Absorption rule in Boolean algebra

I am confused regarding the absorption rule which states: A OR (A AND B) = A. I do not completely understand how the expression simplifies to A and while i have seen proofs for this question, i still ...
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2answers
49 views

If you can represent/model a Conditional IF statement with AND + NOT or OR + NOT

I am still trying to wrap my head around this, which shows how to simulate control-flow without using an if-statement. I've been looking at basic logic today and ...
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2answers
50 views

How “add” could be implemented in only bitshift operations

Typically, add/subtract/multiply/divide are primitive operations in an Instruction Set Architecture (ISA). I am interested to know if they can instead be implemented efficiently using only bitshift ...
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1answer
44 views

does the order of the rows matter? [closed]

from my understanding the truth table is supposed to generate every possible combination of true and false values without the order of the combination taking into account. however one of my teachers ...
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0answers
126 views

Bidirectional search on permutation

Can any one tell me where I will get the source to study this topic and can able to solve the following problems? 1. (max 2 points) Prove that for any positive integer n, the permutation (n, n − 1, . ....
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2answers
30 views

Why we treat sentence letter $Q$ as conclusion in one form and premise in other?

Sorry for asking such a dumb question. I am CS student and I am trying to understand the basic tenets of Logic. I am new to the subject and I am lost understanding Implication. In formal logic, $(P\...
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0answers
16 views

Superposition calculus: greater vs greater-or-equal

Bachmair and Ganzinger 1991, 'Rewrite-Based Equational Theorem Proving With Selection and Simplification', specifies the criterion for using an equation as, by some appropriate ordering, ...
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0answers
183 views

Could you show the intractibility of SAT by showing that the number of variables contributing to an arbitrary unsatisfied clause is not constant? [closed]

Preface: This is not an attempted proof at P vs NP Starting with some CNF Boolean expression ϕ, by the rules of logical disjunction, a clause is only unsatisfied if each of the literals in it are ...
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1answer
29 views

Can you connect an output from a logic gate to 2 or more logic gates or inputs?

I have been given this diagram of a circuit: https://www.google.com/search?q=full+adder+logic+gate&rlz=1C1CHBF_enCA831CA831&source=lnms&tbm=isch&sa=X&ved=...
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1answer
26 views

Simplifying SOP: implementing OR with NAND

I am learning how to implement basic logic gates using NAND. I have learnt that you can use De Morgan's theorem as such: $a+b = \bar{\bar a} + \bar{\bar b} = \overline{(\bar a *\bar b)}$ In other ...
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1answer
23 views

Superposition calculus: Elimination of redundant atoms

Bachmair and Ganzinger (1991), 'Rewrite-Based Equational Theorem Proving With Selection and Simplification', section 5.2, 'Simplification and Deletion Techniques', page 17, 'Elimination of redundant ...
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1answer
38 views

Reasoning about resources: “resource logics”?

Are there extensions of predicate logic which focus on resource models, possibly even in actor models? And if so, would it be possible to reason on a meta-level on how many resources should be ...
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1answer
20 views

Bachmair and Ganzinger, ordering of equations

Bachmair and Ganzinger (1991), 'Rewrite-Based Equational Theorem Proving With Selection and Simplification', page 4, defines an order on equations. (This is an arcane piece of machinery but a critical ...
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1answer
40 views

Find value of $a$ or $b$ of two XOR equations

Is it possible to find $a$ or $b$ given that $a \oplus b = c$ and $c \oplus b = a$ when I only have the value of $b$?
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1answer
36 views

How to “logically” solve boolean logic

I came across of one excellent book Elements of Computing Systems and in chapter 1 we need to implement the "primitive" logic gates (for example: Not, And, Or, Xor, Mux, etc) based on a Nand gate. ...
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1answer
28 views

Check if one condition includes another

I have two conditions A and B in a form of "ast tree". How can I check that B is more strict than A? I.e. if B is true then A is always true. Example A: x = 1 and (b = 2 or c = d) B: y = 5 and x = ...
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0answers
27 views

Why Modus ponens works with Horn clauses and Generalized Modus ponens requires definite clauses?

I am reading the Artificial Intelligence: A Modern Approach book and in the chapters about logic i noticed that in propositional logic the Modus ponens inference rule (used by the forward and backward ...
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1answer
39 views

Validity of CTL formula $s_0 \models EG\ AF\ p$ in given model

I have been learning Verification by model checking recently and I get the following question: Is the CTL formula $s_{0} \models EG\ AF\ p$ valid in the following model? I think it is ...
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1answer
24 views

How to prove a LTL formula correct in a specific model?

I have been learning Verification by model checking recently and I get the following question: $Whether\ the\ LTL\ formula\ M, q_3\ \models (X\ \lnot a) \rightarrow (F\ G\ \lnot a)\ is\ established\ ...
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1answer
111 views

Can this set of propositions be represented and proved in Haskell?

I used a set of natural language statements and their formalization from Gries and Schneider. I attempted to transform the propositions into Haskell equations. For example, for S0 : $a \land w \...
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0answers
18 views

conversion of basic $\text{CTL}^*$ formulas to $\text{CTL}$

Consider the $\text{CTL}^*$ formula $E[pU(qUr)]$. It is not hard to show that it is equivalent to the $\text{CTL}$ formula $E[pU(EqUr)]$. The informal reason is that a path where $p$ is true until $...
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2answers
65 views

Must $x$ and $y$ be different in a statement of the form $\forall x \forall y \cdots$?

Given the following predicate formula $F$: $$\forall x \forall y [(\text{italian}(x) \Rightarrow (\text{winWC}(y) \Rightarrow \text{happy}(x))]$$ I am having trouble understanding whether $x$ and $y$...
3
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1answer
64 views

Roadmap to formal verification

I would like to learn about different approaches to formal verification of software programs that goes beyond what Wikipedia has to offer. Ideally one would not only get an overview but also ...
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2answers
67 views

Validity of □(P→ Q) → (◊P → ◊Q) in linear temporal logic

How can I prove that $\Box(P\rightarrow Q)\rightarrow (\Diamond P\rightarrow\Diamond Q)$ is valid in linear temporal logic (LTL)?
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32 views

Turing machine, tape without blanks, does it halt or no?

So I'm lost on this one. We're given a turing machine and an initial tape. Tape is infinitely long in both ways, but all the blanks are taken out. The head is the leftmost nonblank. So the question is:...
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0answers
11 views

Timed Kripke structures with inequality constraints

I am having problems creating a timed Kripke structure $\mathcal{TK} = \langle S, \mathcal{T}, \rightarrow, L \rangle$ for a system that I have. My system, a timed automaton system (time base $\...
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0answers
23 views

Unification algorithm that directly finds multiple substitutions?

Systems of formal logic generally have inference rules that require certain expressions to be syntactically the same in multiple steps. Typically two steps are involved, as for modus ponens, where ...
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3answers
111 views

Soundness and completeness w.r.t. programming languages

I'm studying programming languages (more specifically type systems) and came across a concept I couldn't quite wrap my head around: soundness and completeness. I'm taking a class, and according to my ...
0
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1answer
39 views

Finding CNF of $(p \rightarrow q) \rightarrow p$ and $\lnot (q \wedge (\lnot p \rightarrow q)) $

I'm trying to find the CNF of the $(p \rightarrow q) \rightarrow p$ and $\lnot (q \wedge (\lnot p \rightarrow q))$, and afterwards proving it's validity. As i'm new to CNF i wanted to ensure i've ...
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1answer
37 views

predicate logic proof of 2 numbers

For any two different numbers there is an number in between. I'm trying to write this in predicate logic and have no idea how to do it, since I need 2 variables X and Y? For all x there exists a y ...
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1answer
27 views

predicate logic/binary relation help

(1) ∀x, y, z (x < y ∧ y < z → x < z) (transitivity) (2) ∀x ¬(x < x) (antisymmetry) (3) ∀x, y (x < y ∨ x = y ∨ y < x) (linearity) I need to give an example of a (nonempty) ...
0
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1answer
34 views

Would hypercomputation machines be capable of simulating/computing/programming everything?

If uncomputable numbers existed, could this hypercomputation machines compute them? Could hypercomputation compute all types of uncomputable things? Even truly inconsistent things? Even things that ...
3
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2answers
69 views

How could a formal system ever be non-obviously unsound?

When reading discussions of Gödel's theorems one is always heeded that just because formal system $F$ proves a theorem $T$ that doesn't necessarily mean that when one applies the intended ...
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1answer
24 views

Determining cycle time and and hold time in logic circuits

First I have general question. In a circuit with both logic and D edge flip flop does hold time have to satisfy $t_{hold} < t_{setup}($D-FF$) + t_{pd-min}$(Logic), or is it enough that $t_{hold} \...
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0answers
17 views

Propositional extentionality in the lean theorem prover?

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’...
2
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1answer
28 views

How do you correctly write this sentence as a CTL formula?

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 ...
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0answers
28 views

Type theory based automated theorem prover?

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 ...
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1answer
60 views

A universal operator necessarily generates $\neg x$ for input $x,…,x$

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 ...
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2answers
121 views

Is there a way to convert a program into a Boolean formula?

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 ...
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1answer
109 views

Given a rng that outputs 0 or 1 with an equal probability, make a rng that generates 1 with a probability p

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, ...
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0answers
30 views

How to minimize large DNF formula into deeper but smaller formula?

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 ...
0
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1answer
32 views

Logic gate which checks if the input is a negative number and changes its output based on that

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 ...
0
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1answer
17 views

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

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